49 research outputs found
The statistics of fixation times for systems with recruitment
We investigate the statistics of the time taken for a system driven by
recruitment to reach fixation. Our model describes a series of experiments
where a population is confronted with two identical options, resulting in the
system fixating on one of the options. For a specific population size, we show
that the time distribution behaves like an inverse Gaussian with an exponential
decay. Varying the population size reveals that the timescale of the decay
depends on the population size and allows the critical population number, below
which fixation occurs, to be estimated from experimental data
Noise-Induced Bistable States and Their Mean Switching Time in Foraging Colonies
We investigate a type of bistability where noise not only causes transitions
between stable states, but also constructs the states themselves. We focus on
the experimentally well-studied system of ants choosing between two food
sources to illustrate the essential points, but the ideas are more general. The
mean time for switching between the two bistable states of the system is
calculated. This suggests a procedure for estimating, in a real system, the
critical population size above which bistability ceases to occur.Comment: 8 pages, 5 figures. See also a "light-hearted" introduction:
http://www.youtube.com/watch?v=m37Fe4qjeZ
Stochastic waves in a Brusselator model with nonlocal interaction
We show that intrinsic noise can induce spatio-temporal phenomena such as
Turing patterns and travelling waves in a Brusselator model with nonlocal
interaction terms. In order to predict and to characterize these quasi-waves we
analyze the nonlocal model using a system-size expansion. The resulting theory
is used to calculate the power spectra of the quasi-waves analytically, and the
outcome is tested successfully against simulations. We discuss the possibility
that nonlocal models in other areas, such as epidemic spread or social
dynamics, may contain similar stochastically-induced patterns.Comment: 13 pages, 6 figure
Noise-induced symmetry breaking far from equilibrium and the emergence of biological homochirality
The origin of homochirality, the observed single-handedness of biological amino acids and sugars, has long been attributed to autocatalysis, a frequently assumed precursor for early life self-replication. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross-inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here we present a theory for a stochastic individual-level model of autocatalytic prebiotic self-replicators that are maintained out of thermal equilibrium. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states. Moreover, we show that this noise-induced bistability is robust with respect to diffusion of molecules of opposite chirality, and systems of diffusively coupled autocatalytic chemical reactions synchronize their final homochiral states when the self-replication is the dominant production mechanism for the chiral molecules. We conclude that nonequilibrium autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.United States. National Aeronautics and Space Administration (NNA13AA91A
Noise-induced metastability in biochemical networks
Intra-cellular biochemical reactions exhibit a rich dynamical phenomenology
which cannot be explained within the framework of mean-field rate equations and
additive noise. Here, we show that the presence of metastable states and
radically different timescales are general features of a broad class of
autocatalyic reaction networks, and moreover, that this fact may be exploited
to gain analytical results. The latter point is demonstrated by a treatment of
the paradigmatic Togashi-Kaneko reaction, which has resisted theoretical
analysis for the last decade.Comment: 4 pages, 3 figure