365 research outputs found
Information-geometric optimization with natural selection
Evolutionary algorithms, inspired by natural evolution, aim to optimize
difficult objective functions without computing derivatives. Here we detail the
relationship between population genetics and evolutionary optimization and
formulate a new evolutionary algorithm. Optimization of a continuous objective
function is analogous to searching for high fitness phenotypes on a fitness
landscape. We summarize how natural selection moves a population along the
non-euclidean gradient that is induced by the population on the fitness
landscape (the natural gradient). Under normal approximations common in
quantitative genetics, we show how selection is related to Newton's method in
optimization. We find that intermediate selection is most informative of the
fitness landscape. We describe the generation of new phenotypes and introduce
an operator that recombines the whole population to generate variants that
preserve normal statistics. Finally, we introduce a proof-of-principle
algorithm that combines natural selection, our recombination operator, and an
adaptive method to increase selection. Our algorithm is similar to covariance
matrix adaptation and natural evolutionary strategies in optimization, and has
similar performance. The algorithm is extremely simple in implementation with
no matrix inversion or factorization, does not require storing a covariance
matrix, and may form the basis of more general model-based optimization
algorithms with natural gradient updates.Comment: changed titl
Speeding up evolutionary search by small fitness fluctuations
We consider a fixed size population that undergoes an evolutionary adaptation
in the weak mutuation rate limit, which we model as a biased Langevin process
in the genotype space. We show analytically and numerically that, if the
fitness landscape has a small highly epistatic (rough) and time-varying
component, then the population genotype exhibits a high effective diffusion in
the genotype space and is able to escape local fitness minima with a large
probability. We argue that our principal finding that even very small
time-dependent fluctuations of fitness can substantially speed up evolution is
valid for a wide class of models.Comment: 12 pages, 5 figure
Fierce selection and interference in B-cell repertoire response to chronic HIV-1
During chronic infection, HIV-1 engages in a rapid coevolutionary arms race
with the host's adaptive immune system. While it is clear that HIV exerts
strong selection on the adaptive immune system, the characteristics of the
somatic evolution that shape the immune response are still unknown. Traditional
population genetics methods fail to distinguish chronic immune response from
healthy repertoire evolution. Here, we infer the evolutionary modes of B-cell
repertoires and identify complex dynamics with a constant production of better
B-cell receptor mutants that compete, maintaining large clonal diversity and
potentially slowing down adaptation. A substantial fraction of mutations that
rise to high frequencies in pathogen engaging CDRs of B-cell receptors (BCRs)
are beneficial, in contrast to many such changes in structurally relevant
frameworks that are deleterious and circulate by hitchhiking. We identify a
pattern where BCRs in patients who experience larger viral expansions undergo
stronger selection with a rapid turnover of beneficial mutations due to clonal
interference in their CDR3 regions. Using population genetics modeling, we show
that the extinction of these beneficial mutations can be attributed to the rise
of competing beneficial alleles and clonal interference. The picture is of a
dynamic repertoire, where better clones may be outcompeted by new mutants
before they fix
Totally Asymmetric Exclusion Process with Hierarchical Long-Range Connections
A non-equilibrium particle transport model, the totally asymmetric exclusion
process, is studied on a one-dimensional lattice with a hierarchy of fixed
long-range connections. This model breaks the particle-hole symmetry observed
on an ordinary one-dimensional lattice and results in a surprisingly simple
phase diagram, without a maximum-current phase. Numerical simulations of the
model with open boundary conditions reveal a number of dynamic features and
suggest possible applications.Comment: 10 pages, revtex4, reorganized, with some new analytical results. For
related articles, see http://www.physics.emory.edu/faculty/boettcher
Learning the shape of protein micro-environments with a holographic convolutional neural network
Proteins play a central role in biology from immune recognition to brain
activity. While major advances in machine learning have improved our ability to
predict protein structure from sequence, determining protein function from
structure remains a major challenge. Here, we introduce Holographic
Convolutional Neural Network (H-CNN) for proteins, which is a physically
motivated machine learning approach to model amino acid preferences in protein
structures. H-CNN reflects physical interactions in a protein structure and
recapitulates the functional information stored in evolutionary data. H-CNN
accurately predicts the impact of mutations on protein function, including
stability and binding of protein complexes. Our interpretable computational
model for protein structure-function maps could guide design of novel proteins
with desired function
Clonal interference and Muller's ratchet in spatial habitats
Competition between independently arising beneficial mutations is enhanced in
spatial populations due to the linear rather than exponential growth of clones.
Recent theoretical studies have pointed out that the resulting fitness dynamics
is analogous to a surface growth process, where new layers nucleate and spread
stochastically, leading to the build up of scale-invariant roughness. This
scenario differs qualitatively from the standard view of adaptation in that the
speed of adaptation becomes independent of population size while the fitness
variance does not. Here we exploit recent progress in the understanding of
surface growth processes to obtain precise predictions for the universal,
non-Gaussian shape of the fitness distribution for one-dimensional habitats,
which are verified by simulations. When the mutations are deleterious rather
than beneficial the problem becomes a spatial version of Muller's ratchet. In
contrast to the case of well-mixed populations, the rate of fitness decline
remains finite even in the limit of an infinite habitat, provided the ratio
between the deleterious mutation rate and the square of the
(negative) selection coefficient is sufficiently large. Using again an analogy
to surface growth models we show that the transition between the stationary and
the moving state of the ratchet is governed by directed percolation
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