Thermodynamic Bounds on Symmetry Breaking in Linear and Catalytic Biochemical Systems.

Living systems are maintained out of equilibrium by external driving forces. At stationarity, they exhibit emergent selection phenomena that break equilibrium symmetries and originate from the expansion of the accessible chemical space due to nonequilibrium conditions. Here, we use the matrix-tree theorem to derive upper and lower thermodynamic bounds on these symmetry-breaking features in linear and catalytic biochemical systems. Our bounds are independent of the kinetics and hold for both closed and open reaction networks. We also extend our results to master equations in the chemical space. Using our framework, we recover the thermodynamic constraints in kinetic proofreading. Finally, we show that the contrast of reaction-diffusion patterns can be bounded only by the nonequilibrium driving force. Our results provide a general framework for understanding the role of nonequilibrium conditions in shaping the steady-state properties of biochemical systems.

Fluctuations of entropy production of a run-and-tumble particle.

Out-of-equilibrium systems continuously generate entropy, with its rate of production being a fingerprint of nonequilibrium conditions. In small-scale dissipative systems subject to thermal noise, fluctuations of entropy production are significant. Hitherto, mean and variance have been abundantly studied, even if higher moments might be important to fully characterize the system of interest. Here, we introduce a graphical method to compute any moment of entropy production for a generic discrete-state system. Then, we focus on a paradigmatic model of active particles, i.e., run-and-tumble dynamics, which resembles the motion observed in several micro-organisms. Employing our framework, we compute the first three cumulants of the entropy production for a discrete version of this model. We also compare our analytical results with numerical simulations. We find that as the number of states increases, the distribution of entropy production deviates from a Gaussian. Finally, we extend our framework to a continuous state-space run-and-tumble model, using an appropriate scaling of the transition rates. The approach presented here might help uncover the features of nonequilibrium fluctuations of any current in biological systems operating out-of-equilibrium.

ABC transporters are billion-year-old Maxwell Demons.

ATP-Binding Cassette (ABC) transporters are a broad family of biological machines, found in most prokaryotic and eukaryotic cells, performing the crucial import or export of substrates through both plasma and organellar membranes, and maintaining a steady concentration gradient driven by ATP hydrolysis. Building upon the present biophysical and biochemical characterization of ABC transporters, we propose here a model whose solution reveals that these machines are an exact molecular realization of the autonomous Maxwell Demon, a century-old abstract device that uses an energy source to drive systems away from thermodynamic equilibrium. In particular, the Maxwell Demon does not perform any direct mechanical work on the system, but simply selects which spontaneous processes to allow and which ones to forbid based on information that it collects and processes. In its autonomous version, the measurement device is embedded in the system itself. In the molecular model introduced here, the different operations that characterize Maxwell Demons (measurement, feedback, resetting) are features that emerge from the biochemical and structural properties of ABC transporters, revealing the crucial role of allostery to process information. Our framework allows us to develop an explicit bridge between the molecular-level description and the higher-level language of information theory for ABC transporters.

Information-driven transitions in projections of underdamped dynamics.

Low-dimensional representations of underdamped systems often provide useful insights and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most information on observed spatial trajectories. We show that, in paradigmatic systems, the minimization of the information loss drives the appearance of a discontinuous transition in the optimal model parameters. Our results raise serious warnings for general inference approaches, and they unravel fundamental properties of effective dynamical representations impacting several fields, from biophysics to dimensionality reduction.

Mutual information in changing environments: Nonlinear interactions, out-of-equilibrium systems, and continuously varying diffusivities.

Biochemistry, ecology, and neuroscience are examples of prominent fields aiming at describing interacting systems that exhibit nontrivial couplings to complex, ever-changing environments. We have recently shown that linear interactions and a switching environment are encoded separately in the mutual information of the overall system. Here we first generalize these findings to a broad class of nonlinear interacting models. We find that a new term in the mutual information appears, quantifying the interplay between nonlinear interactions and environmental changes, and leading to either constructive or destructive information interference. Furthermore, we show that a higher mutual information emerges in out-of-equilibrium environments with respect to an equilibrium scenario. Finally, we generalize our framework to the case of continuously varying environments. We find that environmental changes can be mapped exactly into an effective spatially varying diffusion coefficient, shedding light on modeling of biophysical systems in inhomogeneous media.

Mutual Information Disentangles Interactions from Changing Environments.

Real-world systems are characterized by complex interactions of their internal degrees of freedom, while living in ever-changing environments whose net effect is to act as additional couplings. Here, we introduce a paradigmatic interacting model in a switching, but unobserved, environment. We show that the limiting properties of the mutual information of the system allow for a disentangling of these two sources of couplings. Further, our approach might stand as a general method to discriminate complex internal interactions from equally complex changing environments.

Light-Switchable Buffers.

A visible light-switchable buffer system based on a merocyanine photoacid is presented. Para-substitution of the indolium side with a methoxy group affords a compound suitable for making hydrolytically stable aqueous buffers whose pH can be tuned between 7 and 4 using 500 nm light.

Dissipation-Driven Selection under Finite Diffusion: Hints from Equilibrium and Separation of Time Scales.

When exposed to a thermal gradient, reaction networks can convert thermal energy into the chemical selection of states that would be unfavourable at equilibrium. The kinetics of reaction paths, and thus how fast they dissipate available energy, might be dominant in dictating the stationary populations of all chemical states out of equilibrium. This phenomenology has been theoretically explored mainly in the infinite diffusion limit. Here, we show that the regime in which the diffusion rate is finite, and also slower than some chemical reactions, might bring about interesting features, such as the maximisation of selection or the switch of the selected state at stationarity. We introduce a framework, rooted in a time-scale separation analysis, which is able to capture leading non-equilibrium features using only equilibrium arguments under well-defined conditions. In particular, it is possible to identify fast-dissipation sub-networks of reactions whose Boltzmann equilibrium dominates the steady-state of the entire system as a whole. Finally, we also show that the dissipated heat (and so the entropy production) can be estimated, under some approximations, through the heat capacity of fast-dissipation sub-networks. This work provides a tool to develop an intuitive equilibrium-based grasp on complex non-isothermal reaction networks, which are important paradigms to understand the emergence of complex structures from basic building blocks.

Equilibrium and non-equilibrium furanose selection in the ribose isomerisation network.

The exclusive presence of ß-D-ribofuranose in nucleic acids is still a conundrum in prebiotic chemistry, given that pyranose species are substantially more stable at equilibrium. However, a precise characterisation of the relative furanose/pyranose fraction at temperatures higher than about 50 °C is still lacking. Here, we employ a combination of NMR measurements and statistical mechanics modelling to predict a population inversion between furanose and pyranose at equilibrium at high temperatures. More importantly, we show that a steady temperature gradient may steer an open isomerisation network into a non-equilibrium steady state where furanose is boosted beyond the limits set by equilibrium thermodynamics. Moreover, we demonstrate that nonequilibrium selection of furanose is maximum at optimal dissipation, as gauged by the temperature gradient and energy barriers for isomerisation. The predicted optimum is compatible with temperature drops found in hydrothermal vents associated with extremely fresh lava flows on the seafloor.

Dissipation-driven selection of states in non-equilibrium chemical networks.

Life has most likely originated as a consequence of processes taking place in non-equilibrium conditions (e.g. in the proximity of deep-sea thermal vents) selecting states of matter that would have been otherwise unfavorable at equilibrium. Here we present a simple chemical network in which the selection of states is driven by the thermodynamic necessity of dissipating heat as rapidly as possible in the presence of a thermal gradient: states participating to faster reactions contribute the most to the dissipation rate, and are the most populated ones in non-equilibrium steady-state conditions. Building upon these results, we show that, as the complexity of the chemical network increases, the velocity of the reaction path leading to a given state determines its selection, giving rise to non-trivial localization phenomena in state space. A byproduct of our studies is that, in the presence of a temperature gradient, thermophoresis-like behavior inevitably appears depending on the transport properties of each individual state, thus hinting at a possible microscopic explanation of this intriguing yet still not fully understood phenomenon.

Thermodynamics and kinetics of protonated merocyanine photoacids in water.

Metastable-state photoacids (mPAHs) are chemical species whose photo-activated state is long-lived enough to allow for proton diffusion. Liao's photoacid (1) represents the archetype of mPAHs, and is being widely used on account of its unique capability to change the acidity of aqueous solutions reversibly. The behavior of 1 in water, however, still remains poorly understood. Herein, we provide in-depth insights on the thermodynamics and kinetics of 1 in water through a series of comparative 1H NMR and UV-Vis studies and relative modelling. Under dark conditions, we quantified a three-component equilibrium system where the dissociation (K a) of the open protonated form (MCH) is followed by isomerization (K c) of the open deprotonated form (MC) to the closed spiropyran form (SP) - i.e., in the absence of light, the ground state acidity can be expressed as K GS a = K a(1 + K c). On the other hand, under powerful and continuous light irradiation we were able to assess, for the first time experimentally, the dissociation constant (K MS a) of the protonated metastable state (cis-MCH). In addition, we found that thermal ring-opening of SP is always rate-determining regardless of pH, whereas hydrolysis is reminiscent of what is found for Schiff bases. The proposed methodology is general, and it was applied to two other compounds bearing a shorter (ethyl, 2) and a longer (butyl, 3) alkyl-1-sulfonate bridge. We found that the pK a remains constant, whereas both pK c and pK MS a linearly increase with the length of the alkyl bridge. Importantly, all results are consistent with a four-component model cycle, which describes perfectly the full dynamics of proton release/uptake of 1-3 in water. The superior hydrolytic stability and water solubility of compound 3, together with its relatively high pK GS a (low K c), allowed us to achieve fully reversible jumps of 2.5 pH units over 18 consecutive cycles (6 hours).

Hyperaccurate currents in stochastic thermodynamics.

Thermodynamic observables of mesoscopic systems can be expressed as integrated empirical currents. Their fluctuations are bound by thermodynamic uncertainty relations. We introduce the hyperaccurate current as the integrated empirical current with the least fluctuations in a given nonequilibrium system. For steady-state systems described by overdamped Langevin equations, we derive an equation for the hyperaccurate current by means of a variational principle. We show that the hyperaccurate current coincides with the entropy production if and only if the latter saturates the thermodynamic uncertainty relation, and it can be substantially more precise otherwise. The hyperaccurate current can be used to improve estimates of entropy production from experimental data.