arXiv subjects

Anton S. Zadorin

Publications and source records attributed to Anton S. Zadorin.

6 recordsLinked to original sources

arXiv2022

A fast iterative algorithm for near-diagonal eigenvalue problems

We introduce a novel eigenvalue algorithm for near-diagonal matrices inspired by Rayleigh-Schrödinger perturbation theory and termed Iterative Perturbative Theory (IPT). Contrary to standard eigenvalue algorithms, which are either 'direct' (to compute all eigenpairs) or 'iterative' (to compute just a few), IPT computes any number of eigenpairs with the same basic iterative procedure. Thanks to this perfect parallelism, IPT proves more efficient than classical methods (LAPACK or CUSOLVER for the full-spectrum problem, preconditioned Davidson solvers for extremal eigenvalues). We give sufficient conditions for linear convergence and demonstrate performance on dense and sparse test matrices, including one from quantum chemistry.

math.NA↗

arXiv2022

Exact travelling solution for a reaction-diffusion system with a piecewise constant production supported by a codimension-1 subspace

A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk are important for modelling various biological processes. These include problems of invasive species propagation along boundaries of ecozones, problems of gene spread in such situations, morphogenesis in cavities, intracellular reaction etc. Piecewise linear approximations of reaction terms in reaction-diffusion systems often result in exact solutions of propagation front problems. This article presents an exact travelling solution for a reaction-diffusion system with a piecewise constant production restricted to a codimension-1 subset. The solution is monotone, propagates with the unique constant velocity, and connects the trivial solution to a nontrivial nonhomogeneous stationary solution of the problem. The properties of the solution closely parallel the properties of monotone travelling solutions in classical bistable reaction-diffusion systems.

math.DS↗

arXiv2019

Natural selection in compartmentalized environment with reshuffling

The emerging field of high-throughput compartmentalized in vitro evolution is a promising new approach to protein engineering. In these experiments, libraries of mutant genotypes are randomly distributed and expressed in microscopic compartments - droplets of an emulsion. The selection of desirable variants is performed according to the phenotype of each compartment. The random partitioning leads to a fraction of compartments receiving more than one genotype making the whole process a lab implementation of the group selection. From a practical point of view (where efficient selection is typically sought), it is important to know the impact of the increase in the mean occupancy of compartments on the selection efficiency. We carried out a theoretical investigation of this problem in the context of selection dynamics for an infinite non-mutating subdivided population that randomly colonizes an infinite number of patches (compartments) at each reproduction cycle. We derive here an update equation for any distribution of phenotypes and any value of the mean occupancy. Using this result, we demonstrate that, for the linear additive fitness, the best genotype is still selected regardless of the mean occupancy. Furthermore, the selection process is remarkably resilient to the presence of multiple genotypes per compartments, and slows down approximately inversely proportional to the mean occupancy at high values. We extend out results to more general expressions that cover nonadditive and non-linear fitnesses, as well non-Poissonian distribution among compartments. Our conclusions may also apply to natural genetic compartmentalized replicators, such as viruses or early trans-acting RNA replicators.

q-bio.PE↗

arXiv2019

Selection strategies for randomly partitioned genetic replicators

The amplification cycle of many replicators (natural or artificial) involves the usage of a host compartment, inside of which the replicator express phenotypic compounds necessary to carry out its genetic replication. For example, viruses infect cells, where they express their own proteins and replicate. In this process, the host cell boundary limits the diffusion of the viral protein products, thereby ensuring that phenotypic compounds, such as proteins, promote the replication of the genes that encoded them. This role of maintaining spatial co-localization, also called genotype-phenotype linkage, is a critical function of compartments in natural selection. In most cases however, individual replicating elements do not distribute systematically among the hosts, but are randomly partitioned. Depending on the replicator-to-host ratio, more than one variant may thus occupy some compartments, blurring the genotype-phenotype linkage and affecting the effectiveness of natural selection. We derive selection equations for a variety of such random multiple occupancy situations, in particular considering the effect of replicator population polymorphism and internal replication dynamics. We conclude that the deleterious effect of random multiple occupancy on selection is relatively benign, and may even completely vanish is some specific cases. In addition, given that higher mean occupancy allows larger populations to be channeled through the selection process, and thus provide a better exploration of phenotypic diversity, we show that it may represent a valid strategy in both natural and technological cases.

q-bio.PE↗

arXiv2019

Allostery and conformational changes upon binding as generic features of proteins: a high-dimension geometrical approach

A growing number of experimental evidence shows that it is general for a ligand binding protein to have a potential for allosteric regulation and for further evolution. In addition, such proteins generically change their conformation upon binding. O. Rivoire has recently proposed an evolutionary scenario that explains these properties as a generic byproduct of selection for exquisite discrimination between very similar ligands. The initial claim was supported by two classes of basic examples: continuous protein models with small numbers of degrees of freedom, on which the development of a conformational switch was established, and a 2-dimensional spin glass model supporting the rest of the statement. This work aimed to clarify the implication of the exquisite discrimination for smooth models with large number of degrees of freedom, the situation closer to real biological systems. With the help of differential geometry, jet-space analysis, and transversality theorems, it is shown that the claim holds true for any generic flexible system that can be described in terms of smooth manifolds. The result suggests that, indeed, evolutionary solutions to the exquisite discrimination problem, if exist, are located near a codimension-1 subspace of the appropriate genotypical space. This constraint, in turn, gives rise to a potential for the allosteric regulation of the discrimination via generic conformational changes upon binding.

q-bio.BM↗

arXiv2014

Programmable reaction-diffusion fronts

Morphogenesis is central to biology but remains largely unexplored in chemistry. Reaction-diffusion (RD) mechanisms are, however, essential to understand how shape emerges in the living world. While numerical methods confirm the incredible potential of RD mechanisms to generate patterns, their experimental implementation, despite great efforts, has yet to surpass the paradigm of stationary Turing patterns achieved 25 years ago. The principal reason for our difficulty to synthesize arbitrary concentration patterns from scratch is the lack of fully programmable reaction-diffusion systems. To solve this problem we introduce here a DNA-based system where kinetics and diffusion can be individually tuned. We demonstrate the capability to precisely control reaction-diffusion properties with an autocatalytic network that propagates in a one-dimensional reactor with uniform velocity, typically 100 μm min-1. The diffusion coefficient of the propagating species can be reduced up to a factor 2.7 using a species-specific strategy relying on self-assembled hydrodynamic drags. Our approach is modular as we illustrate by designing three alternative front generating systems, two of which can pass through each other with little interaction. Importantly, the strategies to control kinetics and diffusion are orthogonal to each other resulting in simple programming rules. Our results can be quantitatively predicted from first-principle RD equations and are in excellent agreement with a generalized Fisher- Kolmogorov-Petrovskii-Piscunov analytical model. Together, these advances open the way for the rational engineering of far-from-equilibrium arbitrary patterns and could lead to the synthesis of self-organizing materials.

nlin.PS↗