27 research outputs found
Synthetic approaches to understanding biological constraints
Microbes can be readily cultured and their genomes can be easily manipulated. For these reasons, laboratory systems of unicellular organisms are increasingly used to develop and test theories about biological constraints, which manifest themselves at different levels of biological organization, from optimal gene-expression levels to complex individual and social behaviors. The quantitative description of biological constraints has recently advanced in several areas, such as the formulation of global laws governing the entire economy of a cell, the direct experimental measurement of the trade-offs leading to optimal gene expression, the description of naturally occurring fitness landscapes, and the appreciation of the requirements for a stable bacterial ecosystem.Alfred P. Sloan Foundation (Fellowship)Pew Charitable Trusts (Pew Scholars Program)National Science Foundation (U.S.) (NSF CAREER Award)National Institutes of Health (U.S.) (NIH R00 Pathway to Independence Award
Dynamical arrest and replica symmetry breaking in attractive colloids
Within the Replica Symmetry Breaking (RSB) framework developed by M.Mezard
and G.Parisi we investigate the occurrence of structural glass transitions in a
model of fluid characterized by hard sphere repulsion together with short range
attraction. This model is appropriate for the description of a class of
colloidal suspensions. The transition line in the density-temperature plane
displays a reentrant behavior, in agreement with Mode Coupling Theory (MCT), a
dynamical approach based on the Mori-Zwanzig formalism. Quantitative
differences are however found, together with the absence of the predicted
glass-glass transition at high density. We also perform a systematic study of
the pure hard sphere fluid in order to ascertain the accuracy of the adopted
method and the convergence of the numerical procedure.Comment: 7 pages, 6 figure
Spanning trees for the geometry and dynamics of compact polymers
Using a mapping of compact polymers on the Manhattan lattice to spanning
trees, we calculate exactly the average number of bends at infinite
temperature. We then find, in a high temperature approximation, the energy of
the system as a function of bending rigidity and polymer elasticity. We
identify the universal mechanism for the relaxation of compact polymers and
then endow the model with physically motivated dynamics in the convenient
framework of the trees. We find aging and domain coarsening after quenches in
temperature. We explain the slow dynamics in terms of the geometrical
interconnections between the energy and the dynamics.Comment: 10 pages, 8 figure
On the Brownian gas: a field theory with a Poissonian ground state
As a first step towards a successful field theory of Brownian particles in
interaction, we study exactly the non-interacting case, its combinatorics and
its non-linear time-reversal symmetry. Even though the particles do not
interact, the field theory contains an interaction term: the vertex is the
hallmark of the original particle nature of the gas and it enforces the
constraint of a strictly positive density field, as opposed to a Gaussian free
field. We compute exactly all the n-point density correlation functions,
determine non-perturbatively the Poissonian nature of the ground state and
emphasize the futility of any coarse-graining assumption for the derivation of
the field theory. We finally verify explicitly, on the n-point functions, the
fluctuation-dissipation theorem implied by the time-reversal symmetry of the
action.Comment: 31 page
Field diffeomorphisms and the algebraic structure of perturbative expansions
We consider field diffeomorphisms in the context of real scalar field
theories. Starting from free field theories we apply non-linear field
diffeomorphisms to the fields and study the perturbative expansion for the
transformed theories. We find that tree level amplitudes for the transformed
fields must satisfy BCFW type recursion relations for the S-matrix to remain
trivial. For the massless field theory these relations continue to hold in loop
computations. In the massive field theory the situation is more subtle. A
necessary condition for the Feynman rules to respect the maximal ideal and
co-ideal defined by the core Hopf algebra of the transformed theory is that
upon renormalization all massive tadpole integrals (defined as all integrals
independent of the kinematics of external momenta) are mapped to zero.Comment: 8 pages, 2 figure
Detecting the Collapse of Cooperation in Evolving Networks
The sustainability of biological, social, economic and ecological communities is often determined by the outcome of social conflicts between cooperative and selfish individuals (cheaters). Cheaters avoid the cost of contributing to the community and can occasionally spread in the population leading to the complete collapse of cooperation. Although such collapse often unfolds unexpectedly, it is unclear whether one can detect the risk of cheaterâs invasions and loss of cooperation in an evolving community. Here, we combine dynamical networks and evolutionary game theory to study the abrupt loss of cooperation with tools for studying critical transitions. We estimate the risk of cooperation collapse following the introduction of a single cheater under gradually changing conditions. We observe an increase in the average time it takes for cheaters to be eliminated from the community as the risk of collapse increases. We argue that such slow system response resembles slowing down in recovery rates prior to a critical transition. In addition, we show how changes in community structure reflect the risk of cooperation collapse. We find that these changes strongly depend on the mechanism that governs how cheaters evolve in the community. Our results highlight novel directions for detecting abrupt transitions in evolving networks
The strength of genetic interactions scales weakly with mutational effects
Background:
Genetic interactions pervade every aspect of biology, from evolutionary theory, where they determine the accessibility of evolutionary paths, to medicine, where they can contribute to complex genetic diseases. Until very recently, studies on epistatic interactions have been based on a handful of mutations, providing at best anecdotal evidence about the frequency and the typical strength of genetic interactions. In this study, we analyze a publicly available dataset that contains the growth rates of over five million double knockout mutants of the yeast Saccharomyces cerevisiae.
Results:
We discuss a geometric definition of epistasis that reveals a simple and surprisingly weak scaling law for the characteristic strength of genetic interactions as a function of the effects of the mutations being combined. We then utilized this scaling to quantify the roughness of naturally occurring fitness landscapes. Finally, we show how the observed roughness differs from what is predicted by Fisher's geometric model of epistasis, and discuss the consequences for evolutionary dynamics.
Conclusions:
Although epistatic interactions between specific genes remain largely unpredictable, the statistical properties of an ensemble of interactions can display conspicuous regularities and be described by simple mathematical laws. By exploiting the amount of data produced by modern high-throughput techniques, it is now possible to thoroughly test the predictions of theoretical models of genetic interactions and to build informed computational models of evolution on realistic fitness landscapes.National Institutes of Health (U.S.) (Pathways to Independence Award)National Science Foundation (U.S.) (CAREER Award)Pew Charitable Trusts (Biomedical Scholars Program)Alfred P. Sloan Foundation (Research Fellowship