Thermodynamic bounds on ultrasensitivity in covalent switching.

Switch-like motifs are among the basic building blocks of biochemical networks. A common motif that can serve as an ultrasensitive switch consists of two enzymes acting antagonistically on a substrate, one making and the other removing a covalent modification. To work as a switch, such covalent modification cycles must be held out of thermodynamic equilibrium by continuous expenditure of energy. Here, we exploit the linear framework for timescale separation to establish tight bounds on the performance of any covalent-modification switch in terms of the chemical potential difference driving the cycle. The bounds apply to arbitrary enzyme mechanisms, not just Michaelis-Menten, with arbitrary rate constants and thereby reflect fundamental physical constraints on covalent switching.

Allosteric conformational ensembles have unlimited capacity for integrating information.

Integration of binding information by macromolecular entities is fundamental to cellular functionality. Recent work has shown that such integration cannot be explained by pairwise cooperativities, in which binding is modulated by binding at another site. Higher-order cooperativities (HOCs), in which binding is collectively modulated by multiple other binding events, appear to be necessary but an appropriate mechanism has been lacking. We show here that HOCs arise through allostery, in which effective cooperativity emerges indirectly from an ensemble of dynamically interchanging conformations. Conformational ensembles play important roles in many cellular processes but their integrative capabilities remain poorly understood. We show that sufficiently complex ensembles can implement any form of information integration achievable without energy expenditure, including all patterns of HOCs. Our results provide a rigorous biophysical foundation for analysing the integration of binding information through allostery. We discuss the implications for eukaryotic gene regulation, where complex conformational dynamics accompanies widespread information integration.

Reversal symmetries for cyclic paths away from thermodynamic equilibrium.

If a system is at thermodynamic equilibrium, an observer cannot tell whether a film of it is being played forward or in reverse: any transition will occur with the same frequency in the forward as in the reverse direction. However, if expenditure of energy changes the rate of even a single transition to yield a nonequilibrium steady state, such time-reversal symmetry undergoes a widespread breakdown, far beyond the point at which the energy is expended. An explosion of interdependency also arises, with steady-state probabilities of system states depending in a complicated manner on the rate of every transition in the system. Nevertheless, in the midst of this global nonequilibrium complexity, we find that cyclic paths have reversibility properties that remain local, and which can exhibit symmetry, no matter how far the system is from thermodynamic equilibrium. Specifically, given any cycle of reversible transitions, the ratio of the frequencies with which the cycle occurs in one direction versus the other is determined, in the long-time limit, only by the thermodynamic force on the cycle itself, without requiring knowledge of transition rates elsewhere in the system. In particular, if there is no net energy expenditure on the cycle, then, over long times, the cycle occurrence frequencies are the same in either direction.

Negative reciprocity, not ordered assembly, underlies the interaction of Sox2 and Oct4 on DNA.

The mode of interaction of transcription factors (TFs) on eukaryotic genomes remains a matter of debate. Single-molecule data in living cells for the TFs Sox2 and Oct4 were previously interpreted as evidence of ordered assembly on DNA. However, the quantity that was calculated does not determine binding order but, rather, energy expenditure away from thermodynamic equilibrium. Here, we undertake a rigorous biophysical analysis which leads to the concept of reciprocity. The single-molecule data imply that Sox2 and Oct4 exhibit negative reciprocity, with expression of Sox2 increasing Oct4's genomic binding but expression of Oct4 decreasing Sox2's binding. Models show that negative reciprocity can arise either from energy expenditure or from a mixture of positive and negative cooperativity at distinct genomic loci. Both possibilities imply unexpected complexity in how TFs interact on DNA, for which single-molecule methods provide novel detection capabilities.

Model discrimination for Ca2+ -dependent regulation of myosin light chain kinase in smooth muscle contraction.

Excitation-contraction coupling in smooth muscle is mediated by the Ca2+ - and calmodulin-dependent regulation of myosin light chain kinase. The precise mechanism of this regulation remains controversial, and several mathematical models have been proposed for the interaction of the three species. These models have previously been analyzed at steady state primarily by numerical simulation of differential equations, for which parameter values must be estimated from data. Here, we use the linear framework for timescale separation to demonstrate that models of this general kind can be solved analytically for an equilibrium steady state, without having to determine parameter values. This analysis leads to parameter-independent methods for discriminating between the models, for which we propose experiments that could be performed with existing methods.

Two-structure thermodynamics for the TIP4P/2005 model of water covering supercooled and deeply stretched regions.

One of the most promising frameworks for understanding the anomalies of cold and supercooled water postulates the existence of two competing, interconvertible local structures. If the non-ideality in the Gibbs energy of mixing overcomes the ideal entropy of mixing of these two structures, a liquid-liquid phase transition, terminated at a liquid-liquid critical point, is predicted. Various versions of the "two-structure equation of state" (TSEOS) based on this concept have shown remarkable agreement with both experimental data for metastable, deeply supercooled water and simulations of molecular water models. However, existing TSEOSs were not designed to describe the negative pressure region and do not account for the stability limit of the liquid state with respect to the vapor. While experimental data on supercooled water at negative pressures may shed additional light on the source of the anomalies of water, such data are very limited. To fill this gap, we have analyzed simulation results for TIP4P/2005, one of the most accurate classical water models available. We have used recently published simulation data, and performed additional simulations, over a broad range of positive and negative pressures, from ambient temperature to deeply supercooled conditions. We show that, by explicitly incorporating the liquid-vapor spinodal into a TSEOS, we are able to match the simulation data for TIP4P/2005 with remarkable accuracy. In particular, this equation of state quantitatively reproduces the lines of extrema in density, isothermal compressibility, and isobaric heat capacity. Contrary to an explanation of the thermodynamic anomalies of water based on a "retracing spinodal," the liquid-vapor spinodal in the present TSEOS continues monotonically to lower pressures upon cooling, influencing but not giving rise to density extrema and other thermodynamic anomalies.

Two-state thermodynamics and the possibility of a liquid-liquid phase transition in supercooled TIP4P/2005 water.

Water shows intriguing thermodynamic and dynamic anomalies in the supercooled liquid state. One possible explanation of the origin of these anomalies lies in the existence of a metastable liquid-liquid phase transition (LLPT) between two (high and low density) forms of water. While the anomalies are observed in experiments on bulk and confined water and by computer simulation studies of different water-like models, the existence of a LLPT in water is still debated. Unambiguous experimental proof of the existence of a LLPT in bulk supercooled water is hampered by fast ice nucleation which is a precursor of the hypothesized LLPT. Moreover, the hypothesized LLPT, being metastable, in principle cannot exist in the thermodynamic limit (infinite size, infinite time). Therefore, computer simulations of water models are crucial for exploring the possibility of the metastable LLPT and the nature of the anomalies. In this work, we present new simulation results in the NVT ensemble for one of the most accurate classical molecular models of water, TIP4P/2005. To describe the computed properties and explore the possibility of a LLPT, we have applied two-structure thermodynamics, viewing water as a non-ideal mixture of two interconvertible local structures ("states"). The results suggest the presence of a liquid-liquid critical point and are consistent with the existence of a LLPT in this model for the simulated length and time scales. We have compared the behavior of TIP4P/2005 with other popular water-like models, namely, mW and ST2, and with real water, all of which are well described by two-state thermodynamics. In view of the current debate involving different studies of TIP4P/2005, we discuss consequences of metastability and finite size in observing the liquid-liquid separation. We also address the relationship between the phenomenological order parameter of two-structure thermodynamics and the microscopic nature of the low-density structure.

Behavior of supercooled aqueous solutions stemming from hidden liquid-liquid transition in water.

A popular hypothesis that explains the anomalies of supercooled water is the existence of a metastable liquid-liquid transition hidden below the line of homogeneous nucleation. If this transition exists and if it is terminated by a critical point, the addition of a solute should generate a line of liquid-liquid critical points emanating from the critical point of pure metastable water. We have analyzed thermodynamic consequences of this scenario. In particular, we consider the behavior of two systems, H2O-NaCl and H2O-glycerol. We find the behavior of the heat capacity in supercooled aqueous solutions of NaCl, as reported by Archer and Carter [J. Phys. Chem. B 104, 8563 (2000)], to be consistent with the presence of the metastable liquid-liquid transition. We elucidate the non-conserved nature of the order parameter (extent of "reaction" between two alternative structures of water) and the consequences of its coupling with conserved properties (density and concentration). We also show how the shape of the critical line in a solution controls the difference in concentration of the coexisting liquid phases.

Thermal conductivity of supercooled water.

The heat capacity of supercooled water, measured down to -37°C, shows an anomalous increase as temperature decreases. The thermal diffusivity, i.e., the ratio of the thermal conductivity and the heat capacity per unit volume, shows a decrease. These anomalies may be associated with a hypothesized liquid-liquid critical point in supercooled water below the line of homogeneous nucleation. However, while the thermal conductivity is known to diverge at the vapor-liquid critical point due to critical density fluctuations, the thermal conductivity of supercooled water, calculated as the product of thermal diffusivity and heat capacity, does not show any sign of such an anomaly. We have used mode-coupling theory to investigate the possible effect of critical fluctuations on the thermal conductivity of supercooled water and found that indeed any critical thermal-conductivity enhancement would be too small to be measurable at experimentally accessible temperatures. Moreover, the behavior of thermal conductivity can be explained by the observed anomalies of the thermodynamic properties. In particular, we show that thermal conductivity should go through a minimum when temperature is decreased, as Kumar and Stanley observed in the TIP5P model of water. We discuss physical reasons for the striking difference between the behavior of thermal conductivity in water near the vapor-liquid and liquid-liquid critical points.