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

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

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

Scalable detection of technically challenging variants through modified next‐generation sequencing

Abstract Background Some clinically important genetic variants are not easily evaluated with next‐generation sequencing (NGS) methods due to technical challenges arising from high‐ similarity copies (e.g., PMS2, SMN1/SMN2, GBA1, HBA1/HBA2, CYP21A2), repetitive short sequences (e.g., ARX polyalanine repeats, FMR1 AGG interruptions in CGG repeats, CFTR poly‐T/TG repeats), and other complexities (e.g., MSH2 Boland inversions). Methods We customized our NGS processes to detect the technically challenging variants mentioned above with adaptations including target enrichment and bioinformatic masking of similar sequences. Adaptations were validated with samples of known genotypes. Results Our adaptations provided high‐sensitivity and high‐specificity detection for most of the variants and provided a high‐sensitivity primary assay to be followed with orthogonal disambiguation for the others. The sensitivity of the NGS adaptations was 100% for all of the technically challenging variants. Specificity was 100% for those in PMS2, GBA1, SMN1/SMN2, and HBA1/HBA2, and for the MSH2 Boland inversion; 97.8%–100% for CYP21A2 variants; and 85.7% for ARX polyalanine repeats. Conclusions NGS assays can detect technically challenging variants when chemistries and bioinformatics are jointly refined. The adaptations described support a scalable, cost‐effective path to identifying all clinically relevant variants within a single sample