111 research outputs found
Environmental statistics and optimal regulation
Any organism is embedded in an environment that changes over time. The
timescale for and statistics of environmental change, the precision with which
the organism can detect its environment, and the costs and benefits of
particular protein expression levels all will affect the suitability of
different strategies-such as constitutive expression or graded response-for
regulating protein levels in response to environmental inputs. We propose a
general framework-here specifically applied to the enzymatic regulation of
metabolism in response to changing concentrations of a basic nutrient-to
predict the optimal regulatory strategy given the statistics of fluctuations in
the environment and measurement apparatus, respectively, and the costs
associated with enzyme production. We use this framework to address three
fundamental questions: (i) when a cell should prefer thresholding to a graded
response; (ii) when there is a fitness advantage to implementing a Bayesian
decision rule; and (iii) when retaining memory of the past provides a selective
advantage. We specifically find that: (i) relative convexity of enzyme
expression cost and benefit influences the fitness of thresholding or graded
responses; (ii) intermediate levels of measurement uncertainty call for a
sophisticated Bayesian decision rule; and (iii) in dynamic contexts,
intermediate levels of uncertainty call for retaining memory of the past.
Statistical properties of the environment, such as variability and correlation
times, set optimal biochemical parameters, such as thresholds and decay rates
in signaling pathways. Our framework provides a theoretical basis for
interpreting molecular signal processing algorithms and a classification scheme
that organizes known regulatory strategies and may help conceptualize
heretofore unknown ones.Comment: 21 pages, 7 figure
Allocating and splitting free energy to maximize molecular machine flux
Biomolecular machines transduce between different forms of energy. These
machines make directed progress and increase their speed by consuming free
energy, typically in the form of nonequilibrium chemical concentrations.
Machine dynamics are often modeled by transitions between a set of discrete
metastable conformational states. In general, the free energy change associated
with each transition can increase the forward rate constant, decrease the
reverse rate constant, or both. In contrast to previous optimizations, we find
that in general flux is neither maximized by devoting all free energy changes
to increasing forward rate constants nor by solely decreasing reverse rate
constants. Instead the optimal free energy splitting depends on the detailed
dynamics. Extending our analysis to machines with vulnerable states (from which
they can break down), in the strong driving corresponding to in vivo cellular
conditions, processivity is maximized by reducing the occupation of the
vulnerable state.Comment: 22 pages, 7 figure
Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems
When simulating molecular systems using deterministic equations of motion
(e.g., Newtonian dynamics), such equations are generally numerically integrated
according to a well-developed set of algorithms that share commonly agreed-upon
desirable properties. However, for stochastic equations of motion (e.g.,
Langevin dynamics), there is still broad disagreement over which integration
algorithms are most appropriate. While multiple desiderata have been proposed
throughout the literature, consensus on which criteria are important is absent,
and no published integration scheme satisfies all desiderata simultaneously.
Additional nontrivial complications stem from simulating systems driven out of
equilibrium using existing stochastic integration schemes in conjunction with
recently-developed nonequilibrium fluctuation theorems. Here, we examine a
family of discrete time integration schemes for Langevin dynamics, assessing
how each member satisfies a variety of desiderata that have been enumerated in
prior efforts to construct suitable Langevin integrators. We show that the
incorporation of a novel time step rescaling in the deterministic updates of
position and velocity can correct a number of dynamical defects in these
integrators. Finally, we identify a particular splitting that has essentially
universally appropriate properties for the simulation of Langevin dynamics for
molecular systems in equilibrium, nonequilibrium, and path sampling contexts.Comment: 15 pages, 2 figures, and 2 table
Optimal control of transitions between nonequilibrium steady states
Biological systems fundamentally exist out of equilibrium in order to
preserve organized structures and processes. Many changing cellular conditions
can be represented as transitions between nonequilibrium steady states, and
organisms have an interest in optimizing such transitions. Using the
Hatano-Sasa Y-value, we extend a recently developed geometrical framework for
determining optimal protocols so that it can be applied to systems driven from
nonequilibrium steady states. We calculate and numerically verify optimal
protocols for a colloidal particle dragged through solution by a translating
optical trap with two controllable parameters. We offer experimental
predictions, specifically that optimal protocols are significantly less costly
than naive ones. Optimal protocols similar to these may ultimately point to
design principles for biological energy transduction systems and guide the
design of artificial molecular machines.Comment: Accepted for publication at PLoS ON
Energy and information flows in autonomous systems
Multi-component molecular machines are ubiquitous in biology. We review
recent progress on describing their thermodynamic properties using autonomous
bipartite Markovian dynamics. The first and second laws can be split into local
versions applicable to each subsystem of a two-component system, illustrating
that one can not only resolve energy flows between the subsystems but also
information flows quantifying how each subsystem's dynamics influence the joint
system's entropy balance. Applying the framework to molecular-scale sensors
allows one to derive tighter bounds on their energy requirement. Two-component
strongly coupled machines can be studied from a unifying perspective
quantifying to what extent they operate conventionally by transducing power or
like an information engine by generating information flow to rectify thermal
fluctuations into output power.Comment: review article, 32 pages, 3 figure
Allocating Dissipation Across a Molecular Machine Cycle to Maximize Flux
Biomolecular machines consume free energy to break symmetry and make directed progress. Nonequilibrium ATP concentrations are the typical free energy source, with one cycle of a molecular machine consuming a certain number of ATP, providing a fixed free energy budget. Since evolution is expected to favor rapid-turnover machines that operate efficiently, we investigate how this free energy budget can be allocated to maximize flux. Unconstrained optimization eliminates intermediate metastable states, indicating that flux is enhanced in molecular machines with fewer states. When maintaining a set number of states, we show that—in contrast to previous findings—the flux-maximizing allocation of dissipation is not even. This result is consistent with the coexistence of both “irreversible” and reversible transitions in molecular machine models that successfully describe experimental data, which suggests that, in evolved machines, different transitions differ significantly in their dissipation
Connections between efficient control and spontaneous transitions in an Ising model
A system can be driven between metastable configurations by a time-dependent
driving protocol, which uses external control parameters to change the
potential energy of the system. Here we investigate the correspondence between
driving protocols that are designed to minimize work and the spontaneous
transition paths of the system in the absence of driving. We study the
spin-inversion reaction in a 2D Ising model, quantifying the timing of each
spin flip and heat flow to the system during both a minimum-work protocol and a
spontaneous transition. The general order of spin flips during the transition
mechanism is preserved between the processes, despite the coarseness of control
parameters that are unable to reproduce more detailed features of the
spontaneous mechanism. Additionally, external control parameters provide energy
to each system component to compensate changes in internal energy, showing how
control parameters are tuned during a minimum-work protocol to counteract
underlying energetic features. This study supports a correspondence between
minimum-work protocols and spontaneous transition mechanisms.Comment: 10 pages, 6 figure
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