Journal of Statistical Mechanics: theory and experiment

This volume of the Annual Reviews of Physical Chemistry (ARPC67) once again brings out the sheer breadth of contemporary physical chemistry research. The so-called ‘middle kingdom’ is indeed rather vast – as is eminently clear from the various articles that range from processes happening inside a cell to tracking the motion of electrons. ARPC67 has a good balance between theory and experiments, applied and fundamental, representing frontline research on gas, condensed and solid phase systems.

Annual Review of Physical Chemistry

This chapter contains sections titled: 1.00 Fourier Series, 1.01 Orthogonal Functions, 1.02 The Fourier Integral, 1.04 More on the Fourier Integral; Realizability of Filters, 1.1 Generalized Harmonic Analysis, 1.18 Discrete Arrays and Their Spectra, 1.2 Multiple Harmonic Analysis and Coherency Matrices, 1.3 Smoothing Problems, 1.4 Ergodic Theory, 1.5 Brownian Motion, 1.6 Poisson Distributions, 1.7 Harmonic Analysis in the Complex Domain

Resume of Fundamental Mathematical Notions

When beneficial mutations are rare, they accumulate by a series of selective sweeps. But when they are common, many beneficial mutations will occur before any can fix, so there will be many different mutant lineages in the population concurrently. In an asexual population, these different mutant lineages interfere and not all can fix simultaneously. In addition, further beneficial mutations can accumulate in mutant lineages while these are still a minority of the population. In this paper, we analyze the dynamics of such multiple mutations and the interplay between multiple mutations and interference between clones. These result in substantial variation in fitness accumulating within a single asexual population. The amount of variation is determined by a balance between selection, which destroys variation, and beneficial mutations, which create more. The behavior depends in a subtle way on the population parameters: the population size, the beneficial mutation rate, and the distribution of the fitness increments of the potential beneficial mutations. The mutation-selection balance leads to a continually evolving population with a steady-state fitness variation. This variation increases logarithmically with both population size and mutation rate and sets the rate at which the population accumulates beneficial mutations, which thus also grows only logarithmically with population size and mutation rate. These results imply that mutator phenotypes are less effective in larger asexual populations. They also have consequences for the advantages (or disadvantages) of sex via the Fisher-Muller effect; these are discussed briefly.

Beneficial mutation-selection balance and the effect of linkage on positive selection

Cells are the basic units of all living matter which harness the flow of energy to drive the processes of life. While the biochemical networks involved in energy transduction are well-characterized, the energetic costs and constraints for specific cellular processes remain largely unknown. In particular, what are the energy budgets of cells? What are the constraints and limits energy flows impose on cellular processes? Do cells operate near these limits, and if so how do energetic constraints impact cellular functions? Physics has provided many tools to study nonequilibrium systems and to define physical limits, but applying these tools to cell biology remains a challenge. Physical bioenergetics, which resides at the interface of nonequilibrium physics, energy metabolism, and cell biology, seeks to understand how much energy cells are using, how they partition this energy between different cellular processes, and the associated energetic constraints. Here we review recent advances and discuss open questions and challenges in physical bioenergetics.

Physical bioenergetics: Energy fluxes, budgets, and constraints in cells.

Active matter represents a broad class of systems that evolve far from equilibrium due to the local injection of energy. Like their passive analogues, transformations between distinct metastable states in active matter proceed through rare fluctuations, however their detailed balance violating dynamics renders these events difficult to study. Here, we present a simulation method for evaluating the rate and mechanism of rare events in generic nonequilibrium systems and apply it to study the conformational changes of a passive solute in an active fluid. The method employs a variational optimization of a control force that renders the rare event a typical one, supplying an exact estimate of its rate as a ratio of path partition functions. Using this method we find that increasing activity in the active bath can enhance the rate of conformational switching of the passive solute in a manner consistent with recent bounds from stochastic thermodynamics.

Direct evaluation of rare events in active matter from variational path sampling

The biochemical reaction networks that regulate living systems are all stochastic to varying degrees. The resulting randomness affects biological outcomes at multiple scales, from the functional states of single proteins in a cell to the evolutionary trajectory of whole populations. Controlling how the distribution of these outcomes changes over time—via external interventions like time-varying concentrations of chemical species—is a complex challenge. In this work, we show how counterdiabatic (CD) driving, first developed to control quantum systems, provides a versatile tool for steering biological processes. We develop a practical graph-theoretic framework for CD driving in discrete-state continuous-time Markov networks. We illustrate the formalism with examples from gene regulation and chaperone-assisted protein folding, demonstrating the possibility that nature can exploit CD driving to accelerate response to sudden environmental changes. We generalize the method to continuum Fokker-Planck models, and apply it to study AFM single-molecule pulling experiments in regimes where the typical assumption of adiabaticity breaks down, as well as an evolutionary model with competing genetic variants subject to time-varying selective pressures. The AFM analysis shows how CD driving can eliminate non-equilibrium artifacts due to large force ramps in such experiments, allowing accurate estimation of biomolecular properties.

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Counterdiabatic control of biophysical processes

Recent experiments have uncovered a fundamental information scale for cellular signaling networks: the correlation between input and output concentrations of molecules in a signaling pathway corresponds to at most 1-3 bits of mutual information. Our understanding of the physical constraints and evolutionary pressures that determine this scale remains incomplete. By focusing on a basic element of signaling pathways, the kinase-phosphatase enzymatic push-pull loop, we highlight the pivotal role played by energy resources available for signaling and their expenditure: the chemical potential energy of ATP hydrolysis, and the rate of ATP consumption. Scanning a broad range of reaction parameters based on enzymatic databases, we find that ATP chemical potentials in modern organisms are just above the threshold necessary to achieve empirical mutual information values. We also derive an analytical relation for the minimum ATP consumption required to maintain a certain signal fidelity across a range of input frequencies. Attempting to increase signal fidelity beyond a few bits lowers the bandwidth, the maximum characteristic signal frequency that the network can handle at a given energy cost. The observed information scale thus represents a balancing act between fidelity and the ability to process fast-changing environmental signals. Our analytical relation defines a performance limit for kinase-phosphatase networks, and we find evidence that a component of the yeast osmotic shock pathway may be close to the optimality line. By quantifying the evolutionary pressures that operate on these networks, we argue that this is not a coincidence: natural selection on energy expenditures is capable of pushing signaling systems toward optimality, particularly in unicellular organisms. Our theoretical framework is directly verifiable using existing experimental techniques, and predicts that more examples of such optimality should exist in nature.

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The price of a bit: energetic costs and the evolution of cellular signaling

In this paper, we consider the energy cost of communicating using molecular communication. In a simplified scenario, we show that the energy bound in Landauer's principle can be achieved, implying that molecular communication can approach fundamental thermodynamic limits.

Benjamin Kuznets-Speck

Papers

Direct evaluation of rare events in active matter from variational path sampling

Counterdiabatic control of biophysical processes

The price of a bit: energetic costs and the evolution of cellular signaling

Thermodynamic Properties of Molecular Communication

Thermodynamic Properties of Molecular Communication