282 research outputs found
Thermodynamics of Error Correction
Information processing at the molecular scale is limited by thermal
fluctuations. This can cause undesired consequences in copying information
since thermal noise can lead to errors that can compromise the functionality of
the copy. For example, a high error rate during DNA duplication can lead to
cell death. Given the importance of accurate copying at the molecular scale, it
is fundamental to understand its thermodynamic features. In this paper, we
derive a universal expression for the copy error as a function of entropy
production and {\cred work dissipated by the system during wrong
incorporations}. Its derivation is based on the second law of thermodynamics,
hence its validity is independent of the details of the molecular machinery, be
it any polymerase or artificial copying device. Using this expression, we find
that information can be copied in three different regimes. In two of them, work
is dissipated to either increase or decrease the error. In the third regime,
the protocol extracts work while correcting errors, reminiscent of a Maxwell
demon. As a case study, we apply our framework to study a copy protocol
assisted by kinetic proofreading, and show that it can operate in any of these
three regimes. We finally show that, for any effective proofreading scheme,
error reduction is limited by the chemical driving of the proofreading
reaction.Comment: 9 pages, 5 figure
Selective advantage of diffusing faster
We study a stochastic spatial model of biological competition in which two
species have the same birth and death rates, but different diffusion constants.
In the absence of this difference, the model can be considered as an
off-lattice version of the Voter model and presents similar coarsening
properties. We show that even a relative difference in diffusivity on the order
of a few percent may lead to a strong bias in the coarsening process favoring
the more agile species. We theoretically quantify this selective advantage and
present analytical formulas for the average growth of the fastest species and
its fixation probability.Comment: 8 pages, 5 figures (Main Text + Supplementary Information). Accepted
versio
Mapping of uncertainty relations between continuous and discrete time
Lower bounds on fluctuations of thermodynamic currents depend on the nature
of time: discrete or continuous. To understand the physical reason, we compare
current fluctuations in discrete-time Markov chains and continuous-time master
equations. We prove that current fluctuations in the master equations are
always more likely, due to random timings of transitions. This comparison leads
to a mapping of the moments of a current between discrete and continuous time.
We exploit this mapping to obtain new uncertainty bounds. Our results reduce
the quests for uncertainty bounds in discrete and continuous time to a single
problem.Comment: 5 pages, 3 figure
Kinetic vs. energetic discrimination in biological copying
We study stochastic copying schemes in which discrimination between a right
and a wrong match is achieved via different kinetic barriers or different
binding energies of the two matches. We demonstrate that, in single-step
reactions, the two discrimination mechanisms are strictly alternative and can
not be mixed to further reduce the error fraction. Close to the lowest error
limit, kinetic discrimination results in a diverging copying velocity and
dissipation per copied bit. On the opposite, energetic discrimination reaches
its lowest error limit in an adiabatic regime where dissipation and velocity
vanish. By analyzing experimentally measured kinetic rates of two DNA
polymerases, T7 and Pol{\gamma}, we argue that one of them operates in the
kinetic and the other in the energetic regime. Finally, we show how the two
mechanisms can be combined in copying schemes implementing error correction
through a proofreading pathwayComment: 18 pages, 10 figures, main text+supplementary information. Accepted
for publication in Phys. Rev. Let
A Stochastic Model for the Species Abundance Problem in an Ecological Community
We propose a model based on coupled multiplicative stochastic processes to
understand the dynamics of competing species in an ecosystem. This process can
be conveniently described by a Fokker-Planck equation. We provide an analytical
expression for the marginalized stationary distribution. Our solution is found
in excellent agreement with numerical simulations and compares rather well with
observational data from tropical forests.Comment: 4 pages, 3 figures, submitted to PR
Error-speed correlations in biopolymer synthesis
Synthesis of biopolymers such as DNA, RNA, and proteins are biophysical
processes aided by enzymes. Performance of these enzymes is usually
characterized in terms of their average error rate and speed. However, because
of thermal fluctuations in these single-molecule processes, both error and
speed are inherently stochastic quantities. In this paper, we study
fluctuations of error and speed in biopolymer synthesis and show that they are
in general correlated. This means that, under equal conditions, polymers that
are synthesized faster due to a fluctuation tend to have either better or worse
errors than the average. The error-correction mechanism implemented by the
enzyme determines which of the two cases holds. For example, discrimination in
the forward reaction rates tends to grant smaller errors to polymers with
faster synthesis. The opposite occurs for discrimination in monomer rejection
rates. Our results provide an experimentally feasible way to identify
error-correction mechanisms by measuring the error-speed correlations.Comment: PDF file consist of the main text (pages 1 to 5) and the
supplementary material (pages 6 to 12). Overall, 7 figures split between main
text and S
Entropy production and coarse-graining in Markov processes
We study the large time fluctuations of entropy production in Markov
processes. In particular, we consider the effect of a coarse-graining procedure
which decimates {\em fast states} with respect to a given time threshold. Our
results provide strong evidence that entropy production is not directly
affected by this decimation, provided that it does not entirely remove loops
carrying a net probability current. After the study of some examples of random
walks on simple graphs, we apply our analysis to a network model for the
kinesin cycle, which is an important biomolecular motor. A tentative general
theory of these facts, based on Schnakenberg's network theory, is proposed.Comment: 18 pages, 13 figures, submitted for publicatio
Symbolic dynamics of biological feedback networks
We formulate general rules for a coarse-graining of the dynamics, which we
term `symbolic dynamics', of feedback networks with monotone interactions, such
as most biological modules. Networks which are more complex than simple cyclic
structures can exhibit multiple different symbolic dynamics. Nevertheless, we
show several examples where the symbolic dynamics is dominated by a single
pattern that is very robust to changes in parameters and is consistent with the
dynamics being dictated by a single feedback loop. Our analysis provides a
method for extracting these dominant loops from short time series, even if they
only show transient trajectories.Comment: 4 pages, 4 figure
Integral Fluctuation Relations for Entropy Production at Stopping Times
A stopping time is the first time when a trajectory of a stochastic
process satisfies a specific criterion. In this paper, we use martingale theory
to derive the integral fluctuation relation for the stochastic entropy production in a
stationary physical system at stochastic stopping times . This fluctuation
relation implies the law , which states
that it is not possible to reduce entropy on average, even by stopping a
stochastic process at a stopping time, and which we call the second law of
thermodynamics at stopping times. This law implies bounds on the average amount
of heat and work a system can extract from its environment when stopped at a
random time. Furthermore, the integral fluctuation relation implies that
certain fluctuations of entropy production are universal or are bounded by
universal functions. These universal properties descend from the integral
fluctuation relation by selecting appropriate stopping times: for example, when
is a first-passage time for entropy production, then we obtain a bound on
the statistics of negative records of entropy production. We illustrate these
results on simple models of nonequilibrium systems described by Langevin
equations and reveal two interesting phenomena. First, we demonstrate that
isothermal mesoscopic systems can extract on average heat from their
environment when stopped at a cleverly chosen moment and the second law at
stopping times provides a bound on the average extracted heat. Second, we
demonstrate that the average efficiency at stopping times of an autonomous
stochastic heat engines, such as Feymann's ratchet, can be larger than the
Carnot efficiency and the second law of thermodynamics at stopping times
provides a bound on the average efficiency at stopping times.Comment: 37 pages, 6 figure
Species clustering in competitive Lotka-Volterra models
We study the properties of Lotka-Volterra competitive models in which the
intensity of the interaction among species depends on their position along an
abstract niche space through a competition kernel. We show analytically and
numerically that the properties of these models change dramatically when the
Fourier transform of this kernel is not positive definite, due to a pattern
forming instability. We estimate properties of the species distributions, such
as the steady number of species and their spacings, for different types of
kernels.Comment: 4 pages, 3 figure
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