arXiv subjects

Jeong-Man Park

Publications and source records attributed to Jeong-Man Park.

At least 19 recordsLinked to original sources

arXiv2015

Modularity Enhances the Rate of Evolution in a Rugged Fitness Landscape

Biological systems are modular, and this modularity affects the evolution of biological systems over time and in different environments. We here develop a theory for the dynamics of evolution in a rugged, modular fitness landscape. We show analytically how horizontal gene transfer couples to the modularity in the system and leads to more rapid rates of evolution at short times. The model, in general, analytically demonstrates a selective pressure for the prevalence of modularity in biology. We use this model to show how the evolution of the influenza virus is affected by the modularity of the proteins that are recognized by the human immune system. Approximately 25\% of the observed rate of fitness increase of the virus could be ascribed to a modular viral landscape.

q-bio.PE↗

arXiv2015

Quasispecies Theory for Evolution of Modularity

Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here develop a quasispecies theory for the dynamics of modularity in populations of these systems. We show how the steady-state fitness in a randomly changing environment can be computed. We derive a fluctuation dissipation relation for the rate of change of modularity and use it to derive a relationship between rate of environmental changes and rate of growth of modularity. We also find a principle of least action for the evolved modularity at steady state. Finally, we compare our predictions to simulations of protein evolution and find them to be consistent.

q-bio.PE↗

arXiv2014

On the Universality of the Energy Response Function in the Long-Range Spin Glass Model with Sparse, Modular Couplings

We consider energy relaxation of the long-range spin glass model with sparse couplings, the so-called dilute Sherrington-Kirkpatrick (SK) model, starting from a random initial state. We consider the effect that modularity of the coupling matrix has on this relaxation dynamics. In the absence of finite size effects, the relaxation dynamics appears independent of modularity. For finite sizes, a more modular system reaches a less favorable energy at long times. For small sizes, a more modular system also has a less favorable energy at short times. For large sizes, modularity appears to lead to slightly more favorable energies at intermediate times. We discuss these results in the context of evolutionary theory, where horizontal gene transfer, absent in the Glauber equilibration dynamics of the SK model studied here, endows modular organisms with larger response functions at short times.

cond-mat.stat-mech↗

arXiv2013

Evolutionary Processes in Finite Populations

We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov, Moran process. We show that to $\mathcal O(1/N)$, the time-averaged fitness is lower for the finite population than it is for the infinite population. We also show that fluctuations in the number of individuals for a given genotype can be proportional to a power of the inverse of the mutation rate. Finally, we show that the probability for the system to take a given path through the fitness landscape can be non-monotonic in system size.

q-bio.PE↗

arXiv2010

Quasispecies theory for finite populations

We present stochastic, finite-population formulations of the Crow-Kimura and Eigen models of quasispecies theory, for fitness functions that depend in an arbitrary way on the number of mutations from the wild type. We include back mutations in our description. We show that the fluctuation of the population numbers about the average values are exceedingly large in these physical models of evolution. We further show that horizontal gene transfer reduces by orders of magnitude the fluctuations in the population numbers and reduces the accumulation of deleterious mutations in the finite population due to Muller's ratchet. Indeed the population sizes needed to converge to the infinite population limit are often larger than those found in nature for smooth fitness functions in the absence of horizontal gene transfer. These analytical results are derived for the steady-state by means of a field-theoretic representation. Numerical results are presented that indicate horizontal gene transfer speeds up the dynamics of evolution as well.

q-bio.PE↗

arXiv2009

Solution of the Crow-Kimura and Eigen models for alphabets of arbitrary size by Schwinger spin coherent states

To represent the evolution of nucleic acid and protein sequence, we express the parallel and Eigen models for molecular evolution in terms of a functional integral representation with an $h$-letter alphabet, lifting the two-state, purine/pyrimidine assumption often made in quasi-species theory. For arbitrary $h$ and a general mutation scheme, we obtain the solution of this model in terms of a maximum principle. Euler's theorem for homogeneous functions is used to derive this `thermodynamic' formulation of evolution. The general result for the parallel model reduces to known results for the purine/pyrimidine $h=2$ alphabet and the nucleic acid $h=4$ alphabet for the Kimura 3 ST mutation scheme. Examples are presented for the $h=4$ and $h=20$ cases. We derive the maximum principle for the Eigen model for general $h$. The general result for the Eigen model reduces to a known result for $h=2$. Examples are presented for the nucleic acid $h=4$ and the amino acid $h=20$ alphabet. An error catastrophe phase transition occurs in these models, and the order of the phase transition changes from second to first order for smooth fitness functions when the alphabet size is increased beyond two letters to the generic case. As examples, we analyze the general analytic solution for sharp peak, linear, quadratic, and quartic fitness functions.

q-bio.PE↗

arXiv2008

Quasispecies Theory for Horizontal Gene Transfer and Recombination

We introduce a generalization of the parallel, or Crow-Kimura, and Eigen models of molecular evolution to represent the exchange of genetic information between individuals in a population. We study the effect of different schemes of genetic recombination on the steady-state mean fitness and distribution of individuals in the population, through an analytic field theoretic mapping. We investigate both horizontal gene transfer from a population and recombination between pairs of individuals. Somewhat surprisingly, these nonlinear generalizations of quasi-species theory to modern biology are analytically solvable. For two-parent recombination, we find two selected phases, one of which is spectrally rigid. We present exact analytical formulas for the equilibrium mean fitness of the population, in terms of a maximum principle, which are generally applicable to any permutation invariant replication rate function. For smooth fitness landscapes, we show that when positive epistatic interactions are present, recombination or horizontal gene transfer introduces a mild load against selection. Conversely, if the fitness landscape exhibits negative epistasis, horizontal gene transfer or recombination introduce an advantage by enhancing selection towards the fittest genotypes. These results prove that the mutational deterministic hypothesis holds for quasi-species models. For the discontinuous single sharp peak fitness landscape, we show that horizontal gene transfer has no effect on the fitness, while recombination decreases the fitness, for both the parallel and the Eigen models. We present numerical and analytical results as well as phase diagrams for the different cases.

q-bio.PE↗

arXiv2006

Phase Diagrams of Quasispecies Theory with Recombination and Horizontal Gene Transfer

We consider how transfer of genetic information between individuals influences the phase diagram and mean fitness of both the Eigen and the parallel, or Crow-Kimura, models of evolution. In the absence of genetic transfer, these physical models of evolution consider the replication and point mutation of the genomes of independent individuals in a large population. A phase transition occurs, such that below a critical mutation rate an identifiable quasispecies forms. We generalize these models of quasispecies evolution to include horizontal gene transfer. We show how transfer of genetic information changes the phase diagram and mean fitness and introduces metastability in quasispecies theory, via an analytic field theoretic mapping.

q-bio.PE↗

arXiv2006

Schwinger Boson Formulation and Solution of the Crow-Kimura and Eigen Models of Quasispecies Theory

We express the Crow-Kimura and Eigen models of quasispecies theory in a functional integral representation. We formulate the spin coherent state functional integrals using the Schwinger Boson method. In this formulation, we are able to deduce the long-time behavior of these models for arbitrary replication and degradation functions. We discuss the phase transitions that occur in these models as a function of mutation rate. We derive for these models the leading order corrections to the infinite genome length limit.

q-bio.PE↗

arXiv2005

Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion

The cluster mean-field approximations are performed, up to 13 cluster sizes, to study the critical behavior of the driven pair contact process with diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points are estimated by extrapolating our data to the infinite cluster size limit, which are in good accordance with recent simulation results. Within the cluster mean-field approximation scheme, the PCPD and the DPCPD share the same mean-field critical behavior. The application of the coherent anomaly method, however, shows that the two models develop different coherent anomalies, which lead to different true critical scaling. The values of the critical exponents for the particle density, the pair density, the correlation length, and the relaxation time are fairly well estimated for the DPCPD. These results support and complement our recent simulation results for the DPCPD.

cond-mat.stat-mech↗

arXiv2004

Correlations in the T Cell Response to Altered Peptide Ligands

The vertebrate immune system is a wonder of modern evolution. Occasionally, however, correlations within the immune system lead to inappropriate recruitment of preexisting T cells against novel viral diseases. We present a random energy theory for the correlations in the naive and memory T cell immune responses. The non-linear susceptibility of the random energy model to structural changes captures the correlations in the immune response to mutated antigens. We show how the sequence-level diversity of the T cell repertoire drives the dynamics of the immune response against mutated viral antigens.

q-bio.BM↗

arXiv2003

A Statistical Theory of Isotropic Turbulence Well-Defined within the Context of the $ε$ Expansion

A new statistical field-theory model of isotropic turbulence is introduced. The model renormalizes the effects of turbulent stresses into a velocity-gradient-dependent random force. The model is well-defined within the context of the renormalization group $ε$ expansion, as the effective expansion parameter is $O(ε)$. The Kolmogorov constant and $N$ parameter of turbulence are of order unity, in accord with experimental results. Nontrivial intermittency corrections to the single-time structure functions are calculated as a controlled expansion in $ε$.

cond-mat.stat-mech↗

arXiv2002

Derivation of continuum stochastic equations for discrete growth models

We present a formalism to derive the stochastic differential equations (SDEs) for several solid-on-solid growth models. Our formalism begins with a mapping of the microscopic dynamics of growth models onto the particle systems with reactions and diffusion. We then write the master equations for these corresponding particle systems and find the SDEs for the particle densities. Finally, by connecting the particle densities with the growth heights, we derive the SDEs for the height variables. Applying this formalism to discrete growth models, we find the Edwards-Wilkinson equation for the symmetric body-centered solid-on-solid (BCSOS) model, the Kardar-Parisi-Zhang equation for the asymmetric BCSOS model and the generalized restricted solid-on-solid (RSOS) model, and the Villain--Lai--Das Sarma equation for the conserved RSOS model. In addition to the consistent forms of equations for growth models, we also obtain the coefficients associated with the SDEs.

cond-mat.stat-mech↗

arXiv2002

Universality class of the restricted solid-on-solid model with hopping

We study the restricted solid-on-solid (RSOS) model with finite hopping distance $l_{0}$, using both analytical and numerical methods. Analytically, we use the hard-core bosonic field theory developed by the authors [Phys. Rev. E {\bf 62}, 7642 (2000)] and derive the Villain-Lai-Das Sarma (VLD) equation for the $l_{0}=\infty$ case which corresponds to the conserved RSOS (CRSOS) model and the Kardar-Parisi-Zhang (KPZ) equation for all finite values of $l_{0}$. Consequently, we find that the CRSOS model belongs to the VLD universality class and the RSOS models with any finite hopping distance belong to the KPZ universality class. There is no phase transition at a certain finite hopping distance contrary to the previous result. We confirm the analytic results using the Monte Carlo simulations for several values of the finite hopping distance.

cond-mat.stat-mech↗

arXiv2001

Dispersion Coefficients by a Field-Theoretic Renormalization of Fluid Mechanics

We consider subtle correlations in the scattering of fluid by randomly placed obstacles, which have been suggested to lead to a diverging dispersion coefficient at long times for high Peclet numbers, in contrast to finite mean-field predictions. We develop a new master equation description of the fluid mechanics that incorporates the physically relevant fluctuations, and we treat those fluctuations by a renormalization group procedure. We find a finite dispersion coefficient at low volume fraction of disorder and high Peclet numbers.

cond-mat.stat-mech↗

arXiv2001

Two-point correlation functions of the diffusion-limited annihilation in one dimension

Two-point density-density correlation functions for the diffusive binary reaction system $A+A\to\emptyset$ are obtained in one dimension via Monte Carlo simulation. The long-time behavior of these correlation functions clearly deviates from that of a recent analytical prediction of Bares and Mobilia [Phys. Rev. Lett. {\bf 83}, 5214 (1999)]. An alternative expression for the asymptotic behavior is conjectured from numerical data.

cond-mat.stat-mech↗

arXiv2000

Path-Integral Formulation of Stochastic Processes for the Exclusive Particle Systems

We present the systematic formalism to derive the path-integral formulation for the hard-core particle systems far from equilibrium. Writing the master equation for a stochastic process of the system in terms of the annihilation and creation operators with the mixed commutation relations, we find the Kramers-Moyal coefficients for the corresponding Fokker-Planck equation (FPE) and the stochastic differential equation (SDE) is derived by connecting these coefficients in the FPE to those in the SDE. Finally, the SDE is mapped onto the field-theory using the path-integral, giving the field-theoretic action which may be analyzed by the renormalization group method. We apply this formalism to the two-species reaction-diffusion system with the drift, finding a universal decay expoent for the long-time behavior of the average concentration of particles in arbitrary dimensions.

cond-mat.stat-mech↗

arXiv2000

Comment on ``Solution of Classical Stochastic One-Dimensional Many-Body Systems''

In a recent Letter, Bares and Mobilia proposed the method to find solutions of the stochastic evolution operator $H=H_0 + {γ\over L} H_1$ with a non-trivial quartic term $H_1$. They claim, ``Because of the conservation of probability, an analog of the Wick theorem applies and all multipoint correlation functions can be computed.'' Using the Wick theorem, they expressed the density correlation functions as solutions of a closed set of integro-differential equations. In this Comment, however, we show that applicability of Wick theorem is restricted to the case $γ= 0$ only.

cond-mat.stat-mech↗