Kinetic Proofreading.

Biochemistry and molecular biology rely on the recognition of structural complementarity between molecules. Molecular interactions must be both quickly reversible, i.e., tenuous, and specific. How the cell reconciles these conflicting demands is the subject of this article. The problem and its theoretical solution are discussed within the wider theoretical context of the thermodynamics of stochastic processes (stochastic thermodynamics). The solution-an irreversible reaction cycle that decreases internal error at the expense of entropy export into the environment-is shown to be widely employed by biological processes that transmit genetic and regulatory information.

ER stress transforms random olfactory receptor choice into axon targeting precision.

Olfactory sensory neurons (OSNs) convert the stochastic choice of one of >1,000 olfactory receptor (OR) genes into precise and stereotyped axon targeting of OR-specific glomeruli in the olfactory bulb. Here, we show that the PERK arm of the unfolded protein response (UPR) regulates both the glomerular coalescence of like axons and the specificity of their projections. Subtle differences in OR protein sequences lead to distinct patterns of endoplasmic reticulum (ER) stress during OSN development, converting OR identity into distinct gene expression signatures. We identify the transcription factor Ddit3 as a key effector of PERK signaling that maps OR-dependent ER stress patterns to the transcriptional regulation of axon guidance and cell-adhesion genes, instructing targeting precision. Our results extend the known functions of the UPR from a quality-control pathway that protects cells from misfolded proteins to a sensor of cellular identity that interprets physiological states to direct axon wiring.

Fundamental behaviors emerge from simulations of a living minimal cell.

We present a whole-cell fully dynamical kinetic model (WCM) of JCVI-syn3A, a minimal cell with a reduced genome of 493 genes that has retained few regulatory proteins or small RNAs. Cryo-electron tomograms provide the cell geometry and ribosome distributions. Time-dependent behaviors of concentrations and reaction fluxes from stochastic-deterministic simulations over a cell cycle reveal how the cell balances demands of its metabolism, genetic information processes, and growth, and offer insight into the principles of life for this minimal cell. The energy economy of each process including active transport of amino acids, nucleosides, and ions is analyzed. WCM reveals how emergent imbalances lead to slowdowns in the rates of transcription and translation. Integration of experimental data is critical in building a kinetic model from which emerges a genome-wide distribution of mRNA half-lives, multiple DNA replication events that can be compared to qPCR results, and the experimentally observed doubling behavior.

Dynamic imaging of nascent RNA reveals general principles of transcription dynamics and stochastic splice site selection.

The activities of RNA polymerase and the spliceosome are responsible for the heterogeneity in the abundance and isoform composition of mRNA in human cells. However, the dynamics of these megadalton enzymatic complexes working in concert on endogenous genes have not been described. Here, we establish a quasi-genome-scale platform for observing synthesis and processing kinetics of single nascent RNA molecules in real time. We find that all observed genes show transcriptional bursting. We also observe large kinetic variation in intron removal for single introns in single cells, which is inconsistent with deterministic splice site selection. Transcriptome-wide footprinting of the U2AF complex, nascent RNA profiling, long-read sequencing, and lariat sequencing further reveal widespread stochastic recursive splicing within introns. We propose and validate a unified theoretical model to explain the general features of transcription and pervasive stochastic splice site selection.

Biosensors based on peptide exposure show single molecule conformations in live cells.

We describe an approach to study the conformation of individual proteins during single particle tracking (SPT) in living cells. "Binder/tag" is based on incorporation of a 7-mer peptide (the tag) into a protein where its solvent exposure is controlled by protein conformation. Only upon exposure can the peptide specifically interact with a reporter protein (the binder). Thus, simple fluorescence localization reflects protein conformation. Through direct excitation of bright dyes, the trajectory and conformation of individual proteins can be followed. Simple protein engineering provides highly specific biosensors suitable for SPT and FRET. We describe tagSrc, tagFyn, tagSyk, tagFAK, and an orthogonal binder/tag pair. SPT showed slowly diffusing islands of activated Src within Src clusters and dynamics of activation in adhesions. Quantitative analysis and stochastic modeling revealed in vivo Src kinetics. The simplicity of binder/tag can provide access to diverse proteins.

A Post-Transcriptional Feedback Mechanism for Noise Suppression and Fate Stabilization.

Diverse biological systems utilize fluctuations ("noise") in gene expression to drive lineage-commitment decisions. However, once a commitment is made, noise becomes detrimental to reliable function, and the mechanisms enabling post-commitment noise suppression are unclear. Here, we find that architectural constraints on noise suppression are overcome to stabilize fate commitment. Using single-molecule and time-lapse imaging, we find that-after a noise-driven event-human immunodeficiency virus (HIV) strongly attenuates expression noise through a non-transcriptional negative-feedback circuit. Feedback is established through a serial cascade of post-transcriptional splicing, whereby proteins generated from spliced mRNAs auto-deplete their own precursor unspliced mRNAs. Strikingly, this auto-depletion circuitry minimizes noise to stabilize HIV's commitment decision, and a noise-suppression molecule promotes stabilization. This feedback mechanism for noise suppression suggests a functional role for delayed splicing in other systems and may represent a generalizable architecture of diverse homeostatic signaling circuits.

Writing, Reading, and Translating the Clustered Protocadherin Cell Surface Recognition Code for Neural Circuit Assembly.

The ability of neurites of individual neurons to distinguish between themselves and neurites from other neurons and to avoid self (self-avoidance) plays a key role in neural circuit assembly in both invertebrates and vertebrates. Similarly, when individual neurons of the same type project into receptive fields of the brain, they must avoid each other to maximize target coverage (tiling). Counterintuitively, these processes are driven by highly specific homophilic interactions between cell surface proteins that lead to neurite repulsion rather than adhesion. Among these proteins in vertebrates are the clustered protocadherins (Pcdhs), and key to their function is the generation of enormous cell surface structural diversity. Here we review recent advances in understanding how a Pcdh cell surface code is generated by stochastic promoter choice; how this code is amplified and read by homophilic interactions between Pcdh complexes at the surface of neurons; and, finally, how the Pcdh code is translated to cellular function, which mediates self-avoidance and tiling and thus plays a central role in the development of complex neural circuits. Not surprisingly, Pcdh mutations that diminish homophilic interactions lead to wiring defects and abnormal behavior in mice, and sequence variants in the Pcdh gene cluster are associated with autism spectrum disorders in family-based genetic studies in humans.

Bursting translation on single mRNAs in live cells.

Stochasticity has emerged as a mechanism of gene regulation. Much of this so-called "noise" has been attributed to bursting transcription. Although bursting transcription has been studied extensively, the role of stochasticity in translation has not been fully investigated due to the lack of enabling imaging technology. In this study, we developed techniques to track single mRNAs and their translation in live cells for hours, allowing the measurement of previously uncharacterized translation dynamics. We applied genetic and pharmacological perturbations to control translation kinetics and found that, like transcription, translation is not a constitutive process but instead cycles between inactive and active states, or "bursts." However, unlike transcription, which is largely frequency-modulated, complex structures in the 5'-untranslated region alter burst amplitudes. Bursting frequency can be controlled through cap-proximal sequences and trans-acting factors such as eIF4F. We coupled single-molecule imaging with stochastic modeling to quantitatively determine the kinetic parameters of translational bursting.

Mechanisms and physiological implications of cooperative gating of clustered ion channels.

Ion channels play a central role in the regulation of nearly every cellular process. Dating back to the classic 1952 Hodgkin-Huxley model of the generation of the action potential, ion channels have always been thought of as independent agents. A myriad of recent experimental findings exploiting advances in electrophysiology, structural biology, and imaging techniques, however, have posed a serious challenge to this long-held axiom, as several classes of ion channels appear to open and close in a coordinated, cooperative manner. Ion channel cooperativity ranges from variable-sized oligomeric cooperative gating in voltage-gated, dihydropyridine-sensitive CaV1.2 and CaV1.3 channels to obligatory dimeric assembly and gating of voltage-gated NaV1.5 channels. Potassium channels, transient receptor potential channels, hyperpolarization cyclic nucleotide-activated channels, ryanodine receptors (RyRs), and inositol trisphosphate receptors (IP3Rs) have also been shown to gate cooperatively. The implications of cooperative gating of these ion channels range from fine-tuning excitation-contraction coupling in muscle cells to regulating cardiac function and vascular tone, to modulation of action potential and conduction velocity in neurons and cardiac cells, and to control of pacemaking activity in the heart. In this review, we discuss the mechanisms leading to cooperative gating of ion channels, their physiological consequences, and how alterations in cooperative gating of ion channels may induce a range of clinically significant pathologies.

Monoallelic expression of olfactory receptors.

The sense of smell collects vital information about the environment by detecting a multitude of chemical odorants. Breadth and sensitivity are provided by a huge number of chemosensory receptor proteins, including more than 1,400 olfactory receptors (ORs). Organizing the sensory information generated by these receptors so that it can be processed and evaluated by the central nervous system is a major challenge. This challenge is overcome by monogenic and monoallelic expression of OR genes. The single OR expressed by each olfactory sensory neuron determines the neuron's odor sensitivity and the axonal connections it will make to downstream neurons in the olfactory bulb. The expression of a single OR per neuron is accomplished by coupling a slow chromatin-mediated activation process to a fast negative-feedback signal that prevents activation of additional ORs. Singular OR activation is likely orchestrated by a network of interchromosomal enhancer interactions and large-scale changes in nuclear architecture.

Activation of Clustered IFNγ Target Genes Drives Cohesin-Controlled Transcriptional Memory.

Cytokine activation of cells induces gene networks involved in inflammation and immunity. Transient gene activation can have a lasting effect even in the absence of ongoing transcription, known as long-term transcriptional memory. Here we explore the nature of the establishment and maintenance of interferon γ (IFNγ)-induced priming of human cells. We find that, although ongoing transcription and local chromatin signatures are short-lived, the IFNγ-primed state stably propagates through at least 14 cell division cycles. Single-cell analysis reveals that memory is manifested by an increased probability of primed cells to engage in target gene expression, correlating with the strength of initial gene activation. Further, we find that strongly memorized genes tend to reside in genomic clusters and that long-term memory of these genes is locally restricted by cohesin. We define the duration, stochastic nature, and molecular mechanisms of IFNγ-induced transcriptional memory, relevant to understanding enhanced innate immune signaling.

Live-Cell Single RNA Imaging Reveals Bursts of Translational Frameshifting.

Ribosomal frameshifting during the translation of RNA is implicated in human disease and viral infection. While previous work has uncovered many details about single RNA frameshifting kinetics in vitro, little is known about how single RNA frameshift in living systems. To confront this problem, we have developed technology to quantify live-cell single RNA translation dynamics in frameshifted open reading frames. Applying this technology to RNA encoding the HIV-1 frameshift sequence reveals a small subset (∼8%) of the translating pool robustly frameshift. Frameshifting RNA are translated at similar rates as non-frameshifting RNA (∼3 aa/s) and can continuously frameshift for more than four rounds of translation. Fits to a bursty model of frameshifting constrain frameshifting kinetic rates and demonstrate how ribosomal traffic jams contribute to the persistence of the frameshifting state. These data provide insight into retroviral frameshifting and could lead to alternative strategies to perturb the process in living cells.

The probability of epidemic burnout in the stochastic SIR model with vital dynamics.

We present an approach to computing the probability of epidemic "burnout," i.e., the probability that a newly emergent pathogen will go extinct after a major epidemic. Our analysis is based on the standard stochastic formulation of the Susceptible-Infectious-Removed (SIR) epidemic model including host demography (births and deaths) and corresponds to the standard SIR ordinary differential equations (ODEs) in the infinite population limit. Exploiting a boundary layer approximation to the ODEs and a birth-death process approximation to the stochastic dynamics within the boundary layer, we derive convenient, fully analytical approximations for the burnout probability. We demonstrate-by comparing with computationally demanding individual-based stochastic simulations and with semi-analytical approximations derived previously-that our fully analytical approximations are highly accurate for biologically plausible parameters. We show that the probability of burnout always decreases with increased mean infectious period. However, for typical biological parameters, there is a relevant local minimum in the probability of persistence as a function of the basic reproduction number [Formula: see text]. For the shortest infectious periods, persistence is least likely if [Formula: see text]; for longer infectious periods, the minimum point decreases to [Formula: see text]. For typical acute immunizing infections in human populations of realistic size, our analysis of the SIR model shows that burnout is almost certain in a well-mixed population, implying that susceptible recruitment through births is insufficient on its own to explain disease persistence.

Deep learning probability flows and entropy production rates in active matter.

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. They involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework to estimate the score of this density. We show that the score, together with the microscopic equations of motion, gives access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles. To represent the score, we introduce a spatially local transformer network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of active particles undergoing motility-induced phase separation (MIPS). We show that a single network trained on a system of 4,096 particles at one packing fraction can generalize to other regions of the phase diagram, including to systems with as many as 32,768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.

Distilling dynamical knowledge from stochastic reaction networks.

Stochastic reaction networks are widely used in the modeling of stochastic systems across diverse domains such as biology, chemistry, physics, and ecology. However, the comprehension of the dynamic behaviors inherent in stochastic reaction networks is a formidable undertaking, primarily due to the exponential growth in the number of possible states or trajectories as the state space dimension increases. In this study, we introduce a knowledge distillation method based on reinforcement learning principles, aimed at compressing the dynamical knowledge encoded in stochastic reaction networks into a singular neural network construct. The trained neural network possesses the capability to accurately predict the state conditional joint probability distribution that corresponds to the given query contexts, when prompted with rate parameters, initial conditions, and time values. This obviates the need to track the dynamical process, enabling the direct estimation of normalized state and trajectory probabilities, without necessitating the integration over the complete state space. By applying our method to representative examples, we have observed a high degree of accuracy in both multimodal and high-dimensional systems. Additionally, the trained neural network can serve as a foundational model for developing efficient algorithms for parameter inference and trajectory ensemble generation. These results collectively underscore the efficacy of our approach as a universal means of distilling knowledge from stochastic reaction networks. Importantly, our methodology also spotlights the potential utility in harnessing a singular, pretrained, large-scale model to encapsulate the solution space underpinning a wide spectrum of stochastic dynamical systems.

A unified framework for perceived magnitude and discriminability of sensory stimuli.

The perception of sensory attributes is often quantified through measurements of sensitivity (the ability to detect small stimulus changes), as well as through direct judgments of appearance or intensity. Despite their ubiquity, the relationship between these two measurements remains controversial and unresolved. Here, we propose a framework in which they arise from different aspects of a common representation. Specifically, we assume that judgments of stimulus intensity (e.g., as measured through rating scales) reflect the mean value of an internal representation, and sensitivity reflects a combination of mean value and noise properties, as quantified by the statistical measure of Fisher information. Unique identification of these internal representation properties can be achieved by combining measurements of sensitivity and judgments of intensity. As a central example, we show that Weber's law of perceptual sensitivity can coexist with Stevens' power-law scaling of intensity ratings (for all exponents), when the noise amplitude increases in proportion to the representational mean. We then extend this result beyond the Weber's law range by incorporating a more general and physiology-inspired form of noise and show that the combination of noise properties and sensitivity measurements accurately predicts intensity ratings across a variety of sensory modalities and attributes. Our framework unifies two primary perceptual measurements-thresholds for sensitivity and rating scales for intensity-and provides a neural interpretation for the underlying representation.

Predicting resilience of migratory birds to environmental change.

The pace and scale of environmental change represent major challenges to many organisms. Animals that move long distances, such as migratory birds, are especially vulnerable to change since they need chains of intact habitat along their migratory routes. Estimating the resilience of such species to environmental changes assists in targeting conservation efforts. We developed a migration modeling framework to predict past (1960s), present (2010s), and future (2060s) optimal migration strategies across five shorebird species (Scolopacidae) within the East Asian-Australasian Flyway, which has seen major habitat deterioration and loss over the last century, and compared these predictions to empirical tracks from the present. Our model captured the migration strategies of the five species and identified the changes in migrations needed to respond to habitat deterioration and climate change. Notably, the larger species, with single or few major stopover sites, need to establish new migration routes and strategies, while smaller species can buffer habitat loss by redistributing their stopover areas to novel or less-used sites. Comparing model predictions with empirical tracks also indicates that larger species with the stronger need for adaptations continue to migrate closer to the optimal routes of the past, before habitat deterioration accelerated. Our study not only quantifies the vulnerability of species in the face of global change but also explicitly reveals the extent of adaptations required to sustain their migrations. This modeling framework provides a tool for conservation planning that can accommodate the future needs of migratory species.

Uncovering the dual role of dimensionless radius in buckling of spherical shells with random geometric imperfections.

Localized deformation and randomly shaped imperfections are salient features of buckling-type instabilities in thin-walled load-bearing structures. However, it is generally agreed that their complex interactions in response to mechanical loading are not yet sufficiently understood, as evidenced by buckling-induced catastrophic failures which continue to today. This study investigates how the intimate coupling between localization mechanisms and geometric imperfections combine to determine the statistics of the pressure required to buckle (the illustrative example of) a hemispherical shell. The geometric imperfections, in the form of a surface, are defined by a random field generated over the nominally hemispherical shell geometry, and the probability distribution of the buckling pressure is computed via stochastic finite element analysis. Monte-Carlo simulations are performed for a wide range of the shell's radius to thickness ratio, as well as the correlation length of the spatial distribution of the imperfection. The results show that over this range, the buckling pressure is captured by the Weibull distribution. In addition, the analyses of the deformation patterns observed during the simulations provide insights into the effects of certain characteristic lengths on the local buckling that triggers global instability. In light of the simulation results, a probabilistic model is developed for the statistics of the buckling load that reveals how the dimensionless radius plays a dual role which remained hidden in previous deterministic analyses. The implications of the present model for reliability-based design of shell structures are discussed.

On the different regimes of stochastic gradient descent.

Modern deep networks are trained with stochastic gradient descent (SGD) whose key hyperparameters are the number of data considered at each step or batch size [Formula: see text], and the step size or learning rate [Formula: see text]. For small [Formula: see text] and large [Formula: see text], SGD corresponds to a stochastic evolution of the parameters, whose noise amplitude is governed by the "temperature" [Formula: see text]. Yet this description is observed to break down for sufficiently large batches [Formula: see text], or simplifies to gradient descent (GD) when the temperature is sufficiently small. Understanding where these cross-overs take place remains a central challenge. Here, we resolve these questions for a teacher-student perceptron classification model and show empirically that our key predictions still apply to deep networks. Specifically, we obtain a phase diagram in the [Formula: see text]-[Formula: see text] plane that separates three dynamical phases: i) a noise-dominated SGD governed by temperature, ii) a large-first-step-dominated SGD and iii) GD. These different phases also correspond to different regimes of generalization error. Remarkably, our analysis reveals that the batch size [Formula: see text] separating regimes (i) and (ii) scale with the size [Formula: see text] of the training set, with an exponent that characterizes the hardness of the classification problem.

Homophily modulates double descent generalization in graph convolution networks.

Graph neural networks (GNNs) excel in modeling relational data such as biological, social, and transportation networks, but the underpinnings of their success are not well understood. Traditional complexity measures from statistical learning theory fail to account for observed phenomena like the double descent or the impact of relational semantics on generalization error. Motivated by experimental observations of "transductive" double descent in key networks and datasets, we use analytical tools from statistical physics and random matrix theory to precisely characterize generalization in simple graph convolution networks on the contextual stochastic block model. Our results illuminate the nuances of learning on homophilic versus heterophilic data and predict double descent whose existence in GNNs has been questioned by recent work. We show how risk is shaped by the interplay between the graph noise, feature noise, and the number of training labels. Our findings apply beyond stylized models, capturing qualitative trends in real-world GNNs and datasets. As a case in point, we use our analytic insights to improve performance of state-of-the-art graph convolution networks on heterophilic datasets.