Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9811267

Neutral evolution of model proteins: diffusion in sequence space and overdispersion

Ugo Bastolla·H. Eduardo Roman·Michele Vendruscolo
View original source ↗Read source document ↗Export metadata ↓

Abstract

We simulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves 1) the structure of the ground state, 2) its thermodynamic stability and 3) its kinetic accessibility. All other mutations are considered lethal and are rejected. We adopt a lattice model, amenable to a reliable solution of the protein folding problem. We prove the existence of extended neutral networks in sequence space -- sequences can evolve until their similarity with the starting point is almost the same as for random sequences. Furthermore, we find that the rate of neutral mutations has a broad distribution in sequence space. Due to this fact, the substitution process is overdispersed (the ratio between variance and mean is larger than one). This result is in contrast with the simplest model of neutral evolution, which assumes a Poisson process for substitutions, and in qualitative agreement with biological data.

Explore related subjects

cond-mat.stat-mechcond-mat.softq-bio

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ugo Bastolla, H. Eduardo Roman, Michele Vendruscolo. 1998-11-18. Neutral evolution of model proteins: diffusion in sequence space and overdispersion. https://arxiv.org/abs/cond-mat/9811267

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Feedback percolation on complex networks

Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified framework that dynamically couples the microscopic activation probability to the macroscopic size of the giant component. We show that this simple feedback mechanism produces a rich variety of behaviors both analytically and numerically. Depending on the feedback functions, the system exhibits explosive discontinuous jumps, hybrid transitions, limit-cycle oscillations, and routes to chaos, absent in classical percolation. Our findings establish that macroscopic feedback provides a unifying physical mechanism for phenomena ranging from self-regulating oscillations to systemic infrastructure collapse.

cond-mat.stat-mech↗
arXiv2026

$\mathbb{Z}_2$ gauge and exact solution of the $\pm J$ Edwards-Anderson model in a transverse field

Using the Majorana representation of spin-1/2 operators, we study the $\pm J$ Edwards--Anderson model in a transverse field at $T=0$. We show that, in this representation, the quantity describing the coupling between neighboring spins commutes with the Hamiltonian and, unlike in the Kitaev model, is not subject to any Gauss law. The resulting $\mathbb{Z}_2$ gauge freedom allows the disorder in the signs of the exchange integrals to be eliminated by an exact gauge transformation, so that the spectrum of the system coincides with that of the model with uniform couplings. The resulting theory is quadratic in the Majorana fields. Computing the local Green's functions, we find that the Edwards--Anderson order parameter vanishes for $Δ>J\sqrt{Z}$ and equals $1/4$ for $Δ<J\sqrt{Z}$, which signals a second-order transition from a paramagnetic phase to a spin-glass ground state that is degenerate over spin configurations and replica symmetric at $T=0$.

cond-mat.stat-mech↗
arXiv2026

Thermalization of coarse-grained variables in the Toda lattice: a numerical study

We present here a numerical study of the Toda lattice Hamiltonian dynamics showing how, despite model integrability, it is possible to find many macroscopic observables which display standard equilibrium behavior. In particular, we study numerically the energy time correlation of certain coarse-grained variables, showing that it decays with either exponential or stretched exponential behaviour, thus indicating good thermalization properties. The spirit of our observation is complementary to that of standard Fermi-Pasta-Ulam-Tsingou-like numerical experiments, in which the breaking of integrability is regarded as the key ingredient for relaxation to thermal equilibrium. The present communication corroborates, on the contrary, the view that integrability is not an obstacle to thermalization, provided that a sufficiently weak definition of the latter is accepted. In the Toda lattice we have introduced several kinds of coarse-grained variables, constructed with the purpose to maintain a thermodynamic relevance also for large system sizes, which all show good thermalization properties.

cond-mat.stat-mech↗