Modularity enhances the rate of evolution in a rugged fitness landscape

Abstract

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.

The thermodynamics of protein aggregation reactions may underpin the enhanced metabolic efficiency associated with heterosis, some balancing selection, and the evolution of ploidy levels

“…In fact, proteins that exist separately in some species may be found as parts of multi-domain proteins in other species, a phenomena called "domain accretion" (Koonin et al 2002;Basu et al 2009). Multidomain proteins are important because their modularity makes them capable of adapting to rapidly changing environments (Sun and Deem 2007;He et al 2009;Lorenz et al 2011;Park et al 2015). As expected, multi-domain proteins tend to be larger than singledomain proteins (Tan et al 2005;Tordai et al 2005).…”

Quasispecies theory for evolution of modularity

“…This behavior has been observed in a model of systems evolving in a changing environment, when horizontal gene transfer is included [27]. We have recently proved this canonical behavior for a Moran model of population evolution in a glassy, modular fitness landscape [55]. Glassy evolutionary dynamics has been noted a number of times [56, 57].…”

“…(8) is modified to be $p_{\mathrm{E}}^{\beta /false(\beta +1false)}$ on the left hand side, with $\alpha =-{false[gfalse(\infty false)/\beta false]}^{\beta /false(\beta +1false)}{da}_m^{1/false(\beta +1false)}/dm{\mid }_{m=0}$. Finally, for a logarithmic decay [55] $false\langle g_{m}false\rangle false(tfalse)=gfalse(\infty false)-a_m{ln}^{-2/\nu }false(t/t_m^{0}false)$, we find the fitness to be non-analytic in p / T , since $false(p/Tfalse)t_m^{\ast }gfalse(\infty false)=false(2/\nu false)a_m{ln}^{-2/\nu -1}false(t_m^{\ast }/t_m^{0}false)$. This equation can be solved in terms of powers of the product logarithm, or Lambert W 0 function.…”

Modular knowledge systems accelerate human migration in asymmetric random environments

“…One can estimate how many generations it takes to migrate to the next environment. The rate of change of fitness at short time roughly follows [25]:…”

“…Modularity, coupled with knowledge transfer, accelerates the evolution of a population in a new environment [25]. We now check how modularity and knowledge transfer influence the velocity of migration.…”