134 research outputs found
The arrival of the frequent: how bias in genotype-phenotype maps can steer populations to local optima
Genotype-phenotype (GP) maps specify how the random mutations that change
genotypes generate variation by altering phenotypes, which, in turn, can
trigger selection. Many GP maps share the following general properties: 1) The
number of genotypes is much larger than the number of selectable
phenotypes; 2) Neutral exploration changes the variation that is accessible to
the population; 3) The distribution of phenotype frequencies ,
with the number of genotypes mapping onto phenotype , is highly
biased: the majority of genotypes map to only a small minority of the
phenotypes. Here we explore how these properties affect the evolutionary
dynamics of haploid Wright-Fisher models that are coupled to a simplified and
general random GP map or to a more complex RNA sequence to secondary structure
map. For both maps the probability of a mutation leading to a phenotype
scales to first order as , although for the RNA map there are further
correlations as well. By using mean-field theory, supported by computer
simulations, we show that the discovery time of a phenotype similarly
scales to first order as for a wide range of population sizes and
mutation rates in both the monomorphic and polymorphic regimes. These
differences in the rate at which variation arises can vary over many orders of
magnitude. Phenotypic variation with a larger is therefore be much more
likely to arise than variation with a small . We show, using the RNA
model, that frequent phenotypes (with larger ) can fix in a population
even when alternative, but less frequent, phenotypes with much higher fitness
are potentially accessible. In other words, if the fittest never `arrive' on
the timescales of evolutionary change, then they can't fix. We call this highly
non-ergodic effect the `arrival of the frequent'.Comment: full paper plus supplementary material
Effect of bending rigidity on the knotting of a polymer under tension
A coarse-grained computational model is used to investigate how the bending
rigidity of a polymer under tension affects the formation of a trefoil knot.
Thermodynamic integration techniques are applied to demonstrate that the
free-energy cost of forming a knot has a minimum at non-zero bending rigidity.
The position of the minimum exhibits a power-law dependence on the applied
tension. For knotted polymers with non-uniform bending rigidity, the knots
preferentially localize in the region with a bending rigidity that minimizes
the free-energy.Comment: 15 pages, 6 figures. Corrected problem with references to equation
Correlation of Automorphism Group Size and Topological Properties with Program-size Complexity Evaluations of Graphs and Complex Networks
We show that numerical approximations of Kolmogorov complexity (K) applied to
graph adjacency matrices capture some group-theoretic and topological
properties of graphs and empirical networks ranging from metabolic to social
networks. That K and the size of the group of automorphisms of a graph are
correlated opens up interesting connections to problems in computational
geometry, and thus connects several measures and concepts from complexity
science. We show that approximations of K characterise synthetic and natural
networks by their generating mechanisms, assigning lower algorithmic randomness
to complex network models (Watts-Strogatz and Barabasi-Albert networks) and
high Kolmogorov complexity to (random) Erdos-Renyi graphs. We derive these
results via two different Kolmogorov complexity approximation methods applied
to the adjacency matrices of the graphs and networks. The methods used are the
traditional lossless compression approach to Kolmogorov complexity, and a
normalised version of a Block Decomposition Method (BDM) measure, based on
algorithmic probability theory.Comment: 15 2-column pages, 20 figures. Forthcoming in Physica A: Statistical
Mechanics and its Application
Robustness and Stability of Spin Glass Ground States to Perturbed Interactions
Across many scientific and engineering disciplines, it is important to
consider how much the output of a given system changes due to perturbations of
the input. Here, we study the robustness of the ground states of spin
glasses on random graphs to flips of the interactions. For a sparse graph, a
dense graph, and the fully connected Sherrington-Kirkpatrick model, we find
relatively large sets of interactions that generate the same ground state.
These sets can themselves be analyzed as sub-graphs of the interaction domain,
and we compute many of their topological properties. In particular, we find
that the robustness of these sub-graphs is much higher than one would expect
from a random model. Most notably, it scales in the same logarithmic way with
the size of the sub-graph as has been found in genotype-phenotype maps for RNA
secondary structure folding, protein quaternary structure, gene regulatory
networks, as well as for models for genetic programming. The similarity between
these disparate systems suggests that this scaling may have a more universal
origin
Modelling the Self-Assembly of Virus Capsids
We use computer simulations to study a model, first proposed by Wales [1],
for the reversible and monodisperse self-assembly of simple icosahedral virus
capsid structures. The success and efficiency of assembly as a function of
thermodynamic and geometric factors can be qualitatively related to the
potential energy landscape structure of the assembling system. Even though the
model is strongly coarse-grained, it exhibits a number of features also
observed in experiments, such as sigmoidal assembly dynamics, hysteresis in
capsid formation and numerous kinetic traps. We also investigate the effect of
macromolecular crowding on the assembly dynamics. Crowding agents generally
reduce capsid yields at optimal conditions for non-crowded assembly, but may
increase yields for parameter regimes away from the optimum. Finally, we
generalize the model to a larger triangulation number T = 3, and observe more
complex assembly dynamics than that seen for the original T = 1 model.Comment: 16 pages, 11 figure
Force-induced rupture of a DNA duplex
The rupture of double-stranded DNA under stress is a key process in
biophysics and nanotechnology. In this article we consider the shear-induced
rupture of short DNA duplexes, a system that has been given new importance by
recently designed force sensors and nanotechnological devices. We argue that
rupture must be understood as an activated process, where the duplex state is
metastable and the strands will separate in a finite time that depends on the
duplex length and the force applied. Thus, the critical shearing force required
to rupture a duplex within a given experiment depends strongly on the time
scale of observation. We use simple models of DNA to demonstrate that this
approach naturally captures the experimentally observed dependence of the
critical force on duplex length for a given observation time. In particular,
the critical force is zero for the shortest duplexes, before rising sharply and
then plateauing in the long length limit. The prevailing approach, based on
identifying when the presence of each additional base pair within the duplex is
thermodynamically unfavorable rather than allowing for metastability, does not
predict a time-scale-dependent critical force and does not naturally
incorporate a critical force of zero for the shortest duplexes. Additionally,
motivated by a recently proposed force sensor, we investigate application of
stress to a duplex in a mixed mode that interpolates between shearing and
unzipping. As with pure shearing, the critical force depends on the time scale
of observation; at a fixed time scale and duplex length, the critical force
exhibits a sigmoidal dependence on the fraction of the duplex that is subject
to shearing.Comment: 10 pages, 6 figure
Zigzag transitions and nonequilibrium pattern formation in colloidal chains
Paramagnetic colloidal particles that are optically trapped in a linear array
can form a zigzag pattern when an external magnetic field induces repulsive
interparticle interactions. When the traps are abruptly turned off, the
particles form a nonequilibrium expanding pattern with a zigzag symmetry, even
when the strength of the magnetic interaction is weaker than that required to
break the linear symmetry of the equilibrium state. We show that the transition
to the equilibrium zigzag state is always potentially possible for purely
harmonic traps. For anharmonic traps that have a finite height, the equilibrium
zigzag state becomes unstable above a critical anharmonicity. A normal mode
analysis of the equilibrium line configuration demonstrates that increasing the
magnetic field leads to a hardening and softening of the spring constants in
the longitudinal and transverse directions, respectively. The mode that first
becomes unstable is the mode with the zigzag symmetry, which explains the
symmetry of nonequilibrium patterns. Our analytically tractable models help to
give further insight into the way that the interplay of such factors as the
length of the chain, hydrodynamic interactions, thermal fluctuations affect the
formation and evolution of the experimentally observed nonequilibrium patterns.Comment: 16 pages, 8 figures; to appear in the Journal of Chemical Physic
Evolutionary Dynamics in a Simple Model of Self-Assembly
We investigate the evolutionary dynamics of an idealised model for the robust
self-assembly of two-dimensional structures called polyominoes. The model
includes rules that encode interactions between sets of square tiles that drive
the self-assembly process. The relationship between the model's rule set and
its resulting self-assembled structure can be viewed as a genotype-phenotype
map and incorporated into a genetic algorithm. The rule sets evolve under
selection for specified target structures. The corresponding, complex fitness
landscape generates rich evolutionary dynamics as a function of parameters such
as the population size, search space size, mutation rate, and method of
recombination. Furthermore, these systems are simple enough that in some cases
the associated model genome space can be completely characterised, shedding
light on how the evolutionary dynamics depends on the detailed structure of the
fitness landscape. Finally, we apply the model to study the emergence of the
preference for dihedral over cyclic symmetry observed for homomeric protein
tetramers
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