Stochasticity of infectious outbreaks and consequences for optimal interventions
Morán-Tovar R., Gruell H., Klein F., Lässig M., J. Phys. A: Math. Theor. 55
384008 (2022)
Global strategies to contain a
pandemic, such as social distancing and protective measures, are designed to reduce the overall transmission
rate between individuals. Despite such measures, essential institutions, including hospitals, schools, and
food producing plants, remain focal points of local outbreaks. Here we develop a model for the stochastic
infection dynamics that predicts the statistics of local outbreaks from observables of the underlying global
epidemics. Specifically, we predict two key outbreak characteristics: the probability of proliferation from a
first infection in the local community, and the establishment size, which is the threshold size of local
infection clusters where proliferation becomes likely. We derive these results using a contact network model
of communities, and we show how the proliferation probability depends on the contact degree of the first
infected individual. Based on this model, we suggest surveillance protocols by which individuals are tested
proportionally to their degree in the contact network. We characterize the efficacy of contact-based protocols
as a function of the epidemiological and the contact network parameters, and we show numerically that such
protocols outperform random testing.
Effective high-throughput RT-qPCR screening for SARS-CoV-2 infections in
children
Dewald F., Suárez I., Johnen R., Grossbach J., Moran-Tovar R., Steger G.,
Joachim
A., Rubio G.H., Fries M. , Behr F., Kley J., Lingnau A., Kretschmer A., Gude C., Baeza-Flores G., Laveaga
del
Valle D., Roblero-Hernandez A., Magana-Cerino J., Hernandez A.T., Ruiz-Quinones J., Schega K., Linne V.,
Junker L., Wunsch M., Heger E., Knops E., Di Cristanziano V., Meyer M., Hünseler C., Weber L.T., Lüers L.C.,
Quade G., Wisplinghoff H., Tiemann C., Zotz R., Jomaa H., Pranada A., Herzum I., Cullen P., Schmitz F.J.,
Philipsen P., Kirchner G., Knabbe C., Hellmich M., Buess M., Wolff A., Kossow A., Niessen J., Jeworutzki S.,
Schräpler J.-P., Lässig M., Dötsch J., Fätkenheuer D., Kaiser R., Beyer A., Rybniker J., Klein F., Nature
Communications, 13 (3640) , (2022)
Systematic SARS-CoV-2 testing is
a
valuable tool for infection control and surveillance. However, broad application of high sensitive RT-qPCR
testing in children is often hampered due to unpleasant sample collection, limited RT-qPCR capacities and
high
costs. Here, we developed a high-throughput approach (‘Lolli-Method’) for SARS-CoV-2 detection in children,
combining non-invasive sample collection with an RT-qPCR-pool testing strategy. SARS-CoV-2 infections were
diagnosed with sensitivities of 100% and 93.9% when viral loads were >106 copies/ml and >103 copies/ml in
corresponding Naso-/Oropharyngeal-swabs, respectively. For effective application of the Lolli-Method in
schools and daycare facilities, SEIR-modeling indicated a preferred frequency of two tests per week. The
developed test strategy was implemented in 3,700 schools and 698 daycare facilities in Germany, screening
over
800,000 individuals twice per week. In a period of 3 months, 6,364 pool-RT-qPCRs tested positive (0.64%),
ranging from 0.05% to 2.61% per week. Notably, infections correlated with local SARS-CoV-2 incidences and
with
a school social deprivation index. Moreover, in comparison with the alpha variant, statistical modeling
revealed a 36.8% increase for multiple (≥2 children) infections per class following infections with the
delta
variant. We conclude that the Lolli-Method is a powerful tool for SARS-CoV-2 surveillance and can support
infection control in schools and daycare facilities.
Discovery of ultrapotent broadly neutralizing antibodies from SARS-CoV-2 elite
neutralizers
Vanshylla K., Fan C., Wunsch M., Poopalasingam N., Meijers M., Kreer C.,
Kleipass F., Ruchnewitz D., Ercanoglu M., Gruell H., Münn F. Pohl K., Janicki H., Nolden T., Bartl S., Stein
S., Augustin M., Dewald F., Gieselmann L., Schommers P., Schulz T., Sander L., Koch M., Łuksza M., Lässig
M., Bjorkman P., Klein F., Cell Host & Microbe, 69-82.e10, 30(1), (2022)
A fraction of COVID-19
convalescent individuals mount a potent antibody response to SARS-CoV-2 with cross-reactivity to SARS-CoV-1.
To uncover their humoral response in detail, we performed single B cell analysis from 10 SARS-CoV-2 elite
neutralizers. We isolated and analyzed 126 monoclonal antibodies, many of which were sarbecovirus
cross-reactive, with some displaying merbecovirus- and embecovirus-reactivity. Several isolated broadly
neutralizing antibodies were effective against B.1.1.7, B.1.351, B.1.429, B.1.617, and B.1.617.2 variants
and 19 prominent potential escape sites. Furthermore, assembly of 716,806 SARS-CoV-2 sequences predicted
emerging escape variants, which were also effectively neutralized. One of these broadly neutralizing potent
antibodies, R40-1G8, is a IGHV3-53 RBD-class-1 antibody. Remarkably, cryo-EM analysis revealed that R40-1G8
has a flexible binding mode, targeting both “up” and “down” conformations of the RBD. Given the threat of
emerging SARS-CoV-2 variants, we demonstrate that elite neutralizers are a valuable source for isolating
ultrapotent antibody candidates to prevent and treat SARS-CoV-2 infection.
Clinical and Genomic Characterization of SARS CoV-2 infections in mRNA
Vaccinated Health Care Personnel in New York City
Robilotti E.V., Whiting K., Lucca A., Poon C., Guest R., McMillen T., Jani K.,
Solovyov A., Kelson S., Browne K., Freeswick S., Hohl T.M., Korenstein D., Ruchnewitz D., Lässig M., Łuksza
M., Greenbaum B., Seshan V.E., Babady N.E., Kamboj M., Clinical Infectious Diseases, ciab886, (2022)
Background
Vaccine-induced
clinical protection against SARS CoV-2 variants is an evolving target. There is limited genomic level data
on
SARS CoV-2 breakthrough infections and vaccine effectiveness (VE) since the global spread of the B.1.617.2
(Delta) variant.
Methods
In a retrospective study from November 1st, 2020 - August 31st , 2021,
divided as pre-Delta and Delta-dominant periods, laboratory-confirmed SARS CoV-2 infections among Healthcare
personnel (HCP) at a large tertiary cancer center in New York City (NYC) were examined to compare the weekly
infection rate-ratio in vaccinated, partially vaccinated, and unvaccinated HCP. We describe the clinical and
genomic epidemiologic features of post-vaccine infections to assess for selection of VOC/VOI in the early
post-vaccine period and impact of B.1.617.2 (Delta) variant domination on VE.
Results
Among 13,658
HCP in our cohort, 12,379 received at least one dose of an mRNA vaccine. In the pre-Delta period overall VE
was 94.5%. WGS of 369 isolates in the pre-Delta period did not reveal a clade bias for VOC/VOI specific to
post-vaccine infections. VE in the Delta dominant phase was 75.6%. No hospitalizations occurred among
vaccinated HCP in the entire study period, compared to 17 hospitalizations and one death among unvaccinated
HCP.
Conclusions
Findings show high VE among HCP in NYC in the pre-Delta phase, with moderate
decline in VE post-Delta emergence. SARS CoV-2 clades were similarly distributed among vaccinated and
unvaccinated infected HCP without apparent clustering during the pre-Delta period of diverse clade
circulation. Strong vaccine protection against hospitalization was maintained through the entire study
period.
Predicting in vivo escape dynamics of HIV-1 from a broadly neutralizing
antibody
Meijers M., Vanshylla K., Gruell H., Klein F., Lässig M., PNAS 118 (30)
e2104651118, (2021)
Broadly neutralizing antibodies
are
promising candidates for treatment and prevention of HIV-1 infections. Such antibodies can temporarily
suppress viral load in infected individuals; however, the virus often rebounds by escape mutants that have
evolved resistance. In this paper, we map a fitness model of HIV-1 interacting with broadly neutralizing
antibodies using in vivo data from a recent clinical trial. We identify two fitness factors, antibody dosage
and viral load, that determine viral reproduction rates reproducibly across different hosts. The model
successfully predicts the escape dynamics of HIV-1 in the course of an antibody treatment, including a
characteristic frequency turnover between sensitive and resistant strains. This turnover is governed by a
dosage-dependent fitness ranking, resulting from an evolutionary trade-off between antibody resistance and
its
collateral cost in drug-free growth. Our analysis suggests resistance–cost trade-off curves as a measure of
antibody performance in the presence of resistance evolution.
Antigenic waves of virus–immune coevolution
Marchi J., Lässig M., Walczak A.M., Mora T., PNAS 118 (27) e2103398118, (2021)
Viruses, such as influenza,
evolve
under the selection of host immune systems. Previously infected individuals become immune, forcing the virus
to find susceptible hosts or mutate, chasing it away in antigenic space. We formulate this viral escape
process in terms of a low-dimensional wave moving in antigenic space. The dimensionality of the antigenic
space impacts the persistence, as well as stability, of viral evolution. We uncover a characteristic
timescale
for the persistence of the viral strain, which is an order of magnitude longer than individual host immunity
and emerges collectively from the pressure of the chasing immune systems. These results offer intuition
about
the antigenic turnover of viruses and highlight the importance of the effective dimensionality of
coevolution.
Metabolic fitness landscapes predict the evolution of antibiotic resistance
Pinheiro F., Warsi O., Andersson D.I., Lässig M., Nature Ecol. Evol, in press
(2021)
Bacteria evolve resistance to
antibiotics by a multitude of mechanisms. A central, yet unsolved question is how resistance evolution
affects
cell growth at different drug levels. Here, we develop a fitness model that predicts growth rates of common
resistance mutants from their effects on cell metabolism. The model maps metabolic effects of resistance
mutations in drug-free environments and under drug challenge; the resulting fitness trade-off defines a
Pareto
surface of resistance evolution. We predict evolutionary trajectories of growth rates and resistance levels,
which characterize Pareto resistance mutations emerging at different drug dosages. We also predict the
prevalent resistance mechanism depending on drug and nutrient levels: low-dosage drug defence is mounted by
regulation, evolution of distinct metabolic sectors sets in at successive threshold dosages. Evolutionary
resistance mechanisms include membrane permeability changes and drug target mutations. These predictions are
confirmed by empirical growth inhibition curves and genomic data of Escherichia coli populations. Our
results
show that resistance evolution, by coupling major metabolic pathways, is strongly intertwined with systems
biology and ecology of microbial populations.
Adaptive evolution of hybrid bacteria by horizontal gene transfer
Power J.J., Pinheiro F., Pompei S., Kovacova V., Yüksel M., Rathmann I.,
Förster
M., Lässig M., Maier B., PNAS 11, 118 (10), (2021)
In a parallel evolution
experiment,
we probe lateral gene transfer between two Bacillus subtilis lineages close to the species boundary. We show
that laboratory evolution by horizontal gene transfer can rapidly generate hybrid organisms with broad
genomic
and functional alterations. By combining genomics, transcriptomics, fitness assays, and statistical
modeling,
we map the selective effects underlying gene transfer. We show that transfer takes place under genome-wide
positive and negative selection, generating a net fitness increase in hybrids. The evolutionary dynamics
efficiently navigates this fitness landscape, finding viable paths with increasing fraction of transferred
genes.
Eco-evolutionary control of pathogens
Lässig M., Mustonen V., PNAS 117:19694-19704 (2020)
Vaccinations and therapies
targeting evolving pathogens aim to curb the pathogen and to steer it toward a controlled evolutionary
state.
Control is leveraged against the pathogen’s intrinsic evolutionary forces, which in turn, can drive an
escape
from control. Here, we analyze a simple model of control, in which a host produces antibodies that bind the
pathogen. We show that the leverages of host (or external intervention) and pathogen are often highly
imbalanced: an error threshold separates parameter regions of efficient control from regions of compromised
control, where the pathogen retains the upper hand. Because control efficiency can be predicted from few
measurable fitness parameters, our results establish a proof of principle how control theory can guide
interventions against evolving pathogens.
Horizontal gene transfer overrides mutation in Escherichia coli colonizing the
mammalian gut
Frazão N., Sousa A., Lässig M., and Gordo I., PNAS:201906958 (2019)
Bacteria evolve by mutation
accumulation in laboratory experiments, but tempo and mode of evolution in natural environments are largely
unknown. Here, we study the ubiquitous natural process of host colonization by commensal bacteria. We show,
by
experimental evolution of Escherichia coli in the mouse intestine, that the ecology of the gut controls the
pace and mode of evolution of a new invading bacterial strain. If a resident E. coli strain is present in
the
gut, the invading strain evolves by rapid horizontal gene transfer (HGT), which precedes and outweighs
evolution by accumulation of mutations. HGT is driven by 2 bacteriophages carried by the resident strain,
which cause an epidemic phage infection of the invader. These dynamics are followed by subsequent evolution
by
clonal interference of genetically diverse lineages of phage-carrying (lysogenic) bacteria. We show that the
genes uptaken by HGT enhance the metabolism of specific gut carbon sources and provide a fitness advantage
to
lysogenic invader lineages. A minimal dynamical model explains the temporal pattern of phage epidemics and
the
complex evolutionary outcome of phage-mediated selection. We conclude that phage-driven HGT is a key
eco-evolutionary driving force of gut colonization—it accelerates evolution and promotes genetic diversity
of
commensal bacteria.
Survival of the simplest in microbial evolution
Held T., Klemmer D., Lässig M., Nature Communications 10: 2472 (2019)
The evolution of microbial and
viral organisms often generates clonal interference, a mode of competition between genetic clades within a
population. Here we show how interference impacts systems biology by constraining genetic and phenotypic
complexity. Our analysis uses biophysically grounded evolutionary models for molecular phenotypes, such as
fold stability and enzymatic activity of genes. We find a generic mode of phenotypic interference that
couples
the function of individual genes and the population’s global evolutionary dynamics. Biological implications
of
phenotypic interference include rapid collateral system degradation in adaptation experiments and long-term
selection against genome complexity: each additional gene carries a cost proportional to the total number of
genes. Recombination above a threshold rate can eliminate this cost, which establishes a universal,
biophysically grounded scenario for the evolution of sex. In a broader context, our analysis suggests that
the
systems biology of microbes is strongly intertwined with their mode of evolution.
Fitness cost of reassortment in human influenza
Mara Villa, Michael Lässig, PLOS Pathogens 13(11): e1006685 (2017)
Reassortment, which is the
exchange
of genome sequence between viruses co-infecting a host cell, plays an important role in the evolution of
segmented viruses. In the human influenza virus, reassortment happens most frequently between co-existing
variants within the same lineage. This process breaks genetic linkage and fitness correlations between viral
genome segments, but the resulting net effect on viral fitness has remained unclear. In this paper, we
determine rate and average selective effect of reassortment processes in the human influenza lineage A/H3N2.
For the surface proteins hemagglutinin and neuraminidase, reassortant variants with a mean distance of at
least 3 nucleotides to their parent strains get established at a rate of about 10−2 in units of the neutral
point mutation rate. Our inference is based on a new method to map reassortment events from joint
genealogies
of multiple genome segments, which is tested by extensive simulations. We show that intra-lineage
reassortment
processes are, on average, under substantial negative selection that increases in strength with increasing
sequence distance between the parent strains. The deleterious effects of reassortment manifest themselves in
two ways: there are fewer reassortment events than expected from a null model of neutral reassortment, and
reassortant strains have fewer descendants than their non-reassortant counterparts. Our results suggest that
influenza evolves under ubiquitous epistasis across proteins, which produces fitness barriers against
reassortment even between co-circulating strains within one lineage.
Predictive Modeling of Influenza Shows the Promise of Applied Evolutionary
Biology
Dylan H. Morris, Katelyn M. Gostic, Simone Pompei, Trevor Bedford, Marta
Łuksza,
Richard A. Neher, Bryan T. Grenfell, Michael Lässig, John W. McCauley, Trends in Microbiology, Volume 0 ,
Issue 0 (2017)
Seasonal influenza is controlled
through vaccination campaigns. Evolution of influenza virus antigens means that vaccines must be updated to
match novel strains, and vaccine effectiveness depends on the ability of scientists to predict nearly a year
in advance which influenza variants will dominate in upcoming seasons. In this review, we highlight a
promising new surveillance tool: predictive models. Developed through data-sharing and close collaboration
between the World Health Organization and academic scientists, these models use surveillance data to make
quantitative predictions regarding influenza evolution. Predictive models demonstrate the potential of
applied
evolutionary biology to improve public health and disease control. We review the state of influenza
predictive
modeling and discuss next steps and recommendations to ensure that these models deliver upon their
considerable biomedical promise.
Adaptive Evolution of Gene Expression in Drosophila
Armita Nourmohammad, Joachim Rambeau, Torsten Held, Viera Kovacova, Johannes
Berg, Michael Lässig, Cell Reports 20, 1385-1395 (2017)
Gene expression levels are
important quantitative traits that link genotypes to molecular functions and fitness. In Drosophila,
population-genetic studies have revealed substantial adaptive evolution at the genomic level, but the
evolutionary modes of gene expression remain controversial. Here, we present evidence that adaptation
dominates the evolution of gene expression levels in flies. We show that 64% of the observed expression
divergence across seven Drosophila species are adaptive changes driven by directional selection. Our results
are derived from time-resolved data of gene expression divergence across a family of related species, using
a
probabilistic inference method for gene-specific selection. Adaptive gene expression is stronger in specific
functional classes, including regulation, sensory perception, sexual behavior, and morphology. Moreover, we
identify a large group of genes with sex-specific adaptation of expression, which predominantly occurs in
males. Our analysis opens an avenue to map system-wide selection on molecular quantitative traits
independently of their genetic basis.
Predicting evolution
Michael Lässig, Ville Mustonen, Aleksandra M. Walczak, Nature Ecol. Evol. 1,
077
(9 pages) (2017)
Abstract: The face of
evolutionary
biology is changing: from reconstructing and analysing the past to predicting future evolutionary pro-
cesses.
Recent developments include prediction of reproducible patterns in parallel evolution experiments,
forecasting
the future of individual populations using data from their past, and controlled manipulation of evolutionary
dynamics. Here we undertake a synthesis of central concepts for evolutionary predictions, based on examples
of
microbial and viral systems, can- cer cell populations, and immune receptor repertoires. These systems have
strikingly similar evolutionary dynamics driven by the competition of clades within a population. These
dynamics are the basis for models that predict the evolution of clade frequencies, as well as broad genetic
and phenotypic changes. Moreover, there are strong links between prediction and control, which are important
for interventions such as vaccine or therapy design. All of these are key elements of what may become a
predictive theory of evolution.
Multiple-line inference of selection on quantitative traits
N. Riedel, B. S. Khatri, M. Lässig, J. Berg, Genetics 201, 305-322 (2015)
Trait differences between species
may
be attributable to natural selection. However, quantifying the strength of evidence
for selection acting on a particular trait is a difficult task. Here we develop a population genetics test
for
selection acting on
a quantitative trait that is based on multiple-line crosses. We show that using multiple lines increases
both
the power and the scope of
selection inferences. First, a test based on three or more lines detects selection with strongly increased
statistical significance, and we
show explicitly how the sensitivity of the test depends on the number of lines. Second, a multiple-line test
can distinguish between
different lineage-specific selection scenarios. Our analytical results are complemented by extensive
numerical
simulations. We then
apply the multiple-line test to QTL data on floral character traits in plant species of the Mimulus genus
and
on photoperiodic traits in
different maize strains, where we find a signature of lineage-specific selection not seen in two-line tests.
Dynamic BMP signaling polarized by Toll patterns the dorsoventral axis in a
hemimetabolous insect
L. Sachs, Y.-T. Chen, A. Drechsler, J. A. Lynch, K. A. Panfilio, M. Lässig, J.
Berg, S. Roth, eLife 4:e05502 (2015)
Toll-dependent patterning of the
dorsoventral axis in Drosophila represents one of the
best understood gene regulatory networks. However, its evolutionary origin has remained elusive.
Outside the insects Toll is not known for a patterning function, but rather for a role in pathogen
defense. Here, we show that in the milkweed bug Oncopeltus fasciatus, whose lineage split from
Drosophila’s more than 350 million years ago, Toll is only required to polarize a dynamic BMP
signaling network. A theoretical model reveals that this network has self-regulatory properties and
that shallow Toll signaling gradients are sufficient to initiate axis formation. Such gradients can
account for the experimentally observed twinning of insect embryos upon egg fragmentation and
might have evolved from a state of uniform Toll activity associated with protecting insect eggs
against pathogens.
Rate and cost of adaptation in the Drosophila genome
S. Schiffels, M. Lässig* and V. Mustonen*, arXiv:1409.1946 (2014)
(*) equal contributions
Recent studies have consistently
inferred high rates of adaptive molecular evolution between
Drosophila species. At the same time,
the
Drosophila genome evolves under different rates of recombination, which results in partial genetic
linkage between alleles at neighboring genomic loci. Here we analyze how linkage correlations affect
adaptive
evolution. We develop a new inference method for adaptation that takes into account the effect on an allele
at
a focal site caused by neighboring deleterious alleles (background selection) and by neighboring adaptive
substitutions (hitchhiking). Using complete genome sequence data and fine-scale recombination maps, we infer
a
highly heterogeneous scenario of adaptation in
Drosophila. In high-recombining regions, about 50%
of
all amino acid substitutions are adaptive, together with about 20% of all substitutions in proximal
intergenic
regions. In low-recombining regions, only a small fraction of the amino acid substitutions are adaptive,
while
hitchhiking accounts for the majority of these changes. Hitchhiking of deleterious alleles generates a
substantial collateral cost of adaptation, leading to a fitness decline of about 30/2N per gene and per
million years in the lowest-recombining regions. Our results show how recombination shapes rate and efficacy
of the adaptive dynamics in eukaryotic genomes.
Can we read the future from a tree?
M. Lässig and M. Łuksza, insight article, eLife, 3:e05060 (2014)
Adaptive evolution of molecular phenotypes
T. Held, A. Nourmohammad, and M. Lässig, J. Stat. Mech., P09029 (39 pages)
(2014)
Molecular phenotypes link genomic
information with organismic functions, fitness, and evolution. Quantitative traits are complex phenotypes
that
depend on multiple genomic loci. In this paper, we study the adaptive evolution of a quantitative trait
under
time-dependent selection, which arises from environmental changes or through fitness interactions with other
co-evolving phenotypes. We analyze a model of trait evolution under mutations and genetic drift in a
single-peak fitness seascape. The fitness peak performs a constrained random walk in the trait amplitude,
which determines the time-dependent trait optimum in a given population. We derive analytical expressions
for
the distribution of the time-dependent trait divergence between populations and of the trait diversity
within
populations. Based on this solution, we develop a method to infer adaptive evolution of quantitative traits.
Specifically, we show that the ratio of the average trait divergence and the diversity is a universal
function
of evolutionary time, which predicts the stabilizing strength and the driving rate of the fitness seascape.
From an information-theoretic point of view, this function measures the macro-evolutionary entropy in a
population ensemble, which determines the predictability of the evolutionary process. Our solution also
quantifies two key characteristics of adapting populations: the cumulative fitness flux, which measures the
total amount of adaptation, and the adaptive load, which is the fitness cost due to a population's lag
behind
the fitness peak.
A predictive fitness model for influenza
M. Łuksza and M. Lässig, Nature, 507, 57-61 (2014)
The seasonal human influenza A
(H3N2)
virus undergoes rapid evolution, which produces significant year-to-year sequence turnover in the population
of circulating strains. Adaptive mutations respond to human immune challenge and occur primarily in
antigenic
epitopes, the antibody-binding domains of the viral surface protein haemagglutinin. Here we develop a
fitness
model for haemagglutinin that predicts the evolution of the viral population from one year to the next. Two
factors are shown to determine the fitness of a strain: adaptive epitope changes and deleterious mutations
outside the epitopes. We infer both fitness components for the strains circulating in a given year, using
population-genetic data of all previous strains. From fitness and frequency of each strain, we predict the
frequency of its descendent strains in the following year. This fitness model maps the adaptive history of
influenza A and suggests a principled method for vaccine selection. Our results call for a more
comprehensive
epidemiology of influenza and other fast-evolving pathogens that integrates antigenic phenotypes with other
viral functions coupled by genetic linkage.
Press releases
Press coverage
Universality and predictability in molecular quantitative genetics
A. Nourmohammad*, T. Held*, and M. Lässig, Current Opinion in Genetics and
Development 23, 684-93 (2013)
(*) equal contributions
Molecular traits, such as gene
expression levels or protein binding affinities, are increasingly accessible to quantitative measurement by
modern high-throughput techniques. Such traits measure molecular functions and, from an evolutionary point
of
view, are important as targets of natural selection. We review recent developments in evolutionary theory
and
experiments that are expected to become building blocks of a quantitative genetics of molecular traits. We
focus on universal evolutionary characteristics: these are largely independent of a trait's genetic basis,
which is often at least partially unknown. We show that universal measurements can be used to infer
selection
on a quantitative trait, which determines its evolutionary mode of conservation or adaptation. Furthermore,
universality is closely linked to predictability of trait evolution across lineages. We argue that universal
trait statistics extends over a range of cellular scales and opens new avenues of quantitative evolutionary
systems biology.
Fitness landscape of nucleosome positioning
D. Weghorn and M. Lässig, Proc. Natl. Acad. Sci. 110, 10988–93 (2013)
Histone–DNA complexes, so-called
nucleosomes, are the building blocks of DNA packaging in eukaryotic cells. The histone-binding affinity of a
local DNA segment depends on its elastic properties and determines its accessibility within the nucleus,
which
plays an important role in the regulation of gene expression. Here, we derive a fitness landscape for
intergenic DNA segments in yeast as a function of two molecular phenotypes: their elasticity-dependent
histone
affinity and their coverage with transcription factor binding sites. This landscape reveals substantial
selection against nucleosome formation over a wide range of both phenotypes. We use it as the core component
of a quantitative evolutionary model for intergenic DNA segments. This model consistently predicts the
observed diversity of histone affinities within wild Saccharomyces paradoxus populations, as well as the
affinity divergence between neighboring Saccharomyces species. Our analysis establishes histone binding and
transcription factor binding as two separable modes of sequence evolution, each of which is a direct target
of
natural selection.
Evolution of molecular phenotypes under stabilizing selection
A. Nourmohammad, S. Schiffels, and M. Lässig, J. Stat. Mech. P01012 (34 pages),
(2013)
Molecular phenotypes are important
links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes,
which
are also called quantitative traits, often depend on multiple genomic loci. Their evolution builds on genome
evolution in a complicated way, which involves selection, genetic drift, mutations and recombination. Here
we
develop a coarse-grained evolutionary statistics for phenotypes, which decouples from details of the
underlying genotypes. We derive approximate evolution equations for the distribution of phenotype values
within and across populations. This dynamics covers evolutionary processes at high and low recombination
rates, that is, it applies to sexual and asexual populations. In a fitness landscape with a single optimal
phenotype value, the phenotypic diversity within populations and the divergence between populations reach
evolutionary equilibria, which describe stabilizing selection. We compute the equilibrium distributions of
both quantities analytically and we show that the ratio of mean divergence and diversity depends on the
strength of selection in a universal way: it is largely independent of the phenotype’s genomic encoding and
of
the recombination rate. This establishes a new method for the inference of selection on molecular phenotypes
beyond the genome level. We discuss the implications of our findings for the predictability of evolutionary
processes.
GraphAlignment: Bayesian pairwise alignment of biological networks
M. Kolar, J. Meier, V. Mustonen, M. Lässig, and J. Berg, BMC Systems Biology 6,
144, (2012)
BackgroundWith
increased experimental availability and accuracy of bio-molecular networks, tools for their comparative and
evolutionary analysis are needed. A key component for such studies is the alignment of
networks.
ResultsWe introduce the Bioconductor package GraphAlignment for
pairwise
alignment of bio-molecular networks. The alignment incorporates information both from network vertices and
network edges and is based on an explicit evolutionary model, allowing inference of all scoring parameters
directly from empirical data. We compare the performance of our algorithm to an alternative algorithm,
Græmlin
2.0. On simulated data, GraphAlignment outperforms Græmlin 2.0 in several benchmarks except for
computational
complexity. When there is little or no noise in the data, GraphAlignment is slower than Græmlin 2.0. It is
faster than Græmlin 2.0 when processing noisy data containing spurious vertex associations. Its typical case
complexity grows approximately as O(N 2.6 ). On empirical bacterial protein-protein interaction networks
(PIN)
and gene co-expression networks, GraphAlignment outperforms Græmlin 2.0 with respect to coverage and
specificity, albeit by a small margin. On large eukaryotic PIN, Græmlin 2.0 outperforms
GraphAlignment.
ConclusionsThe GraphAlignment algorithm is robust to spurious
vertex associations, correctly resolves paralogs, and shows very good performance in identification of
homologous vertices defined by high vertex and/or interaction similarity.
Clonal interference in the evolution of influenza
N. Strelkowa and M. Lässig, Genetics 192, 671 - 682 (2012)
Blah. The seasonal influenza A virus
undergoes rapid evolution to escape human immune response. Adaptive changes occur primarily in antigenic
epitopes, the antibody-binding domains of the viral haemagglutinin. This process involves recurrent
selective
sweeps, in which clusters of simultaneous nucleotide fixations in the haemagglutinin coding sequence are
observed about every 4 years. Here, we show that influenza A (H3N2) evolves by strong clonal interference.
This mode of evolution is a red queen race between viral strains with different beneficial mutations. Clonal
interference explains and quantifies the observed sweep pattern: We find an average of at least one strongly
beneficial amino acid substitution per year, and a given selective sweep has three to four driving mutations
on average. The inference of selection and clonal interference is based on frequency time-series of
single-nucleotide polymorphisms, which are obtained from a sample of influenza genome sequences over 39
years.
Our results imply that mode and speed of influenza evolution are governed not only by positive selection
within, but also by background selection outside antigenic epitopes: immune adaptation and conservation of
other viral functions interfere with each other. Hence, adapting viral proteins are predicted to be
particularly brittle. We conclude that a quantitative understanding of influenza's evolutionary and
epidemiological dynamics must be based on all genomic domains and functions coupled by clonal interference.
Chance and risk in adaptive evolution
M.Lässig, Proc. Natl. Acad. Sci. 109, 4719-20, (2012)
Formation of regulatory modules by local sequence duplication
A. Nourmohammad and M. Lässig, PLoS Comp. Biol., PLoS Comput Biol 7, e1002167
(12
pages), (2011)
Turnover of regulatory sequence and
function is an important part of molecular evolution. But what are the modes of sequence evolution leading
to
rapid formation and loss of regulatory sites? Here, we show that a large fraction of neighboring
transcription
factor binding sites in the fly genome have formed from a common sequence origin by local duplications. This
mode of evolution is found to produce regulatory information: duplications can seed new sites in the
neighborhood of existing sites. Duplicate seeds evolve subsequently by point mutations, often towards
binding
a different factor than their ancestral neighbor sites. These results are based on a statistical analysis of
346 cis-regulatory modules in the Drosophila melanogaster genome, and a comparison set of intergenic
regulatory sequences in Saccharomyces cerevisiae. In fly regulatory modules, pairs of binding sites show
significantly enhanced sequence similarity up to distances of about 50 bp. We analyze these data in terms of
an evolutionary model with two distinct modes of site formation: (i) evolution from independent sequence
origin and (ii) divergent evolution following duplication of a common ancestor sequence. Our results suggest
that pervasive formation of binding sites by local sequence duplications distinguishes the complex
regulatory
architecture of higher eukaryotes from the simpler architecture of unicellular organisms.
Emergent Neutrality in Adaptive Asexual Evolution
Stephan Schiffels, Gergely Szöllösi, Ville Mustonen, and Michael Lässig,
Genetics
189, 1361 - 75, (2011)
In non-recombining genomes, genetic
linkage can be an important evolutionary force. Linkage generates interference interactions, by which
simultaneously occurring mutations affect each other’s chance of fixation. Here, we develop a comprehensive
model of adaptive evolution in linked genomes. By an approximate analytical solution, we predict fixation
rates of beneficial and deleterious mutations, as well as the statistics of beneficial and deleterious
alleles
at fixed genomic sites. We find that interference interactions generate a regime of effective neutrality:
all
genomic sites with selection coefficients smaller in magnitude than a characteristic threshold have nearly
random fixed alleles, and both beneficial and deleterious mutations at these sites have nearly neutral
fixation rates. We show that this dynamics limits not only the speed of adaptation, but also a population’s
degree of adaptation in its current environment. Our model integrates interference between beneficial
mutations, genetic hitchhiking of weakly selected mutations, and background selection by strongly
deleterious
mutations into a unified framework of interference interactions. We apply the model to different adaptive
scenarios: stationary adaptation in a time-dependent environment, and approach to equilibrium in a fixed
environment (as in long-term evolution experiments). In both cases, the analytical predictions are in good
agreement with numerical simulations. Our results suggest that interference can severely compromise
biological
functions in an adapting population, which sets viability limits on adaptive evolution under linkage.
Nonlinear fitness landscape of a molecular pathway
Lilia Perfeito, Stéphane Ghozzi, Johannes Berg, Karin Schnetz, Michael Lässig,
PloS Genetics 7, e1002160 (10 pages), (2011)
Genes are regulated because their
expression involves a fitness cost to the organism. The production of proteins by transcription and
translation is a well-known cost factor, but the enzymatic activity of the proteins produced can also reduce
fitness, depending on the internal state and the environment of the cell. Here, we map the fitness costs of
a
key metabolic network, the lactose utilization pathway in Escherichia coli. We measure the growth of several
regulatory lac operon mutants in different environments inducing expression of the genes. We find a
strikingly
nonlinear fitness landscape, which depends on the production rate and on the activity rate of the lac
proteins. A simple fitness model of the lac pathway, based on elementary biophysical processes, predicts the
growth rate of all observed strains. The nonlinearity of fitness is explained by a feedback loop: production
and activity of the lac proteins reduce growth, but growth also affects the density of these molecules. This
nonlinearity has important consequences for molecular function and evolution. It generates a cliff in the
fitness landscape, beyond which populations cannot maintain growth. In viable populations, there is an
expression barrier of the lac genes, which cannot be exceeded in any stationary growth process. Furthermore,
the nonlinearity determines how the fitness of operon mutants depends on the inducer environment. We argue
that fitness nonlinearities, expression barriers, and gene-environment interactions are generic features of
fitness landscapes for metabolic pathways, and we discuss their implications for the evolution of
regulation.
Fitness flux and ubiquity of adaptive evolution
V. Mustonen and M. Lässig, Proc. Natl. Acad. Sci. 107, 4248-53, (2010)
Natural selection favors fitter
variants in a population, but actual evolutionary processes may decrease fitness by mutations and genetic
drift. How is the stochastic evolution of molecular biological systems shaped by natural selection? Here, we
derive a theorem on the fitness flux in a population, defined as the selective effect of its genotype
frequency changes. The fitness-flux theorem generalizes Fisher's fundamental theorem of natural selection to
evolutionary processes including mutations, genetic drift, and time-dependent selection. It shows that a
generic state of populations is adaptive evolution: there is a positive fitness flux resulting from a
surplus
of beneficial over deleterious changes. In particular, stationary nonequilibrium evolution processes are
predicted to be adaptive. Under specific nonstationary conditions, notably during a decrease in population
size, the average fitness flux can become negative. We show that these predictions are in accordance with
experiments in bacteria and bacteriophages and with genomic data in Drosophila. Our analysis establishes
fitness flux as a universal measure of adaptation in molecular evolution.
Significance analysis and statistical mechanics: an application to clustering
M. Luksza, M. Lässig, and J. Berg, Phys. Rev. Lett. 105, 220601 (4 pages),
(2010)
This paper addresses the statistical
significance of structures in random data: Given a set of vectors and a measure of mutual similarity, how
likely does a subset of these vectors form a cluster with enhanced similarity among its elements? The
computation of this cluster p-value for randomly distributed vectors is mapped onto a well-defined problem
of
statistical mechanics. We solve this problem analytically, establishing a connection between the physics of
quenched disorder and multiple testing statistics in clustering and related problems. In an application to
gene expression data, we find a remarkable link between the statistical significance of a cluster and the
functional relationships between its genes.
From fitness landscapes to seascapes: non-equilibrium dynamics of selection
and
adaptation
V. Mustonen and M. Lässig, Trends Genet 25, 111-9, (2009)
Evolution is a quest for innovation.
Organisms adapt to changing natural selection by evolving new phenotypes. Can we read this dynamics in their
genomes? Not every mutation under positive selection responds to a change in selection: beneficial changes
also occur at evolutionary equilibrium, repairing previous deleterious changes and restoring existing
functions. Adaptation, by contrast, is viewed here as a non-equilibrium phenomenon: the genomic response to
time-dependent selection. Our approach extends the static concept of fitness landscapes to dynamic fitness
seascapes. It shows that adaptation requires a surplus of beneficial substitutions over deleterious ones.
Here, we focus on the evolution of yeast and Drosophila genomes, providing examples where adaptive evolution
can and cannot be inferred, despite the presence of positive selection
Energy-dependent fitness: a quantitative model for the evolution of yeast
transcription factor binding sites
V. Mustonen, J. Kinney, CG. Callan Jr, and M. Lässig, Proc. Natl. Acad. Sci.
105,
12376-81, (2008)
We present a genomewide cross-species
analysis of regulation for broad-acting transcription factors in yeast. Our model for binding site evolution
is founded on biophysics: the binding energy between transcription factor and site is a quantitative
phenotype
of regulatory function, and selection is given by a fitness landscape that depends on this phenotype. The
model quantifies conservation, as well as loss and gain, of functional binding sites in a coherent way. Its
predictions are supported by direct cross-species comparison between four yeast species. We find ubiquitous
compensatory mutations within functional sites, such that the energy phenotype and the function of a site
evolve in a significantly more constrained way than does its sequence. We also find evidence for substantial
evolution of regulatory function involving point mutations as well as sequence insertions and deletions
within
binding sites. Genes lose their regulatory link to a given transcription factor at a rate similar to the
neutral point mutation rate, from which we infer a moderate average fitness advantage of functional over
nonfunctional sites. In a wider context, this study provides an example of inference of selection acting on
a
quantitative molecular trait.
From protein interactions to functional annotation: graph alignment in Herpes
M. Kolar, Lässig, and J. Berg, BMC Syst Biol. 2, 90, (2008)
Background: Sequence alignment is a prolific basis of functional annotation, but remains a
challenging problem in the 'twilight zone' of high sequence divergence or short gene length. Here we
demonstrate how information on gene interactions can help to resolve ambiguous sequence alignments. We
compare two distant Herpes viruses by constructing a graph alignment, which is based jointly on the
similarity of their protein interaction networks and on sequence similarity. This hybrid method provides
functional associations between proteins of the two organisms that cannot be obtained from sequence or
interaction data alone.
Results: We find proteins where interaction similarity and sequence similarity are individually
weak, but together provide significant evidence of orthology. There are also proteins with high
interaction
similarity but without any detectable sequence similarity, providing evidence of functional association
beyond sequence homology. The functional predictions derived from our alignment are consistent with
genomic
position and gene expression data.
Conclusion: Our approach shows that evolutionary conservation is a powerful filter to make protein
interaction data informative about functional similarities between the interacting proteins, and it
establishes graph alignment as a powerful tool for the comparative analysis of data from highly diverged
species.
Molecular evolution under fitness fluctuations
V. Mustonen and M. Lässig, Phys Rev Lett. 100, 108101, (2008)
Molecular evolution is a stochastic
process governed by fitness, mutations, and reproductive fluctuations in a population. Here, we study
evolution where fitness itself is stochastic, with random switches in the direction of selection at
individual
genomic loci. As the correlation time of these fluctuations becomes larger than the diffusion time of
mutations within the population, fitness changes from an annealed to a quenched random variable. We show
that
the rate of evolution has its maximum in the crossover regime, where both time scales are comparable.
Adaptive
evolution emerges in the quenched fitness regime (evidence for such fitness fluctuations has recently been
found in genomic data). The joint statistical theory of reproductive and fitness fluctuations establishes a
conceptual connection between evolutionary genetics and statistical physics of disordered system
Adaptations to fluctuating selection in Drosophila
V. Mustonen and M. Lässig, Proc. Natl. Acad. Sci. 104, 2277-82, (2007)
Time-dependent selection causes the
adaptive evolution of new phenotypes, and this dynamics can be traced in genomic data. We have analyzed
polymorphisms and substitutions in Drosophila, using a more sensitive inference method for adaptations than
the standard population-genetic tests. We find evidence that selection itself is strongly time-dependent,
with
changes occurring at nearly the rate of neutral evolution. At the same time, higher than previously
estimated
levels of selection make adaptive responses by a factor 10-100 faster than the pace of selection changes,
ensuring that adaptations are an efficient mode of evolution under time-dependent selection. The rate of
selection changes is faster in noncoding DNA, i.e., the inference of functional elements can less be based
on
sequence conservation than for proteins. Our results suggest that selection acts not only as a constraint
but
as a major driving force of genomic change.
From biophysics to evolutionary genetics: statistical aspects of gene
regulation
M. Lässig, BMC Bioinformatics 8 Suppl 6, S7, (2007)
This is an introductory review on how
genes interact to produce biological functions. Transcriptional interactions involve the binding of proteins
to regulatory DNA. Specific binding sites can be identified by genomic analysis, and these undergo a
stochastic evolution process governed by selection, mutations, and genetic drift. We focus on the links
between the biophysical function and the evolution of regulatory elements. In particular, we infer fitness
landscapes of binding sites from genomic data, leading to a quantitative evolutionary picture of regulation.
Cross-species analysis of biological networks by Bayesian alignment
J. Berg and M. Lässig, Proc. Natl. Acad. Sci. 103, 10967, (2006)
Complex interactions between genes or
proteins contribute a substantial part to phenotypic evolution. Here we develop an evolutionarily grounded
method for the cross-species analysis of interaction networks by alignment, which maps bona fide functional
relationships between genes in different organisms. Network alignment is based on a scoring function
measuring
mutual similarities between networks, taking into account their interaction patterns as well as sequence
similarities between their nodes. High-scoring alignments and optimal alignment parameters are inferred by a
systematic Bayesian analysis. We apply this method to analyze the evolution of coexpression networks between
humans and mice. We find evidence for significant conservation of gene expression clusters and give
network-based predictions of gene function. We discuss examples where cross-species functional relationships
between genes do not concur with sequence similarity.
Freezing of random RNA
M. Lässig and K. Wiese, Phys. Rev. Lett. 96, 228101, (2006)
We study secondary structures of
random RNA molecules by means of a renormalized field theory based on an expansion in the sequence disorder.
We show that there is a continuous phase transition from a molten phase at higher temperatures to a
low-temperature glass phase. The primary freezing occurs above the critical temperature, with local islands
of
stable folds forming within the molten phase. The size of these islands defines the correlation length of
the
transition. Our results include critical exponents at the transition and in the glass phase.
A minimal stochastic model for influenza evolution
F. Tria, M. Lässig, L. Peliti, S. Franz, J. Stat. Mech. P07008 (2005)
We introduce and discuss a minimal
individual based model for influenza dynamics. The model takes into account the effects of specific
immunization against viral strains, but also infectivity randomness and the presence of a short lived
strain-transcending immunity recently suggested in the literature. We show by simulations that the resulting
model exhibits substitution of viral strains along the years, but that their divergence remains bounded. We
also show that dropping any of these features results in a drastically different behaviour, leading either
to
the extinction of the disease, to the proliferation of the viral strains or to their divergence.
Biodiversity and productivity in model ecosystems I: Coexistence conditions
for
competing species
U. Bastolla, M. Lässig, S. Manrubia, and A. Valleriani, J. Theor. Biol. 235,
521,
(2005)
This is the first of two papers
where
we discuss the limits imposed by competition to the biodiversity of species communities. In this first
paper,
we study the coexistence of competing species at the fixed point of population dynamic equations. For many
simple models, this imposes a limit on the width of the productivity distribution, which is more severe the
more diverse the ecosystem is (1994, Theor. Popul. Biol. 45, 227-276). Here we review and generalize this
analysis, beyond the "mean-field"-like approximation of the competition matrix used in previous works, and
extend it to structured food webs. In all cases analysed, we obtain qualitatively similar relations between
biodiversity and competition: the narrower the productivity distribution is, the more species can stably
coexist. We discuss how this result, considered together with environmental fluctuations, limits the maximal
biodiversity that a trophic level can host.
Biodiversity and productivity in model ecosystems II: Species assembly and
food
web structure
U. Bastolla, M. Lässig, S. Manrubia, and A. Valleriani, J. Theor. Biol. 235,
531,
(2005)
This is the second of two papers
dedicated to the relationshipbetween population models of competition and biodiversity. Here we consider
species assembly models where the population dynamics is kept far from fixed points through the continuous
introduction of new species, and generalize to such models the coexistence condition derived for systems at
the fixed point. The ecological overlap between species with shared preys,that we define here, provides a
quantitative measure of the effective interspecies competition and of the trophic network topology. We obtain
distributions of the overlap from simulations of a new model based both on immigration and speciation, and
show that they are in good agreement with those measured for three large natural food webs. As discussed in
the first paper, rapid environmental fluctuations, interacting with the condition for coexistence of competing
species, limit the maximal biodiversity that a trophic level can host. This horizontal limitation to
biodiversity is here combined with either dissipation of energy or growth of fluctuations, which in our model
limit the length of foodwebs in the vertical direction. These ingredients yield an effective model of food
webs
that produce a biodiversity profile with a maximum at an intermediate trophic level, inagreement with field
studies.
Evolutionary population genetics of promoters: predicting binding sites and
functional phylogenies
V. Mustonen and M. Lässig, Proc. Natl. Acad. Sci. 103, 10967, (2005)
We study the evolution of
transcription factor-binding sites in prokaryotes, using an empirically grounded model with point mutations
and genetic drift. Selection acts on the site sequence via its binding affinity to the corresponding
transcription factor. Calibrating the model with populations of functional binding sites, we verify this
form
of selection and show that typical sites are under substantial selection pressure for functionality: for
cAMP
response protein sites in Escherichia coli, the product of fitness difference and effective population size
takes values 2NΔF of order 10. We apply this model to cross-species comparisons of binding sites in
bacteria and obtain a prediction method for binding sites that uses evolutionary information in a
quantitative
way. At the same time, this method predicts the functional histories of orthologous sites in a phylogeny,
evaluating the likelihood for conservation or loss or gain of function during evolution. We have performed,
as
an example, a cross-species analysis of
E. coli,
Salmonella typhimurium, and
Yersinia
pseudotuberculosis. Detailed lists of predicted sites and their functional phylogenies are available.
Solvable sequence evolution models and genomic correlations
P.W. Messer, P.F. Arndt, and M. Lässig, Phys. Rev. Lett. 94, 138103, (2005)
We study a minimal model for genome
evolution whose elementary processes are single site mutation, duplication and deletion of sequence regions,
and insertion of random segments. These processes are found to generate long-range correlations in the
composition of letters as long as the sequence length is growing; i.e., the combined rates of duplications
and
insertions are higher than the deletion rate. For constant sequence length, on the other hand, all initial
correlations decay exponentially. These results are obtained analytically and by simulations. They are
compared with the long-range correlations observed in genomic DNA, and the implications for genome evolution
are discussed.
Toward an accurate statistics of gapped alignments
M. Kschischo, M. Lässig, and Y.-K. Yu, Bull. Math. Biol. 67, 169, (2005)
Sequence alignment has been an
invaluable tool for finding homologous sequences. The significance of the homology found is often quantified
statistically by p-values. Theory for computing p-values exists for gapless alignments [Karlin and Altschul
1990, Karlin and Dembo A 1992], but a full generalization to alignments with gaps is not yet complete. We
present a unified statistical analysis of two common sequence comparison algorithms: maximum-score
(Smith-Waterman) alignments and their generalized probabilistic counterparts, including maximum-likelihood
alignments and hidden Markov models. The most important statistical characteristic of these algorithms is
the
distribution function of the maximum score S
max, resp. the maximum free energy
F
max, for mutually uncorrelated random sequences. This distribution is known
empirically to be of the Gumbel form with an exponential tail P(S
max > x)
approximately exp(-λx) for maximum-score alignment and P(F
max > x)
approximately
exp(-λx) for some classes of probabilistic alignment. We derive an exact expression for lambda for
particular
probabilistic alignments. This result is then used to obtain accurate lambda values for generic
probabilistic
and maximum-score alignments. Although the result demonstrated uses a simple match-mismatch scoring system,
it
is expected to be a good starting point for more general scoring functions.
Universality of log-range correlations in expansion-randomization systems
P.W. Messer, M. Lässig, and P.F. Arndt, J. Stat. Mech., P10004, (2005)
We study the stochastic dynamics of
sequences evolving by single site mutations, segmental duplications, deletions, and random insertions. These
processes are relevant for the evolution of genomic DNA. They define a universality class of non-equilibrium
1D expansion–randomization systems with generic stationary long-range correlations in a regime of growing
sequence length. We obtain explicitly the two-point correlation function of the sequence composition and the
distribution function of the composition bias in sequences of finite length. The characteristic exponent χ
of
these quantities is determined by the ratio of two effective rates, which are explicitly calculated for
several specific sequence evolution dynamics of the universality class. Depending on the value of χ, we find
two different scaling regimes, which are distinguished by the detectability of the initial composition bias.
All analytic results are accurately verified by numerical simulations. We also discuss the non-stationary
build-up and decay of correlations, as well as more complex evolutionary scenarios, where the rates of the
processes vary in time. Our findings provide a possible example for the emergence of universality in
molecular
biology.
Adaptive evolution of transcription factor binding sites
J. Berg, S. Willmann, and M. Lässig, BMC Evol. Biol. 4, 42, (2004)
Background
The regulation of a gene depends on the binding of transcription factors to specific sites located in the
regulatory region of the gene. The generation of these binding sites and of cooperativity between them are
essential building blocks in the evolution of complex regulatory networks. We study a theoretical model
for
the sequence evolution of binding sites by point mutations. The approach is based on biophysical models
for
the binding of transcription factors to DNA. Hence we derive empirically grounded fitness landscapes,
which
enter a population genetics model including mutations, genetic drift, and selection.
Results
We show that the selection for factor binding generically leads to specific correlations between
nucleotide
frequencies at different positions of a binding site. We demonstrate the possibility of rapid adaptive
evolution generating a new binding site for a given transcription factor by point mutations. The
evolutionary time required is estimated in terms of the neutral (background) mutation rate, the selection
coefficient, and the effective population size.
Conclusions
The efficiency of binding site formation is seen to depend on two joint conditions: the binding site
motif
must be short enough and the promoter region must be long enough. These constraints on promoter
architecture
are indeed seen in eukaryotic systems. Furthermore, we analyse the adaptive evolution of genetic switches
and of signal integration through binding cooperativity between different sites. Experimental tests of
this
picture involving the statistics of polymorphisms and phylogenies of sites are discussed.
Local graph alignment and motif search in biological networks
J. Berg and M. Lässig, Proc. Natl. Acad. Sci. 101, 14689, (2004)
Interaction networks are of central
importance in postgenomic molecular biology, with increasing amounts of data becoming available by
high-throughput methods. Examples are gene regulatory networks or protein interaction maps. The main
challenge
in the analysis of these data is to read off biological functions from the topology of the network.
Topological motifs, i.e., patterns occurring repeatedly at different positions in the network, have recently
been identified as basic modules of molecular information processing. In this article, we discuss motifs
derived from families of mutually similar but not necessarily identical patterns. We establish a statistical
model for the occurrence of such motifs, from which we derive a scoring function for their statistical
significance. Based on this scoring function, we develop a search algorithm for topological motifs called
graph alignment, a procedure with some analogies to sequence alignment. The algorithm is applied to the gene
regulation network of Escherichia coli.
Of statistics and genomes
D. Tautz and M. Lässig, Trends in Genetics 20, 344, (2004)
Higher organisms have more genes and
larger genomes than simple organisms. This statement sounds almost too trivial to ask the question: why? But
there are at least two different answers. Either there is an inherent necessity to increase genome size when
more complexity is required or genome size increases because of other reasons that then enable complexity to
"latch on". Recently, an article by Lynch and Conery, which used arguments of evolutionary population
dynamics, proposed that low population size leads to larger genomes. This then provides the opportunity to
generate more complex organisms.
Structure and evolution of protein networks: a statistical model for link
dynamics and gene duplications
J. Berg, M. Lässig, and A. Wagner, BMC Evol. Biol. 4, 51, (2004)
Background
The structure of molecular networks derives from dynamical processes on evolutionary time scales. For
protein interaction networks, global statistical features of their structure can now be inferred
consistently from several large-throughput datasets. Understanding the underlying evolutionary dynamics is
crucial for discerning random parts of the network from biologically important properties shaped by
natural
selection.
Results
We present a detailed statistical analysis of the protein interactions in Saccharomyces cerevisiae based
on
several large-throughput datasets. Protein pairs resulting from gene duplications are used as tracers into
the evolutionary past of the network. From this analysis, we infer rate estimates for two key evolutionary
processes shaping the network: (i) gene duplications and (ii) gain and loss of interactions through
mutations in existing proteins, which are referred to as link dynamics. Importantly, the link dynamics is
asymmetric, i.e., the evolutionary steps are mutations in just one of the binding parters. The link
turnover
is shown to be much faster than gene duplications. Both processes are assembled into an empirically
grounded, quantitative model for the evolution of protein interaction networks.
Conclusions
According to this model, the link dynamics is the dominant evolutionary force shaping the statistical
structure of the network, while the slower gene duplication dynamics mainly affects its size.
Specifically,
the model predicts (i) a broad distribution of the connectivities (i.e., the number of binding partners of
a
protein) and (ii) correlations between the connectivities of interacting proteins, a specific consequence
of
the asymmetry of the link dynamics. Both features have been observed in the protein interaction network of
S. cerevisiae.
Evolutionary games and quasispecies
F. Tria, M. Lässig, L. Peliti, Europhys. Lett. 62, 446 (2003)
We discuss a population of sequences
subject to mutations and frequency- dependent selection, where the fitness of a sequence depends on the
composition of the entire population. This type of dynamics is crucial to understand, for example, the
coupled
evolution of different strands in a viral population. Mathematically, it takes the form of a reaction-
diffusion problem that is nonlinear in the population state. In our model system, the fitness is determined
by
a simple mathematical game, the hawk-dove game. The stationary population distribution is found to be a
quasispecies with properties different from those which hold in fixed fitness landscapes.
Stochastic evolution of transcription factor binding sites
J. Berg and M. Lässig, Biophysics (Moscow) 48, Suppl. 1 (2003)
A key step in the process of genetic
transcription is the binding of one or several transcription factors to specific sites in the regulatory
region of a gene. These binding sites may differ strongly across even closely related species, and the
generation of new binding sites is an essential part of the evolution of regulatory networks. In this paper
we
consider the sequence evolution of binding sites, using empirically grounded fitness landscapes. We
demonstrate how a new binding site for a given transcription factor may be generated de novo, and estimate
the
time required for this process in terms of the neutral mutation rate, the selection coefficient, and the
effective population size. We also consider how several sites binding to the same type of factor can coexist
in the regulatory region of a gene.
Correlated Random Networks
J. Berg and M. Lässig, Phys. Rev. Lett. 89, 228701, (2002)
We develop a statistical theory of
networks. A network is a set of vertices and links given by its adjacency matrix c, and the relevant
statistical ensembles are defined in terms of a partition function Z=Σexp([-βH(c)]. The simplest
cases are uncorrelated random networks such as the well-known Erdös-Rényi graphs. Here we study more general
interactions H(c) which lead to correlations, for example, between the connectivities of adjacent vertices.
In
particular, such correlations occur in optimized networks described by partition functions in the limit
β
--> infinity. They are argued to be a crucial signature of evolutionary design in biological networks.
Delocalization transitions of semiflexible manifolds
R. Bundschuh and M. Lässig, Phys. Rev. E65, 61502, (2002)
Semiflexible manifolds such as fluid
membranes or semiflexible polymers undergo delocalization transitions if they are subject to attractive
interactions. We study manifolds with short-ranged interactions by field-theoretic methods based on the
operator product expansion of local interaction fields. We apply this approach to manifolds in a random
potential. Randomness is always relevant for fluid membranes, while for semiflexible polymers there is a
first-order transition to the strong coupling regime at a finite temperature.
Dynamics and topology of species networks
U. Bastolla, M. Lässig, S. Manrubia, and A. Valleriani, in Biological
Evolution and Statistical Physics, ed. M. Lässig and A. Valleriani, Springer Verlag (2002) (refereed)
We study communities formed by a
large
number of species, which are an example of dynamical networks in biology. Interactions between species, such
as prey-predator relationships and mutual competition, define the links of these networks.They also govern
the
dynamics of their population sizes. This dynamics acts as a selection mechanism, which can lead to the
extinction of species. Adaptive changes of the interactions or the generation of new species involve random
mutations as well as selection. We show how this dynamics determines key topological characteristics of
species networks. The results are in agreement with observations.
Spatio-Temporal Modes of Speciation
M. Rost and M. Lässig, in Biological Evolution and Statistical Physics,
ed. M. Lässig and A.Valleriani, Springer Verlag (2002), (refereed)
The split of a population into two
reproductively isolated subpopulations is studied within a model including spatial heterogeneity. We find
three dynamical pathways of speciation resulting from a coupling of space, competition and mating behaviour:
(i) sympatric at small habitat heterogeneity, (ii) sympatric with subsequent spatial differentiation at
intermediate heterogeneity, and (iii) allopatric under strong heterogeneity.
Diversity patterns from ecological models at dynamical equilibrium
U. Bastolla, M. Lässig, S. Manrubia, and A. Valleriani, J. Theor. Biol. 212,
11,
(2001)
We study a dynamic model of
ecosystems
where an immigration flux assembles the species community and maintains its biodiversity. This framework is
particularly relevant for insular ecosystems. Population dynamics is represented either as an
individual-based
model or as a set of deterministic equations for population abundances. Local extinctions and immigrations
balance at a statistically stationary state where biodiversity fluctuates around a constant mean value. We
find a number of scaling laws characterizing this stationary state. In particular, the number of species
increases as a power law of the immigration rate. With additional assumptions on the immigration flux, we
obtain species-area relationships in agreement with observations for archipelagos. We also find power-law
distributions for species abundances and lifetimes.
Shape of ecological networks
M. Lässig, U. Bastolla, S. Manrubia, and A. Valleriani, Phys. Rev. Lett. 86,
4418, (2001)
We study the statistics of
ecosystems
with a variable number of coevolving species. The species interact in two ways: by prey-predator
relationships
and by direct competition with similar kinds. The interaction coefficients change slowly through successful
adaptations and speciations. They are treated as quenched random variables. These interactions determine
long-term topological features of the species network, which are found to agree with those of biological
systems.
Dynamical anomalies and intermittency in Burgers turbulence
M. Lässig, Phys. Rev. Lett. 84, 2618, (2000)
We analyze the field theory of fully
developed Burgers turbulence. Its key elements are shock fields, which characterize the singularity
statistics
of the velocity field. The shock fields enter an operator product expansion describing intermittency. The
latter is found to be constrained by dynamical anomalies expressing finite dissipation in the inviscid
limit.
The link between dynamical anomalies and intermittency is argued to be important in a wider context of
turbulence.
Finite-temperature sequence alignment
M. Kschischo and M. Lässig, Pacific Symposium on Biocomputing 5, (2000)
(refereed)
We develop a statistical theory of
probabilistic sequence alignments derived from a 'thermodynamic' partition function at finite temperature.
Such alignments are a generalization of those obtained from information-theoretic approaches.
Finite-temperature statistics can be used to characterize the significance of an alignment and the
reliability
of its single element pairs.
Scaling laws and similarity detection in sequence alignment with gaps
D. Drasdo, T. Hwa, and M. Lässig, J. Comput. Biol. 7, 115, (2000)
We study the problem of similarity
detection by sequence alignment with gaps, using a recently established theoretical framework based on the
morphology of alignment paths. Alignments of sequences without mutual correlations are found to have
scale-invariant statistics. This is the basis for a scaling theory of alignments of correlated sequences.
Using a simple Markov model of evolution, we generate sequences with well-defined mutual correlations and
quantify the fidelity of an alignment in an unambiguous way. The scaling theory predicts the dependence of
the
fidelity on the alignment parameters and on the statistical evolution parameters characterizing the sequence
correlations. Specific criteria for the optimal choice of alignment parameters emerge from this theory. The
results are verified by extensive numerical simulations.
Semiflexible polymers with attractive interactions
R. Bundschuh, M. Lässig, and R. Lipowsky, Eur. Phys. J. B 3, 295, (2000)
The delocalization and unbinding
transitions of two semi-flexible polymers which experience attractive interactions are studied by a variety
of
theoretical methods. In two-dimensional systems, one has to distinguish four different universality classes
for
the interaction potentials. In particular, the delocalization transitions from a potential well and the
unbinding transitions from such a well in the presence of a hard wall exhibit distinct critical behavior
governed by different critical exponents. In three-dimensional systems, we predict first-order transitions
with
a jump in the energy density but with critical or self-similar fluctuations leading to distribution functions
with power law tails. The predicted critical behavior is con- firmed numerically by transfer matrix
calculations in two dimensions and by Monte Carlo simulations in three dimensions. This behavior should be
accessible to experiments on biopolymers such as actin filaments or microtubuli.
Optimizing Smith-Waterman alignments
R. Olsen, T. Hwa, and M. Lässig, Pacific Symposium on Biocomputing 4, 302
(1999)
(refereed)
Mutual correlation between segments
of
DNA or protein sequences can be detected by Smith-Waterman local alignments. We present a statistical
analysis
of alignment of such sequences, based on a recent scaling theory. A new fidelity measure is introduced and
shown to capture the significance of the local alignment, i.e., the extent to which the correlated
subsequences are correctly identified. It is demonstrated how the fidelity may be optimized in the space of
penalty parameters using only the alignment score data of a single sequence pair.
A statistical theory of sequence alignment with gaps
D. Drasdo, T. Hwa, and M. Lässig, Proceedings of the sixth international
conference on intelligent systems for molecular biology (ISMB 98), AAAI Press, Menlo Park (1998) (refereed)
A statistical theory of local
alignment algorithms with gaps is presented. Both the linear and logarithmic phases, as well as the phase
transition separating the two phases, are described in a quantitative way. Markov sequences without mutual
correlations are shown to have scale-invariant alignment statistics. Deviations from scale invariance
indicate
the presence of mutual correlations detectable by alignment algorithms. Conditions are obtained for the
optimal detection of a class of mutual sequence correlations.
On growth, disorder, and field theory (review article)
M. Lässig, J. Phys. C 10, 9905 (1998)
This article reviews recent
developments in statistical field theory far from equilibrium. It focuses on the Kardar-Parisi-Zhang
equation
of stochastic surface growth and its mathematical relatives, namely the stochastic Burgers equation in fluid
mechanics and directed polymers in a medium with quenched disorder. At strong stochastic driving - or at
strong disorder, respectively - these systems develop non-perturbative scale invariance. Presumably exact
values of the scaling exponents follow from a self-consistent asymptotic theory. This theory is based on the
concept of an operator product expansion formed by the local scaling fields. The key difference from
standard
Lagrangian field theory is the appearance of a dangerous irrelevant coupling constant generating dynamical
anomalies in the continuum limit.
Optimal detection of sequence similarity by local alignment
T. Hwa and M. Lässig, Proceedings of the second annual conference on
computational molecular biology (RECOMB 98), ACM Press, New York (1998) (refereed)
The statistical properties of local
alignment algorithms with gaps are analyzed theoretically for uncorrelated and correlated random sequences.
In
the vicinity of the log-linear phase transition, the statistics of alignment with gaps is shown to be
characteristically different from that of gapless alignment. The optimal scores obtained for uncorrelated
sequences obey certain robust scaling laws. Deviation from these scaling laws signals sequence homology, and
can be used to guide the empirical selection of scoring parameters for the optimal detection of sequence
similarities. This can be accomplished in a computationally efficient way by using a novel approach focusing
on the score profiles. Furthermore, by assuming a few gross features characterizing the statistics of
underlying sequence-sequence correlations, quantitative criteria are obtained for the choice of optimal
scoring parameters: Optimal similarity detection is most likely to occur in a region close to the log side
of
the loglinear phase transition.
Quantized scaling of growing surfaces
M. Lässig, Phys Rev. Lett. 80, 2366 (1998)
The Kardar-Parisi-Zhang universality
class of stochastic surface growth is studied by exact field-theoretic methods. From previous numerical
results, a few qualitative assumptions are inferred. In particular, height correlations should satisfy an
operator product expansion and, unlike the correlations in a turbulent fluid, exhibit no multiscaling. These
properties impose a quantization condition on the roughness exponent χ and the dynamic exponent z. Hence the
exact values χ = 2/5, z = 8/5 for two-dimensional and χ = 2/7, z = 12/7 for three-dimensional surfaces are
derived.
Reply on a Comment to Upper critical dimension of the Kardar-Parisi-Zhang
equation
H. Kinzelbach and M. Lässig, Phys. Rev. Lett. 80, 889 (1998)
DNA sequence alignment and critical phenomena
D. Drasdo, T. Hwa, and M. Lässig, in Statistical Mechanics in Physics and
Biology, ed. D. Wirtz et al., Boston (1997) (refereed)
Alignment algorithms are commonly
used
to detect and quantify similarities between DNA sequences. We study these algorithms in the framework of a
recent theory viewing similarity detection as a geometrical critical phenomenon of directed random walks. We
show that the roughness of these random walks governs the fidelity of an alignment, i.e., its ability to
capture the correlations between the sequences compared. Criteria for the optimization of alignment
algorithms
emerge from this theory.
Upper critical dimension of the Kardar-Parisi-Zhang equation
M. Lässig and H. Kinzelbach, Phys. Rev. Lett. 78, 903, (1997)
The strong-coupling regime of
Kardar-Parisi-Zhang surface growth driven by short-ranged noise is shown to have an upper critical dimension
d> less than or equal to four [where the dynamic exponent z takes the value z(d
>) = 2]. To derive this, we use the mapping onto directed polymers with quenched
disorder. Two such polymers coupled by a small contact attraction of strength u are shown to form a bound
state at all temperatures 1/β ≤ 1/βc, the roughening temperature of a single polymer. Comparing
singularities
of the (de-)localization transition at u = 0 below 1/βc and at 1/βc then yields d
>≤4.
Comment on "Simplest possible self-organized critical system"
R. Bundschuh and M. Lässig, Phys. Rev. Lett. 77, 4273, (1996)
Directed polymers in high dimensions
R. Bundschuh and M. Lässig, Phys. Rev. E 54, 304, (1996)
We study directed polymers subject
to
a quenched random potential in d transversal dimensions. This system is closely related to the
Kardar-Parisi-Zhang equation of nonlinear stochastic growth. By a careful analysis of the perturbation
theory
we show that physical quantities develop singular behavior for d→4. For example, the universal finite-size
amplitude of the free energy at the roughening transition is proportional to √4-d. This shows that the
dimension d=4 plays a special role for the Kardar-Parisi-Zhang problem.
Similarity detection and localization
T. Hwa and M. Lässig, Phys. Rev. Lett. 76, 2591, (1996)
The detection of similarities
between
long DNA and protein sequences is studied using concepts of statistical physics. It is shown that mutual
similarities can be detected by sequence alignment methods only if their amount exceeds a threshold value.
The
onset of detection is a critical phase transition viewed as a localization-delocalization transition. The
fidelity of the alignment is the order parameter of that transition; it leads to criteria to select optimal
alignment parameters.
Vicinal surfaces and the Calogero-Sutherland model
M. Lässig, Phys. Rev. Lett. 77, 526, (1996)
A miscut (vicinal) crystal surface
can
be regarded as an array of meandering but noncrossing steps. Interactions between the steps are shown to
induce a faceting transition of the rough surface between a homogeneous Tomonaga-Luttinger liquid state and
a
low-temperature regime of local step clusters in coexistence with ideal facets. This morphological
transition
is governed by a hitherto neglected critical line of the well-known Calogero-Sutherland model. Its exact
solution yields expressions for measurable quantities that compare favorably with recent experiments on Si
surfaces.
Depinning in a random medium
H. Kinzelbach and M. Lässig, J. Phys. A 28, 6535, (1995)
We develop a renormalized continuum
field theory for a directed polymer interacting with a random medium and a single extended defect. The
renormalization group is based on the operator algebra of the pinning potential; it has novel features due
to
the break down of hyperscaling in a random system. There is a second-order transition between a localized
and
a delocalized phase of the polymer; we obtain analytic results on ist critical pinning strength and scaling
exponents. Our results are directly related to spatially inhomogeneous Kardar-Parisi-Zhang surface growth.
Interacting flux lines in a random medium
H. Kinzelbach and M. Lässig, Phys. Rev. Lett. 75, 2208, (1995)
We study the continuum field theory
for an ensemble of directed lines r
i(t) in 1+d′ dimensions that live in a medium
with quenched point disorder and interact via short-range pair forces gΨ(r
i-r
j). In the strong-disorder (or low-temperature) regime,
attractive forces generate a
bound state with localization length ξ⊥∼|g|
-ν⊥; repulsive forces lead to mutual
avoidance with a pair distribution function P(r
i-r
j)∼
|r
i-r
j|
θ reminiscent of
fermions. In the experimentally important dimension d′=2, we obtain ν⊥≈0.8 and θ≈0.4.
On the renormalization of the Kardar-Parisi-Zhang equation
M. Lässig, Nucl. Phys. B448, 559, (1995)
The Kardar-Parisi-Zhang (KPZ)
equation
of nonlinear stochastic growth in d dimensions is studied using the mapping on to a system of directed
polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally subtracted
perturbation expansion about d=2. For the KPZ roughening transition in dimensions d>2, this renormalization
group yields the dynamic exponent z⋆=2 and the roughness exponent χ⋆=0, which are exact to all orders in
ε≡(2−d)/2. The expansion becomes singular in d=4, which is hence identified with the upper critical dimension
of the KPZ equation. The implications of this perturbation theory for the strong-coupling phase are
discussed.
In particular, it is shown that the correlation functions and the coupling constant defined in minimal
subtraction develop an essential singularity at the strong-coupling fixed point.
Strongly inhomogeneous surface growth and directed polymers
H. Kallabis and M. Lässig, Phys. Rev. Lett. 75, 1578, (1995)
We study nonlinear surface growth
driven by spatially localized noise, a model that can be mapped onto directed polymers with random contact
interactions. These systems are asymptotically free and show nonperturbative strong-coupling behavior on
large
scales in one dimension; hence they are possibly the simplest examples with these properties. The
strong-coupling regime represents new universality classes of directed growth and of polymer delocalization
transitions, which we analyze in detail.
Bundles of interacting strings in two dimensions
C. Hiergeist, M. Lässig, and R. Lipowsky, Europhys. Lett. 28, 103, (1994)
Bundles of strings which interact
via
short-ranged pair potentials are studied in two dimensions. The corresponding transfer matrix problem is
solved analytically for arbitrary string number N by Bethe ansatz methods. Bundles consisting of N identical
strings exhibit a unique unbinding transition. If the string bundle interacts with a hard wall, the bundle
may
unbind from the wall via a unique transition or a sequence of N successive transitions. In all cases, the
critical exponents are independent of N and the density profile of the strings exhibits a scaling form that
approaches a mean-field profiie in the limit of large N.
New criticality of 1D fermions
M. Lässig, Phys. Rev. Lett. 73, 561, (1994)
One-dimensional massive quantum
particles [or (1 + 1)-dimensional random walks] with short-ranged multiparticle interactions are studied by
exact renormalization group methods. With repulsive pair forces, such particles are known to scale as free
fermions. With finite m-body forces (m=3,4,…), a critical instability is found, indicating the transition to
a
fermionic bound state. These unbinding transitions represent new universality classes of interacting
fermions
relevant to polymer and membrane systems. Implications for massless fermions, e.g., in the Hubbard model,
are
also noted.
Critical roughening of interfaces: A new class of renormalizable field
theories
M. Lässig and R. Lipowsky, Phys. Rev. Lett. 70, 1131, (1993)
A renormalizable field theory is
developed for (multi)critical roughening of interacting interfaces in systems of dimension d<3. There is
an
infinite hierarchy of universality classes that mirrors the series of multicritical points in Ising systems.
The relevant operator algebra of these theories is built up by local scaling fields that are singular
distributions of the basic field variable. Critical indices, e.g., the exponent α, of the specific heat, are
obtained analytically in an ɛ expansion. The extension of our results to d=3 is discussed.
Multiple crossover phenomena and scale hopping in two dimensions
M. Lässig, Nucl. Phys. B 380, 601, (1992)
We study the renormalization group
for
nearly marginal perturbations of a minimal conformal field theory M
p with p
>> 1. To leading order in perturbation theory, we find a unique one-parameter family of “hopping
trajectories” that is characterized by a staircase-like renormalization group flow of the C-function and the
anomalous dimensions and that is related to a factorizable scattering theory recently solved by Al. B.
Zamolodchikov. We argue that this system is described by interactions of the form . As a function of the
relevant parameter t, it undergoes a phase transition with new critical exponents simultaneously governed by
all fixed points M
p, M
p−1,…, M
3. Integrable lattice models represent different phases of the same integrable system
that are distinguished by the sign of the irrelevant parameter .
Exact universal amplitude ratios in two-dimensional systems near criticality
M. Lässig, Phys. Rev. Lett. 67, 3737, (1991)
Universal amplitude relations
associated with hyperscaling are obtained exactly for several integrable perturbations of two-dimensional
(multi)critical points described by minimal models. The results are confirmed numerically and it is
discussed
how they can be verified by experiment.
Finite-size effects in theories with factorizable S-matrices
M. Lässig and M.J. Martins, Nucl. Phys. B354, 666, (1991)
We study the energy spectrum of (1 +
1)-dimensional perturbed conformal field theories defined on the cylinder. The finite-size dependence of the
two-particle levels allows a direct numerical measurement of the elastic S-matrix which we compare with the
conjectured minimal S-matrix for several perturbations of minimal models. We discuss the simplifications
that
integrability imposes on the spectrum above threshold. In particular, the ultraviolet limit of the elastic
phase shift of two lightest particles is related in a simple way to scaling dimensions of the conformal
field
theory.
Hilbert space and structure constants of descendant fields in two-dimensional
conformal theories
M. Lässig and G. Mussardo, Comput. Phys. Comm. 66, 71, (1991)
We have developed an algorithm to
compute the Hilbert-space basis and the operator algebra of descendant fields for (1+1)-dimensional
conformal
field theories. Implemented as a Mathematica computer program, this algorithm is used to obtain
nonperturbatively the spectrum of the transfer matrix theories, seen as deformations of a massless conformal
theory.
New hierarchies of multicriticality in two-dimensional field theory
M. Lässig, Phys. Lett. B 278, 439, (1991)
The minimal conformal model M
p,q, perturbed by the relevant scaling field φ
1,3, is
argued to undergo a crossover to the model M
p-(q-p),q-(q-p), at least for large
values of p/(q − p). Hence its critical manifold is nested into all manifolds of lower criticality.
The scaling region of the tricritical Ising model in two dimensions
M. Lässig, G. Mussardo and J.L. Cardy, Nucl. Phys. B348, 591 (1991)
We study the scaling region spanned
by
all four relevant perturbations of the tricritical Ising model in two dimensions. We analyze the spectrum of
the (1 + 1)-dimensional off-critical hamiltonian on a truncated Hilbert space, a method recently proposed by
Yurov and AL Zamolodchikov. In the phase coexistence regions the massive excitations are kink states. On the
temperature-driven two-phase coexistence line, they form bound states, which we analyze for periodic as well
as for twisted boundary conditions. We find a new asymmetric two-phase region driven by the subleading
magnetic field. There are some indications of massless states along the crossover line to the Ising model.
The
effects of off-critical integrability on the spectra are also observed and discussed.
Geometry of the renormalization group, with an application in two dimensions
M. Lässig, Nucl. Phys. B334, 652, (1990)
The renormalization group is viewed
as
a theory of the geometry of action space. A general covariant relation between coupling constant and field
renormalization is derived. As an application, the crossover between the two-dimensional minimal modes
M
m and M
m−1 is calculated to two-loop order in a
minimal
subtraction scheme.
Book, book contributions, and other publications
Epidemiological and evolutionary analysis of the 2014 Ebola virus outbreak
M. Łuksza, T.Bedford, and M. Lässig, arxiv:1411.1722 (2014)
The 2014 epidemic of the Ebola virus
is governed by a genetically diverse viral population. In the early Sierra Leone outbreak, a recent study
has
identified new mutations that generate genetically distinct sequence clades. Here we find evidence that
major
Sierra Leone clades have systematic differences in growth rate and reproduction number. If this growth
heterogeneity remains stable, it will generate major shifts in clade frequencies and influence the overall
epidemic dynamics on time scales within the current outbreak. Our method is based on simple summary
statistics
of clade growth, which can be inferred from genealogical trees with an underlying clade-specific birth-death
model of the infection dynamics. This method can be used to perform realtime tracking of an evolving
epidemic
and identify emerging clades of epidemiological or evolutionary significance.
Evolutionary Dynamics and Statistical Physics
Special Volume, J. Stat. Mech., (2013)
Bayesian analysis of biological networks: Clusters, motifs, cross-species
correlations
J. Berg and M. Lässig, in Statistical and evolutionary analysis of
biological networks, ed. M.P.H. Stumpf and C. Wiuf, Imperial College Press, London (2009)
An important part of the analysis of
bio-molecular networks is to detect different functional units. Different functions are reflected in a
different evolutionary dynamics, and hence in different statistical characteristics of network parts. In
this
sense, the
global statistics of a biological network, e.g., its connectivity distribution, provides a
background, and
local deviations from this background signal functional units. In the computational
analysis of biological networks, we thus typically have to discriminate between different statistical models
governing different parts of the dataset. The nature of these models depends on the biological question
asked.
We illustrate this rationale here with three examples: identification of functional parts as highly
connected
network clusters, finding
network motifs, which occur in a similar form at different places in
the network, and the analysis of
cross-species network correlations, which reflect evolutionary
dynamics between species.
From biophysics to evolutionary genetics: Statistical aspects of gene
regulation
in Structural approaches to sequence evolution: Molecules, networks,
populations, U. Bastolla et al. eds., Springer Verlag (2006)
This is an introductory review on
how
genes interact to produce biological functions. Transcriptional interactions involve the binding of proteins
to regulatory DNA. Specific binding sites can be identified by genomic analysis, and these undergo a
stochastic evolution process governed by selection, mutations, and genetic drift. We focus on the links
between the biophysical function and the evolution of regulatory elements. In particular, we infer fitness
landscapes of binding sites from genomic data, leading to a quantitative evolutionary picture of regulation.
Den Text des Lebens verstehen - Herausforderungen postgenomischer Forschung an
Biologie und Physik in Deutschland (Understanding the text of life - challenges to post-genomic research in
Germany)
M. Lässig, E. Sackmann, D. Tautz, and M. Vingron, PhysikJournal 3 Nr. 10, 24,
(2004)
Die Lebenswissenschaften erleben
derzeit weltweit eine stürmische Entwicklung, die zu einer Konvergenz biologischer und physikalischer
Forschungsthemen und Forschungsstrukturen führt. In diesem Beitrag wollen wir zukunftsweisende
wissenschaftliche Ansätze diskutieren, Perspektiven insbesondere für die Physik aufzeigen und daraus ein
Plädoyer für neue Wissenschaftseinrichtungen ableiten, die zur Umsetzung dieser Perspektiven geeignet sind.
Biological Evolution and Statistical Physics
ed. M. Lässig and A. Valleriani, Springer Verlag (2002)
Quantum game theory
M.Lässig, e-print arXiv:cond-mat/0207711 (2002)
A systematic theory is introduced
that
describes stochastic effects in game theory. In a biological context, such effects are relevant for the
evolution of finite populations with frequency-dependent selection. They are characterized by quantum Nash
equilibria, a generalization of the well-known Nash equilibrium points in classical game theory. The
implications of this theory for biological systems are discussed in detail.
Universal aspects of interacting lines and surfaces
M. Lässig and R.Lipowsky, in Fundamental Problems in Statistical
Mechanics
VIII, ed.H.van Beijeren and M.H. Ernst, Elsevier, Amsterdam (1994)
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