arXiv subjects

Benjamin B. Machta

Publications and source records attributed to Benjamin B. Machta.

At least 19 recordsLinked to original sources

arXiv2026

On the Information Required for Feedback Control

Biological systems across scales, along with many engineering problems, must control noisy systems with limited information. Here we study information-limited feedback control of stochastic systems to achieve target steady states, and derive a lower bound on the information rate from controlled system to controller. This framework allows us to obtain performance-information Pareto frontiers for wide-ranging control problems with limited information. For systems with state-independent passive dynamics, the bound is saturated by an explicit optimal control protocol which probabilistically time-reverses the passive dynamics. We showcase these results through applications to nonlinear particle localization, microbial navigation, and experimentally realized information engines.

cond-mat.stat-mech↗

arXiv2026

Thermal fluctuations set fundamental limits on ion channel function

Voltage-gated ion channels are essential for propagating signals in neurons. Each channel senses the local membrane potential created by nearby ions. Fluctuations in these ions introduce two fundamental noise sources: (i) shot noise, from the discreteness of ionic charge, and (ii) Johnson-Nyquist noise, from long-wavelength thermal fluctuations of the electric field. We show that, for an individual channel, shot noise dominates and sets an intrinsic limit to voltage sensing. On the $10$ $\mu$s timescales relevant to channel gating, this limit corresponds to an accuracy of about $10$ mV -- close to measured channel sensitivities. When signals from many channels are aggregated, Johnson-Nyquist noise eventually overtakes shot noise and bounds the total information that can be sensed from the environment. This transition occurs at an ion channel density of $< 1$ channel/$\mu$m$^2$ for slow signals and around $10^2-10^4$ channels/$\mu$m$^2$ for signals with $10$ $\mu$s timescales, both of which are within the range of experimentally-measured densities for somas and axon initial segments, respectively. These results provide design principles for single-channel architecture and collective sensing and suggest that neuronal computation is ultimately constrained by thermal fluctuations.

physics.bio-ph↗

arXiv2026

In-vivo entropy production of A. subaru

Entropy production is often used as a proxy for energy consumption of a non-equilibrium system. Lower bounds can be estimated from coarse-grained observations, and this has been done for various biological systems. Here, we apply these tools to a more macroscopic system whose true energy consumption is also known. We find that while entropy production does give a lower bound, it is some 25 orders of magnitude away from being saturated. To be certain of this result, we survey different methods of estimating irreversibility, and write down a novel kNN estimator.

physics.bio-ph↗

arXiv2026

On the Analytic Origin of Two Species of Cochlear Eigenmodes

After entering the ear, sound waves propagate as surface waves along the cochlea's basilar membrane. In recent work, we showed numerically that the system supports two types of modes: localized resonant modes, which underpin the modern understanding of cochlear mechanics, and a novel class of spatially extended modes. Here, we develop an analytic framework that explains the emergence of this mode structure. We show that extended modes arise from globally continuous standing-wave solutions, whereas localized modes result from internal resonance requiring matching across a singular point. These results clarify the generic structure of cochlear wave equations.

physics.bio-ph↗

arXiv2026

Discrete turn strategies emerge in information-limited navigation

Navigation up a smooth sensory gradient is one of the simplest behavioural tasks, and some organisms solve it by making continuous adjustments to their course. Bacteria instead employ a variety of discrete strategies, including run and tumble motion, direction reversals, and turns by specific angles. Here we ask what drives the choice of these strategies, framing the problem as maximising up-gradient speed with a given amount of sensory information per unit time. We find that, without directional information on which way to turn, behavioural strategies that take discrete actions perform better than gradual steering. As the amount of information is increased, we see a series of transitions between optimal strategies, including a shift from direction reversals to fully re-orienting tumbles. Among more complex re-orientation strategies, we show that discrete turn angles are best, and observe transitions in the number of angles employed by the optimal strategy. More broadly, such emergent simplicity in behaviour is a tractable example of a widespread phenomenon in which biology chooses a discrete solution, despite the underlying physics being continuous.

physics.bio-ph↗

arXiv2025

Protein-protein interaction networks can be highly sensitive to the membrane phase transition

Many protein-protein interaction (PPI) networks take place in the fluid yet structured plasma membrane. Lipid domains, sometimes termed rafts, have been implicated in the functioning of various membrane-bound signaling processes. Here, we present a model and a Monte Carlo simulation framework to investigate how changes in the domain size that arise from perturbations to membrane criticality can lead to changes in the rate of interactions among components, leading to altered outcomes. For simple PPI networks, we show that the activity can be highly sensitive to thermodynamic parameters near the critical point of the membrane phase transition. When protein-protein interactions change the partitioning of some components, our system sometimes forms out of equilibrium domains we term pockets, driven by a mixture of thermodynamic interactions and kinetic sorting. More generally, we predict that near the critical point many different PPI networks will have their outcomes depend sensitively on perturbations that influence critical behavior.

physics.bio-ph↗

arXiv2025

In-Context Learning can distort the relationship between sequence likelihoods and biological fitness

Language models have emerged as powerful predictors of the viability of biological sequences. During training these models learn the rules of the grammar obeyed by sequences of amino acids or nucleotides. Once trained, these models can take a sequence as input and produce a likelihood score as an output; a higher likelihood implies adherence to the learned grammar and correlates with experimental fitness measurements. Here we show that in-context learning can distort the relationship between fitness and likelihood scores of sequences. This phenomenon most prominently manifests as anomalously high likelihood scores for sequences that contain repeated motifs. We use protein language models with different architectures trained on the masked language modeling objective for our experiments, and find transformer-based models to be particularly vulnerable to this effect. This behavior is mediated by a look-up operation where the model seeks the identity of the masked position by using the other copy of the repeated motif as a reference. This retrieval behavior can override the model's learned priors. This phenomenon persists for imperfectly repeated sequences, and extends to other kinds of biologically relevant features such as reversed complement motifs in RNA sequences that fold into hairpin structures.

cs.LG↗

arXiv2024

High fitness paths can connect proteins with low sequence overlap

The structure and function of a protein are determined by its amino acid sequence. While random mutations change a protein's sequence, evolutionary forces shape its structural fold and biological activity. Studies have shown that neutral networks can connect a local region of sequence space by single residue mutations that preserve viability. However, the larger-scale connectedness of protein morphospace remains poorly understood. Recent advances in artificial intelligence have enabled us to computationally predict a protein's structure and quantify its functional plausibility. Here we build on these tools to develop an algorithm that generates viable paths between distantly related extant protein pairs. The intermediate sequences in these paths differ by single residue changes over subsequent steps - substitutions, insertions and deletions are admissible moves. Their fitness is evaluated using the protein language model ESM2, and maintained as high as possible subject to the constraints of the traversal. We document the qualitative variation across paths generated between progressively divergent protein pairs, some of which do not even acquire the same structural fold. The ease of interpolating between two sequences could be used as a proxy for the likelihood of homology between them.

q-bio.BM↗

arXiv2024

Hair cells in the cochlea must tune resonant modes to the edge of instability without destabilizing collective modes

Sound produces surface waves along the cochlea's basilar membrane. To achieve the ear's astonishing frequency resolution and sensitivity to faint sounds, dissipation in the cochlea must be canceled via active processes in hair cells, effectively bringing the cochlea to the edge of instability. But how can the cochlea be globally tuned to the edge of instability with only local feedback? To address this question, we use a discretized version of a standard model of basilar membrane dynamics, but with an explicit contribution from active processes in hair cells. Surprisingly, we find the basilar membrane supports two qualitatively distinct sets of modes: a continuum of localized modes and a small number of collective extended modes. Localized modes sharply peak at their resonant position and are largely uncoupled. As a result, they can be amplified almost independently from each other by local hair cells via feedback reminiscent of self-organized criticality. However, this amplification can destabilize the collective extended modes; avoiding such instabilities places limits on possible molecular mechanisms for active feedback in hair cells. Our work illuminates how and under what conditions individual hair cells can collectively create a critical cochlea.

physics.bio-ph↗

arXiv2024

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.

q-bio.BM↗

arXiv2024

Chemotaxing E. coli do not count single molecules

Organisms use specialized sensors to measure their environments, but the fundamental principles that determine their accuracy remain largely unknown. In Escherichia coli chemotaxis, we previously found that gradient-climbing speed is bounded by the amount of information that cells acquire from their environment, and that E. coli operate near this bound. However, it remains unclear what prevents them from acquiring more information. Past work argued that E. coli's chemosensing is limited by the physics of molecules stochastically arriving at cells' receptors, without direct evidence. Here, we show instead that E. coli are far from this physical limit. To show this, we develop a theoretical approach that uses information rates to quantify how accurately behaviorally-relevant signals can be estimated from available observations: molecule arrivals for the physical limit; chemotaxis signaling activity for E. coli. Measuring these information rates in single-cell experiments across multiple background concentrations, we find that E. coli encode two orders of magnitude less information than the physical limit. Thus, E. coli chemosensing is limited by internal noise in signal processing rather than the physics of molecule diffusion, motivating investigation of what specific physical and biological constraints shaped the evolution of this prototypical sensory system.

physics.bio-ph↗

arXiv2024

Lattice ultrasensitivity amplifies signals in E. coli without fine-tuning

The E. coli chemosensory lattice, consisting of receptors, kinases, and adaptor proteins, is an important test case for biochemical signal processing. 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 concentration. Existing models of this lattice achieve their gain through allosteric interactions between either receptors or core units of receptors and kinases. Here we introduce a model which operates through an entirely different mechanism in which receptors gate inherently far from equilibrium enzymatic reactions between neighboring kinases. Our lattice model achieves gain through a mechanism more closely related to zero-order ultrasensitivity than to allostery. Thus, we call it lattice ultrasensitivity (LU). Unlike other lattice critical models, the LU model can achieve arbitrarily high gain through time-scale separation, rather than through fine-tuning. The model also captures qualitative experimental results which are difficult to reconcile with existing models. We discuss possible implementations in the lattice's baseplate where long flexible linkers could potentially mediate interactions between neighboring core units.

physics.bio-ph↗

arXiv2024

Protein-DNA Co-condensation is Prewetting to a Collapsed Polymer

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.

physics.bio-ph↗

arXiv2023

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.

physics.bio-ph↗

arXiv2022

Far from Asymptopia

Inference from limited data requires a notion of measure on parameter space, most explicit in the Bayesian framework as a prior. Here we demonstrate that Jeffreys prior, the best-known uninformative choice, introduces enormous bias when applied to typical scientific models. Such models have a relevant effective dimensionality much smaller than the number of microscopic parameters. Because Jeffreys prior treats all microscopic parameters equally, it is 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, leading to unbiased inference in complex models. This optimal prior depends on the quantity of data to be gathered, and approaches Jeffreys prior in the asymptotic limit. However, this limit cannot be justified without an impossibly large amount of data, exponential in the number of microscopic parameters.

stat.OT↗

arXiv2021

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

Complex models in physics, biology, economics, and engineering are often sloppy, 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 the model manifold of predictions, whose coordinates are the model parameters. Its hyperribbon structure 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.

cond-mat.stat-mech↗

arXiv2021

Thermodynamic stability and critical points in multicomponent mixtures with structured interactions

Theoretical work has shed light on the phase behavior of idealized mixtures of many components with random interactions. But typical mixtures interact through particular physical features, leading to a structured, non-random interaction matrix of lower rank. Here we develop a theoretical framework for such mixtures and derive mean-field conditions for thermodynamic stability and critical behavior. Irrespective of the number of components and features, this framework allows for a generally lower-dimensional representation in the space of features and proposes a principled way to coarse-grain multicomponent mixtures as binary mixtures. Moreover, it suggests a way to systematically characterize different series of critical points and their codimensions in mean-field. Since every pairwise interaction matrix can be expressed in terms of features, our work is applicable to a broad class of mean-field models.

cond-mat.stat-mech↗

arXiv2021

E. coli chemotaxis is information-limited

Organisms must acquire and use environmental information to guide their behaviors. However, it is unclear whether and how information quantitatively limits behavioral performance. Here, we relate information to behavioral performance in Escherichia coli chemotaxis. First, we derive a theoretical limit for the maximum achievable gradient-climbing speed given a cell's information acquisition rate. Next, we measure cells' gradient-climbing speeds and the rate of information acquisition by the chemotaxis pathway. We find that E. coli make behavioral decisions with much less than the 1 bit required to determine whether they are swimming up-gradient. However, they use this information efficiently, performing near the theoretical limit. Thus, information can limit organisms' performance, and sensory-motor pathways may have evolved to efficiently use information from the environment.

physics.bio-ph↗