A bifurcation integrates information from many noisy ion channels and allows for milli-Kelvin thermal sensitivity in the snake pit organ.

In various biological systems, information from many noisy molecular receptors must be integrated into a collective response. A striking example is the thermal imaging organ of pit vipers. Single nerve fibers in the organ reliably respond to milli-Kelvin (mK) temperature increases, a thousand times more sensitive than their molecular sensors, thermo-transient receptor potential (TRP) ion channels. Here, we propose a mechanism for the integration of this molecular information. In our model, amplification arises due to proximity to a dynamical bifurcation, separating a regime with frequent and regular action potentials (APs), from a regime where APs are irregular and infrequent. Near the transition, AP frequency can have an extremely sharp dependence on temperature, naturally accounting for the thousand-fold amplification. Furthermore, close to the bifurcation, most of the information about temperature available in the TRP channels' kinetics can be read out from the times between consecutive APs even in the presence of readout noise. A key model prediction is that the coefficient of variation in the distribution of interspike times decreases with AP frequency, and quantitative comparison with experiments indeed suggests that nerve fibers of snakes are located very close to the bifurcation. While proximity to such bifurcation points typically requires fine-tuning of parameters, we propose that having feedback act from the order parameter (AP frequency) onto the control parameter robustly maintains the system in the vicinity of the bifurcation. This robustness suggests that similar feedback mechanisms might be found in other sensory systems which also need to detect tiny signals in a varying environment.

Surface densities prewet a near-critical membrane.

Recent work has highlighted roles for thermodynamic phase behavior in diverse cellular processes. Proteins and nucleic acids can phase separate into three-dimensional liquid droplets in the cytoplasm and nucleus and the plasma membrane of animal cells appears tuned close to a two-dimensional liquid-liquid critical point. In some examples, cytoplasmic proteins aggregate at plasma membrane domains, forming structures such as the postsynaptic density and diverse signaling clusters. Here we examine the physics of these surface densities, employing minimal simulations of polymers prone to phase separation coupled to an Ising membrane surface in conjunction with a complementary Landau theory. We argue that these surface densities are a phase reminiscent of prewetting, in which a molecularly thin three-dimensional liquid forms on a usually solid surface. However, in surface densities the solid surface is replaced by a membrane with an independent propensity to phase separate. We show that proximity to criticality in the membrane dramatically increases the parameter regime in which a prewetting-like transition occurs, leading to a broad region where coexisting surface phases can form even when a bulk phase is unstable. Our simulations naturally exhibit three-surface phase coexistence even though both the membrane and the polymer bulk only display two-phase coexistence on their own. We argue that the physics of these surface densities may be shared with diverse functional structures seen in eukaryotic cells.

Chemical potential measurements constrain models of cholesterol-phosphatidylcholine interactions.

Bilayer membranes composed of cholesterol and phospholipids exhibit diverse forms of nonideal mixing. In particular, many previous studies document macroscopic liquid-liquid phase separation as well as nanometer-scale heterogeneity in membranes of phosphatidylcholine (PC) lipids and cholesterol. Here, we present experimental measurements of cholesterol chemical potential (µc) in binary membranes containing dioleoyl PC (DOPC), 1-palmitoyl-2-oleoyl PC (POPC), or dipalmitoyl PC (DPPC), and in ternary membranes of DOPC and DPPC, referenced to crystalline cholesterol. µc is the thermodynamic quantity that dictates the availability of cholesterol to bind other factors, and notably must be equal between coexisting phases of a phase separated mixture. It is simply related to concentration under conditions of ideal mixing, but is far from ideal for the majority of lipid mixtures investigated here. Measurements of µc can vary with phospholipid composition by 1.5 kBT at constant cholesterol mole fraction implying a more than fivefold change in its availability for binding receptors and other reactions. Experimental measurements are fit to thermodynamic models including cholesterol-DPPC complexes or pairwise interactions between lipid species to provide intuition about the magnitude of interactions. These findings reinforce that µc depends on membrane composition overall, suggesting avenues for cells to alter the availability of cholesterol without varying cholesterol concentration.

Physical Constraints in Intracellular Signaling: The Cost of Sending a Bit.

Many biological processes require timely communication between molecular components. Cells employ diverse physical channels to this end, transmitting information through diffusion, electrical depolarization, and mechanical waves among other strategies. Here we bound the energetic cost of transmitting information through these physical channels, in k_{B}T/bit, as a function of the size of the sender and receiver, their spatial separation, and the communication latency. These calculations provide an estimate for the energy costs associated with information processing arising from the physical constraints of the cellular environment, which we find to be many orders of magnitude larger than unity in natural units. From these calculations, we construct a phase diagram indicating where each strategy is most efficient. Our results suggest that intracellular information transfer may constitute a substantial energetic cost. This provides a new tool for understanding tradeoffs in cellular network function.

Energy dissipation bounds for autonomous thermodynamic cycles.

How much free energy is irreversibly lost during a thermodynamic process? For deterministic protocols, lower bounds on energy dissipation arise from the thermodynamic friction associated with pushing a system out of equilibrium in finite time. Recent work has also bounded the cost of precisely moving a single degree of freedom. Using stochastic thermodynamics, we compute the total energy cost of an autonomously controlled system by considering both thermodynamic friction and the entropic cost of precisely directing a single control parameter. Our result suggests a challenge to the usual understanding of the adiabatic limit: Here, even infinitely slow protocols are energetically irreversible.

Far from Asymptopia: Unbiased High-Dimensional Inference Cannot Assume Unlimited Data.

Inference from limited data requires a notion of measure on parameter space, which is most explicit in the Bayesian framework as a prior distribution. Jeffreys prior is the best-known uninformative choice, the invariant volume element from information geometry, but we demonstrate here that this leads to enormous bias in typical high-dimensional models. This is because models found in science typically have an effective dimensionality of accessible behaviors much smaller than the number of microscopic parameters. Any measure which treats all of these parameters equally is far from uniform when projected onto the sub-space of relevant parameters, due to variations in the local co-volume of irrelevant directions. We present results on a principled choice of measure which avoids this issue and leads to unbiased posteriors by focusing on relevant parameters. This optimal prior depends on the quantity of data to be gathered, and approaches Jeffreys prior in the asymptotic limit. However, for typical models, this limit cannot be justified without an impossibly large increase in the quantity of data, exponential in the number of microscopic parameters.

Information geometry for multiparameter models: new perspectives on the origin of simplicity.

Complex models in physics, biology, economics, and engineering are oftensloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades without significant changes in the predictions. This review uses information geometry to explore sloppiness and its deep relation to emergent theories. We introduce themodel manifoldof predictions, whose coordinates are the model parameters. Itshyperribbonstructure explains why only a few parameter combinations matter for the behavior. We review recent rigorous results that connect the hierarchy of hyperribbon widths to approximation theory, and to the smoothness of model predictions under changes of the control variables. We discuss recent geodesic methods to find simpler models on nearby boundaries of the model manifold-emergent theories with fewer parameters that explain the behavior equally well. We discuss a Bayesian prior which optimizes the mutual information between model parameters and experimental data, naturally favoring points on the emergent boundary theories and thus simpler models. We introduce a 'projected maximum likelihood' prior that efficiently approximates this optimal prior, and contrast both to the poor behavior of the traditional Jeffreys prior. We discuss the way the renormalization group coarse-graining in statistical mechanics introduces a flow of the model manifold, and connect stiff and sloppy directions along the model manifold with relevant and irrelevant eigendirections of the renormalization group. Finally, we discuss recently developed 'intensive' embedding methods, allowing one to visualize the predictions of arbitrary probabilistic models as low-dimensional projections of an isometric embedding, and illustrate our method by generating the model manifold of the Ising model.

Maximizing the information learned from finite data selects a simple model.

We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as much as possible from limited data. When many parameters are poorly constrained by the available data, we find that this prior puts weight only on boundaries of the parameter space. Thus, it selects a lower-dimensional effective theory in a principled way, ignoring irrelevant parameter directions. In the limit where there are sufficient data to tightly constrain any number of parameters, this reduces to the Jeffreys prior. However, we argue that this limit is pathological when applied to the hyperribbon parameter manifolds generic in science, because it leads to dramatic dependence on effects invisible to experiment.

Conditions that Stabilize Membrane Domains Also Antagonize n-Alcohol Anesthesia.

Diverse molecules induce general anesthesia with potency strongly correlated with both their hydrophobicity and their effects on certain ion channels. We recently observed that several n-alcohol anesthetics inhibit heterogeneity in plasma-membrane-derived vesicles by lowering the critical temperature (Tc) for phase separation. Here, we exploit conditions that stabilize membrane heterogeneity to further test the correlation between the anesthetic potency of n-alcohols and effects on Tc. First, we show that hexadecanol acts oppositely to n-alcohol anesthetics on membrane mixing and antagonizes ethanol-induced anesthesia in a tadpole behavioral assay. Second, we show that two previously described "intoxication reversers" raise Tc and counter ethanol's effects in vesicles, mimicking the findings of previous electrophysiological and behavioral measurements. Third, we find that elevated hydrostatic pressure, long known to reverse anesthesia, also raises Tc in vesicles with a magnitude that counters the effect of butanol at relevant concentrations and pressures. Taken together, these results demonstrate that ΔTc predicts anesthetic potency for n-alcohols better than hydrophobicity in a range of contexts, supporting a mechanistic role for membrane heterogeneity in general anesthesia.

Dissipation Bound for Thermodynamic Control.

Biological and engineered systems operate by coupling function to the transfer of heat and/or particles down a thermal or chemical gradient. In idealized deterministically driven systems, thermodynamic control can be exerted reversibly, with no entropy production, as long as the rate of the protocol is made slow compared to the equilibration time of the system. Here we consider fully realizable, entropically driven systems where the control parameters themselves obey rules that are reversible and that acquire directionality in time solely through dissipation. We show that when such a system moves in a directed way through thermodynamic space, it must produce entropy that is on average larger than its generalized displacement as measured by the Fisher information metric. This distance measure is subextensive but cannot be made small by slowing the rate of the protocol.

Perspective: Sloppiness and emergent theories in physics, biology, and beyond.

Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are "sloppy," i.e., exhibit behavior controlled by a relatively small number of parameter combinations. We review an information theoretic framework for analyzing sloppy models. This formalism is based on the Fisher information matrix, which is interpreted as a Riemannian metric on a parameterized space of models. Distance in this space is a measure of how distinguishable two models are based on their predictions. Sloppy model manifolds are bounded with a hierarchy of widths and extrinsic curvatures. The manifold boundary approximation can extract the simple, hidden theory from complicated sloppy models. We attribute the success of simple effective models in physics as likewise emerging from complicated processes exhibiting a low effective dimensionality. We discuss the ramifications and consequences of sloppy models for biochemistry and science more generally. We suggest that the reason our complex world is understandable is due to the same fundamental reason: simple theories of macroscopic behavior are hidden inside complicated microscopic processes.

Polymer Collapse & Liquid-Liquid Phase-Separation are Coupled in a Generalized Prewetting Transition.

The three-dimensional organization of chromatin is thought to play an important role in controlling gene expression. Specificity in expression is achieved through the interaction of transcription factors and other nuclear proteins with particular sequences of DNA. At unphysiological concentrations many of these nuclear proteins can phase-separate in the absence of DNA, and it has been hypothesized that, in vivo, the thermodynamic forces driving these phases help determine chromosomal organization. However it is unclear how DNA, itself a long polymer subject to configurational transitions, interacts with three-dimensional protein phases. Here we show that a long compressible polymer can be coupled to interacting protein mixtures, leading to a generalized prewetting transition where polymer collapse is coincident with a locally stabilized liquid droplet. We use lattice Monte-Carlo simulations and a mean-field theory to show that these phases can be stable even in regimes where both polymer collapse and coexisting liquid phases are unstable in isolation, and that these new transitions can be either abrupt or continuous. For polymers with internal linear structure we further show that changes in the concentration of bulk components can lead to changes in three-dimensional polymer structure. In the nucleus there are many distinct proteins that interact with many different regions of chromatin, potentially giving rise to many different Prewet phases. The simple systems we consider here highlight chromatin's role as a lower-dimensional surface whose interactions with proteins are required for these novel phases.

Polymer Collapse & Liquid-Liquid Phase-Separation are Coupled in a Generalized Prewetting Transition.

The three-dimensional organization of chromatin is thought to play an important role in controlling gene expression. Specificity in expression is achieved through the interaction of transcription factors and other nuclear proteins with particular sequences of DNA. At unphysiological concentrations many of these nuclear proteins can phase-separate in the absence of DNA, and it has been hypothesized that, in vivo, the thermodynamic forces driving these phases help determine chromosomal organization. However it is unclear how DNA, itself a long polymer subject to configurational transitions, interacts with three-dimensional protein phases. Here we show that a long compressible polymer can be coupled to interacting protein mixtures, leading to a generalized prewetting transition where polymer collapse is coincident with a locally stabilized liquid droplet. We use lattice Monte-Carlo simulations and a mean-field theory to show that these phases can be stable even in regimes where both polymer collapse and coexisting liquid phases are unstable in isolation, and that these new transitions can be either abrupt or continuous. For polymers with internal linear structure we further show that changes in the concentration of bulk components can lead to changes in three-dimensional polymer structure. In the nucleus there are many distinct proteins that interact with many different regions of chromatin, potentially giving rise to many different Prewet phases. The simple systems we consider here highlight chromatin's role as a lower-dimensional surface whose interactions with proteins are required for these novel phases.

Pseudo-perplexity in One Fell Swoop for Protein Fitness Estimation.

Protein language models trained on the masked language modeling objective learn to predict the identity of hidden amino acid residues within a sequence using the remaining observable sequence as context. They do so by embedding the residues into a high dimensional space that encapsulates the relevant contextual cues. These embedding vectors serve as an informative context-sensitive representation that not only aids with the defined training objective, but can also be used for other tasks by downstream models. We propose a scheme to use the embeddings of an unmasked sequence to estimate the corresponding masked probability vectors for all the positions in a single forward pass through the language model. This One Fell Swoop (OFS) approach allows us to efficiently estimate the pseudo-perplexity of the sequence, a measure of the model's uncertainty in its predictions, that can also serve as a fitness estimate. We find that ESM2 OFS pseudo-perplexity performs nearly as well as the true pseudo-perplexity at fitness estimation, and more notably it defines a new state of the art on the ProteinGym Indels benchmark. The strong performance of the fitness measure prompted us to investigate if it could be used to detect the elevated stability reported in reconstructed ancestral sequences. We find that this measure ranks ancestral reconstructions as more fit than extant sequences. Finally, we show that the computational efficiency of the technique allows for the use of Monte Carlo methods that can rapidly explore functional sequence space.

Lattice ultrasensitivity produces large gain in E. coli chemosensing.

E. coli use a regular lattice of receptors and attached kinases to detect and amplify faint chemical signals. Kinase output is characterized by precise adaptation to a wide range of background ligand levels and large gain in response to small relative changes in ligand concentration. These characteristics are well described by models which achieve their gain through equilibrium cooperativity. But these models are challenged by two experimental results. First, neither adaptation nor large gain are present in receptor binding assays. Second, in cells lacking adaptation machinery, fluctuations can sometimes be enormous, with essentially all kinases transitioning together. Here we introduce a far-from equilibrium model in which receptors gate the spread of activity between neighboring kinases. This model achieves large gain through a mechanism we term lattice ultrasensitivity (LU). In our LU model, kinase and receptor states are separate degrees of freedom, and kinase kinetics are dominated by chemical rates far-from-equilibrium rather than by equilibrium allostery. The model recapitulates the successes of past models, but also matches the challenging experimental findings. Importantly, unlike past lattice critical models, our LU model does not require parameters to be fine tuned for function.

Lattice ultrasensitivity produces large gain in E. coli chemosensing.

E. coli use a regular lattice of receptors and attached kinases to detect and amplify faint chemical signals. Kinase output is characterized by precise adaptation to a wide range of background ligand levels and large gain in response to small relative changes in ligand concentration. These characteristics are well described by models which achieve their gain through equilibrium cooperativity. But these models are challenged by two experimental results. First, neither adaptation nor large gain are present in receptor binding assays. Second, in cells lacking adaptation machinery, fluctuations can sometimes be enormous, with essentially all kinases transitioning together. Here we introduce a far-from equilibrium model in which receptors gate the spread of activity between neighboring kinases. This model achieves large gain through a mechanism we term lattice ultrasensitivity (LU). In our LU model, kinase and receptor states are separate degrees of freedom, and kinase kinetics are dominated by chemical rates far-from-equilibrium rather than by equilibrium allostery. The model recapitulates the successes of past models, but also matches the challenging experimental findings. Importantly, unlike past lattice critical models, our LU model does not require parameters to be fine tuned for function.

E. coli do not count single molecules.

Organisms must perform sensory-motor behaviors to survive. What bounds or constraints limit behavioral performance? Previously, we found that the gradient-climbing speed of a chemotaxing Escherichia coli is near a bound set by the limited information they acquire from their chemical environments. Here we ask what limits their sensory accuracy. Past theoretical analyses have shown that the stochasticity of single molecule arrivals sets a fundamental limit on the precision of chemical sensing. Although it has been argued that bacteria approach this limit, direct evidence is lacking. Here, using information theory and quantitative experiments, we find that E. coli's chemosensing is not limited by the physics of particle counting. First, we derive the physical limit on the behaviorally-relevant information that any sensor can get about a changing chemical concentration, assuming that every molecule arriving at the sensor is recorded. Then, we derive and measure how much information E. coli's signaling pathway encodes during chemotaxis. We find that E. coli encode two orders of magnitude less information than an ideal sensor limited only by shot noise in particle arrivals. These results strongly suggest that constraints other than particle arrival noise limit E. coli's sensory fidelity.

Liquid general anesthetics lower critical temperatures in plasma membrane vesicles.

A large and diverse array of small hydrophobic molecules induce general anesthesia. Their efficacy as anesthetics has been shown to correlate both with their affinity for a hydrophobic environment and with their potency in inhibiting certain ligand-gated ion channels. In this study we explore the effects that n-alcohols and other liquid anesthetics have on the two-dimensional miscibility critical point observed in cell-derived giant plasma membrane vesicles (GPMVs). We show that anesthetics depress the critical temperature (Tc) of these GPMVs without strongly altering the ratio of the two liquid phases found below Tc. The magnitude of this affect is consistent across n-alcohols when their concentration is rescaled by the median anesthetic concentration (AC50) for tadpole anesthesia, but not when plotted against the overall concentration in solution. At AC50 we see a 4°C downward shift in Tc, much larger than is typically seen in the main chain transition at these anesthetic concentrations. GPMV miscibility critical temperatures are also lowered to a similar extent by propofol, phenylethanol, and isopropanol when added at anesthetic concentrations, but not by tetradecanol or 2,6 diterbutylphenol, two structural analogs of general anesthetics that are hydrophobic but have no anesthetic potency. We propose that liquid general anesthetics provide an experimental tool for lowering critical temperatures in plasma membranes of intact cells, which we predict will reduce lipid-mediated heterogeneity in a way that is complimentary to increasing or decreasing cholesterol. Also, several possible implications of our results are discussed in the context of current models of anesthetic action on ligand-gated ion channels.

A bifurcation integrates information from many noisy ion channels.

In various biological systems information from many noisy molecular receptors must be integrated into a collective response. A striking example is the thermal imaging organ of pit vipers. Single nerve fibers in the organ reliably respond to mK temperature increases, a thousand times more sensitive than their molecular sensors, thermo-TRP ion channels. Here, we propose a mechanism for the integration of this molecular information. In our model, amplification arises due to proximity to a dynamical bifurcation, separating a regime with frequent and regular action potentials (APs), from a regime where APs are irregular and infrequent. Near the transition, AP frequency can have an extremely sharp dependence on temperature, naturally accounting for the thousand-fold amplification. Furthermore, close to the bifurcation, most of the information about temperature available in the TRP channels' kinetics can be read out from the timing of APs even in the presence of readout noise. While proximity to such bifurcation points typically requires fine-tuning of parameters, we propose that having feedback act from the order parameter (AP frequency) onto the control parameter robustly maintains the system in the vicinity of the bifurcation. This robustness suggests that similar feedback mechanisms might be found in other sensory systems which also need to detect tiny signals in a varying environment.

Critical Casimir forces in cellular membranes.

Recent experiments suggest that membranes of living cells are tuned close to a miscibility critical point in the two-dimensional Ising universality class. We propose that one role for this proximity to criticality in live cells is to provide a conduit for relatively long-range critical Casimir forces. Using techniques from conformal field theory we calculate potentials of mean force between membrane bound inclusions mediated by their local interactions with the composition order parameter. We verify these calculations using Monte Carlo simulations where we also compare critical and off-critical results. Our findings suggest that membrane bound proteins experience weak yet long-range forces mediated by critical composition fluctuations in the plasma membranes of living cells.