Biological Cybernetics

Ampullary electroreceptors are widespread across aquatic vertebrates. The purpose of sensing exogeneous electric fields is conserved across species but the implementations differ and the encoding mechanisms remain incompletely understood. We compared baseline and stimulus-driven response properties of ampullary electroreceptor afferents in the weakly electric fish Apteronotus leptorhynchus and Eigenmannia virescens. We find that their activity is well captured by an extended leaky integrate-and-fire model that generalizes across both species. The model shares similarities to a previous model of the tuberous electroreceptor afferents but further incorporates a low-pass pre-filtering and additional noise sources to reproduce the observed spectral response characteristics. The low-pass is essential to shape stimulus encoding in the high-frequency range. Accurate prediction of low-frequency stimulus encoding further requires two distinct noise sources: stimulus-independent white current noise and activity-dependent noise in the adaptation current, which is shaped by the adaptation time constant to yield effective pink noise dynamics. Using simulation-based inference, we trained a neural network to map model parameters to neuronal response features. This approach enables the generation of heterogeneous, biologically plausible model populations that may serve as a realistic input layer for studying neuronal processing on the next level. With this, we provide a unified and mechanistic model of ampullary electroreceptor encoding in these species and possibly beyond.

Length and time constants are foundational to the study of conduction in neurons and other biological cables but are exactly defined only for passive membranes. Here we define and derive exact length and time constants for propagating action potentials in unmyelinated axons. This derivation exploits specific instants during action potential conduction when the net transmembrane ionic current is zero, but axial current remains non-zero. At these instants, we define a curvature parameter,{kappa} , explore its determinants using computer modelling, demonstrate that it is the local real Laplace exponent of the action potential upstroke, and suggest practical approaches for its experimental measurement. From{kappa} , we define action potential length and time constants, {lambda}AP = 1/{surd}({kappa}racm) and {tau}AP = 1/{kappa}, and show that action potential propagation velocity is exactly {lambda}AP/{tau}AP.

Although muscle spindle sensory signals have been extensively studied, little is known about how and why muscle spindle firing is modulated by the central nervous system during movement. Specialized motor neurons to the muscle spindle, i.e. gamma motor neurons, can profoundly alter spindle firing during behavior, but technological limitations hinder our ability to record gamma motor and muscle spindle sensory signals during most behaviors. We used a biophysical model of a muscle spindle within a muscle-tendon unit to simulate how gamma drive may modulate muscle spindle Ia firing during locomotion. Based on a few available recordings from decerebrate animals, we demonstrate that our model, tuned to passive stretch conditions, can reproduce profound changes in muscle spindle firing in response to identical joint motions in locomotor vs. relaxed stretch conditions. Our model can discover phasic patterns of two types of gamma motor neuron drive based on recorded muscle spindle Ia firing and joint motion. By simulating perturbations, we conclude that: 1) sinusoidal activation of static gamma motor neurons during locomotion, encoding intended movement, modulates muscle spindle signals such that they act as sensorimotor feedback signals based on errors from the intended muscle fascicle length; 2) phasic on/off activation of dynamic gamma motor neurons during locomotion acts as an event detector, heightening muscle spindle Ia responses to discrete perturbations. As such, their muscle-within-muscle structure allows the muscle spindle to act as a highly tunable physical internal model of muscle state to guide movement. Our model supports proposed but as-yet-untested theories of muscle spindle function and offers a framework for extending the testing of muscle spindle function to active, behavioral conditions.

Conductance-based models of neuronal excitability depend critically on the mathematical form used to describe voltage-dependent ion channel gating. The classical Hodgkin-Huxley (HH) formalism employs empirically derived rate expressions fitted to squid giant axon data that are not readily transferable across cell types or interpretable in terms of measurable gating properties. Here we introduce a Hill-based reformulation of the HH model in which steady-state sodium and potassium activation curves and the sodium inactivation rate are recast using Hill-type sigmoidal functions, a biologically motivated family widely used to describe cooperative and saturating processes in enzyme kinetics, gene regulation, and receptor binding. Systematic benchmarking against four compact sigmoid alternatives demonstrates that Hill functions provide superior fits to the original HH-derived gating data across all three targets. The resulting hybrid model reproduced canonical spike waveforms and frequency-current behavior, preserving the broad input-output organization of the original model. Importantly, the reformulation linked specific gating parameters to firing regimes and spike features, revealing how shifts in activation, inactivation, and steepness can systematically reshape excitability phenotypes. By making the relationship between channel kinetics and neuronal output more transparent, this framework provides an interpretable route for adapting conductance-based models to cell-specific excitability and channel-dependent changes in neural function.

Biological and robotic systems must solve two related computations to move: inverse dynamics, which determines the forces or torques needed to produce a desired movement, and forward dynamics, which maps applied forces to motion. Although these computations are coupled by the same equations of motion, they are usually estimated or implemented as distinct inverse and forward mappings, in both model-based and data-driven formulations. This separation can obscure the shared structure that constrains both problems. Here, we present ANNet, a physics-informed neural network that places both computations on a common learned representation by learning a single scalar quantity from classical mechanics--Appell acceleration energy. The network maps kinematic state and candidate accelerations to this scalar function, and inverse dynamics is obtained by differentiating the learned energy function with respect to acceleration to recover joint torques. Forward dynamics is then calculated without retraining by embedding the same learned energy landscape in an optimization objective whose unconstrained minimum satisfies the Gibbs- Appell equation. The resulting accelerations are integrated forward in time. We evaluate ANNet on a double pendulum paradigm. In trials unseen by the network during training, inverse and optimization-based forward simulations are real-time accurate. Our results provide a first-principles route for using a single learned representation to support both prediction and control. SignificanceRobots and animals must solve two problems to move: computing the forces or torques needed for a desired motion (inverse dynamics) and determining the motion produced by applied forces (forward dynamics), which are usually modeled separately. We show that both problems can be expressed using a single scalar function from classical mechanics, Appell acceleration energy. A neural network trained so that the derivative of this learned function matches reference joint torques performs inverse dynamics. The same network then computes forward dynamics by minimizing an objective built from the learned energy landscape, without retraining. This framework provides a unified representation for prediction and control in both neuroscience and robotics.

A novel mathematical framework to define the threshold of action potentials in excitable cells is presented. Unlike previously applied methods that rely on approximations or specific fixed-point bifurcations, the approach focuses on the geometry of membrane potential trajectories. Specifically, the focus is on the concavity changes during the upstroke of an electrical pulse. These changes in concavity form a curve of inflection points that defines a region in phase space crossed by all the action potentials in the system, and containing no non-action potential trajectories. Such region is called the excitability region and its size can be measured, thus providing a measure for the excitability of a dynamical system, and a way to compare the excitability between systems representing different biological phenotypes and stimulus conditions. The work transforms the traditionally vague physiological concept of excitability into a rigorous analytical description applicable across continuous, single compartment models of electrical excitability.

Dopaminergic signalling is central to value learning and decision making. It has been observed that multiple pathways with different patterns of connectivity project to midbrain dopaminergic neurons, some involving direct excitatory projections while others involve disinhibition. However, the respective contributions of these patterns to dopamine control, and their computational and functional advantages remain unclear. In the current work we simulate and evaluate two fully spiking neural models of dopaminergic control, based either solely on disinhibition, or solely on direct inhibitory and excitatory projections. We compare these models in terms of their engineering properties, their resulting spiking profiles, and their ability to successfully acquire representations of expected value in a 3-armed bandit task. We find that both models are able to operate at an asynchronous-irregular firing regime, but that the firing profile of the direct integration model is less resilient to disruption and more sensitive to incoming signals. In addition, the disinhibition model performs better in the learning task. We conclude that while the direct model is more parsimonious, disinhibition-based control remains advantageous in the operational context. Our results have implications for the study of decision-making brain circuits as well as for the design of brain-inspired systems.

In many brain regions, the stimulus tuning of neurons is stable on a timescale of hours but not on a timescale of weeks, a phenomenon often called representational drift. This would seem to imply that these brain regions cannot be used for stable recognition of sensory stimuli or the retrieval of associative memories learned several weeks prior. However, decoding approaches have demonstrated that in some cases, stable decoding of drifting representations is possible. In principle, adaptive decoding provides a plausible resolution to the paradox of how the brain operates with drifting representations, but we lack a deep understanding of what the requirements are for stable decoding to be possible. Here, we offer a general mathematical framework that explains when and why stable decoding from a drifting representation can be achieved. First, we demonstrate that both feedforward and recurrent networks preserve the geometry of their inputs when the network is sufficiently large, meaning that representational drift must also preserve geometry in these networks. Second, we demonstrate that drifting representations that have stable geometry are decodable with adaptive decoders. Therefore, not only the existence of preserved geometry in the presence of representational drift but also the ability to decode from drifting representations simply requires the population of neurons exhibiting representational drift to be large. This theoretical framework not only suggests that preserved geometry should be a general feature of drifting representations, it also explains the conditions under which empirical efforts to measure stable geometry will be successful.

Predictions of skeletal muscle energy consumption under a diverse range of muscle contractile conditions are critical for improving our understanding of locomotion. Existing mathematical models, while capturing the mechanical dependence of energy consuming processes, neglect the time-dependent behaviour and recovery costs associated with regenerating ATP. This time-dependence is important for predicting the energetic response of muscles during repetitive or cyclical tasks like locomotion, where muscle undergoes many contraction cycles. This study presents a novel model to predict energetic rates based on physiological processes: Ca2+ transport costs, cross-bridge cycling costs, and ATP regeneration. Previous mathematical models include the dependence on Ca2+ transport and cross-bridge cycling, but neglect the time-dependent response and the subsequent recovery of ATP following the contraction. Model parameters were obtained from existing data on isolated muscle preparations, and predicted energetic rates were validated on separate datasets across a range of contractile conditions including dynamic, sub-maximal, and twitch contractions. The time-dependent model was able to capture the influence of contraction frequency on peak energetic rates and the time-course of energetic recovery observed experimentally. The model captures key physiological processes while maintaining a minimal number of free parameters and low computational cost. This enables generalisability across muscles and species, and implementation into larger scale musculoskeletal models.

The cross-correlation model has long served as the standard computational framework for describing interaural time difference (ITD) processing in the barn owls auditory system. While successful in explaining initial sinusoidal responses at the site of coincidence detection in the nucleus laminaris, this previous standard model fails to capture the full diversity of ITD tuning observed in the inferior colliculus (IC), where neurons exhibit sharper-than-sinusoidal ITD tuning, nonlinear frequency integration, level-dependent gain control, and interaural level difference (ILD)-dependent modulation of ITD selectivity. Here we present a modified cross-correlation model that addresses these limitations through the addition of parameterized gain control, linear filters with inhibitory surround structure, static nonlinearities, and ILD-dependent modulation of the cross-correlation computation. We show that divisive gain control produces realistic rate-level functions, including non-monotonic responses. Furthermore, inhibitory weights in the linear filter, combined with a threshold or expansive nonlinearity, generate sharper-than-sinusoidal ITD tuning consistent with experimental observations. This model reproduces both linear and nonlinear two-tone frequency integration and demonstrates that independent variation of filter bandwidth and nonlinearity shape accounts for the experimentally observed lack of correlation between side-peak suppression and frequency tuning width across the neuronal population. In addition, ILD-dependent modifications to the model produce shifts in best ITD and reductions in ITD tuning strength, as observed in the lateral shell of the central nucleus of the IC. The model parameters can be efficiently determined using simulation-based inference, enabling generation of realistic neuronal populations. Thus, this flexible, analytically tractable framework provides a foundation for investigating population coding of auditory space in the owls midbrain.

Seamless interaction between humans and machines requires interfaces that remain robust to the variability inherent in biological signals and physical environments. Advanced human-machine interfaces (HMIs) increasingly rely on machine learning to predict or control limb dynamics. These systems must learn input-to-output mappings between control variables and limb state, such as the mapping from muscle forces or joint torques acting about segmented arm joints to limb posture over time. Such statistical input-to-output transformations can result in numerical instability of predicted musculoskeletal kinematics and dynamics. Achieving the robustness of biological motor control requires solving both forward and inverse dynamics problems; however, these problems are computationally asymmetric because they entail opposing operations-integration and differentiation. Since we have previously shown that neural networks solve the inverse dynamics problem when trained to map kinematic to dynamic signals during reaching, we hypothesized that representing separately the approximation of equations of motion (EOM) and their temporal numerical integration may capture the relevant computational structure of the forward dynamics problem. We tested this hypothesis by comparing a conventional direct-mapping recurrent neural network (RNN) with a two-stage model, the artificial physics engine (APE). When predicting the state of a two-segment system under external perturbations not encountered during training, the direct-mapping, monolithic model produced large prediction errors inconsistent with the expected interaction torque, whereas the APE maintained low error and remained stable under novel initial conditions and perturbations. Mapping system dynamics in the terms of the EOM improves robustness against intrinsic and extrinsic sources of variability by imposing a causal, physics-based structure on HMI design.

Rhythm is a key building block of human music, speech and numerous other human activities. Understanding the computational substrates of rhythm perception requires models that bridge algorithmic function with biological implementation. We propose a physiologically grounded spiking neural network (SNN) framework to investigate the emergent representation and interpretation of auditory rhythms. Utilizing a recurrent SNN architecture trained on an auditory entrainment task, we characterize the networks latent dynamics through the analysis of firing rates and membrane potential fluctuations. Our results demonstrate that simulated neural populations exhibit phase-locking to the stimulus beat, with endogenous oscillations driven by rhythmic input. We further show that anticipatory dynamics--characterized by pre-stimulus depolarization--emerge naturally from the networks synaptic plasticity and temporal integration properties, rather than from explicitly defined oscillators. By treating network layers as functional analogs of cortical populations, this framework allows for the application of spectral and information-theoretic analyses typical of empirical electrophysiology. More in general, this approach establishes SNNs as robust exploratory tools for uncovering how predictive coding and rhythmic entrainment arise from the inherent constraints of biological neural computation.

Stabilizing synaptic plasticity together with the neurons activity has remained a central challenge in theoretical neuroscience since the introduction of Hebbian learning principles. Classical Hebbian learning rules typically lead to unbounded synaptic growth, motivating the development of stabilization mechanisms such as normalization methods, BCM-type learning, synaptic scaling and others. While these approaches can prevent divergence, they can also exhibit different limitations e.g. resulting in too-sparse synaptic configurations or leading to poor scalability with increasing network size. A recently introduced meta-plasticity mechanism, termed annealed linear learning (ALL), dynamically reduces the learning rate as neuronal output increases, thereby preserving stable and interpretable fixed-point behavior of the output. However, the original formulation leads to an irreversible decay of the learning rate, preventing adaptation to changing environmental conditions. To address this, in the present study, we balance learning rate reduction at large outputs with recovery at small outputs and in addition introduce forgetting that gradually reduces synaptic weights. These extensions allow the system to discard outdated representations and adapt to novel input conditions. Analytical investigations demonstrate that the favorable output fixed-point properties of the original ALL framework are preserved under the extended rule. Furthermore, simulations with an artificial agent show that the proposed mechanism enables robust and fast re-learning and adaptation in changing environments.

Segregation of speech into syllables is a key step in neural speech processing. It relies on the alignment of neural activity with the rhythmic structure of speech. Two competing hypotheses explain this neural speech tracking, phase-resetting and evoked responses. While phenomenological modelling of these hypotheses has been successful, we still lack understanding of the underlying cortical circuits. To investigate these mechanisms, we evaluate whether a biophysical next-generation neural mass model can reproduce several features of neural speech tracking, using phenomenological models of the competing hypotheses as algorithmic baselines. We investigate the models dynamics with four tests: recreating in-silico an EEG experiment that identified a correlation between tracking strength and phoneme sharpness, computing the Phase Concentration Metric, testing the effect of varying syllabic rates, and evaluating the Inter Event Phase Coherence across phoneme onsets. While all of the models that we study reproduce the sharpness-tuned rhythmic speech tracking, the evoked model requires a pre-processed acoustic edge impulse stimulus. We demonstrate that the neural mass model is performing thresholded phase-resetting triggered by sharp onsets in the continuous speech envelope. This produces cross-frequency nested oscillations that qualitatively match an experimentally-observed dual-peak signature in the Inter Event Phase Coherence. Our results indicate that the biophysical neural mass model provides a mechanistic bridge between generic oscillatory dynamics in cortical populations and the cognitive computations of speech tracking. Indeed, the non-linear dynamics of the neural mass model offer an explanation for how peak-rate event representations in auditory cortex activity arise in response to continuous acoustic input. Significance StatementSyllable segregation is crucial but challenging as natural speech lacks clear boundaries, yet humans perform this computation effortlessly. Speech aligns neural activity to syllabic rhythms, predicting syllable timing, but the underlying cortical mechanisms remain unknown. Relating this macroscopic behaviour to neurobiology is challenging; however, next-generation neural mass models promise to resolve this. We demonstrate that these models reproduce sharpness-tuned tracking and acoustic edge extraction. Dynamical analyses indicate this occurs through thresholded phase-resetting to phoneme onsets, triggering cross-frequency nested oscillations. Our results both advance biophysical understanding of syllable segregation and validate the models capacity for simulating macroscopic neural activity. These models offer a bridge between the neurobiology of the auditory cortex and speech processing dynamics that phenomenological models cannot provide.

The learning dynamics of biological brains and artificial neural networks are of interest to both neuroscience and machine learning. A key difference between them is that neural networks are often trained from a randomly initialized state whereas each brain is the product of generations of evolutionary optimization, yielding innate structures that enable few-shot learning and inbuilt reflexes. Artificial neural networks, by contrast, require non-ethological quantities of training data to attain comparable performance. To investigate the effect of evolutionary optimization on the learning dynamics of neural networks, we combined algorithms simulating natural selection and online learning to produce a method for evolutionarily conditioning artificial neural networks, and applied it to both reinforcement and supervised learning contexts. We found the evolutionary conditioning algorithm, by itself, performs comparably to an unoptimized baseline. However, evolutionarily conditioned networks show signs of unique and latent learning dynamics, and can be rapidly fine-tuned to optimal performance. These results suggest evolution constitutes an inductive bias that tunes neural systems to enable rapid learning.

Temperature influences neuronal and circuit output and extreme temperatures can disrupt neuronal performance. Acclimation invokes a form of neuronal plasticity that we call robustness tuning, that preserves nervous system performance during seasonal alterations in environmental conditions. The stomatogastric nervous system (STNS) of the American lobster, Homarus americanus, produces stereotyped rhythmic motor patterns that are maintained over a range of acute temperature changes, but lost under more extreme conditions. In the wild, H. americanus experience water temperatures from [~]2{degrees}C to 25{degrees}C during the course of a year. We acclimated lobsters to 18{degrees}C versus 4{degrees}C for [~]3 weeks, and found that the pyloric rhythm from warm-acclimated animals maintained its characteristic properties over an extended temperature range, when compared to those recorded from cold-acclimated animals. There were acclimation and temperature dependent differences in the responses of pyloric neurons to the neuropeptide, Crustacean Cardioactive Peptide (CCAP). Computational models suggest that pyloric neuron morphology and neuromodulator conductance distribution play a role in robustness tuning, the reversible changes that allow animals to repeatedly adapt to seasonal change.

AO_SCPLOWBSTRACTC_SCPLOWThere is a gap between neuroscientific theories of learning and the speed of learning observed in many experiments. Since the Cognitive Revolution of the 1950s, compositionality has played a central role in efforts to bridge this gap. Roughly, a compositional system is one where distinct modules are combined according to a set of rules in order to accomplish complex tasks. Recently, significant progress has been made in understanding the emergence of modules in both biological and artificial neural systems. How, and under what conditions, the rules of module recombination are represented in these systems remains an open question. Here we present a neural model that can leverage these rules to dramatically speed up learning. We first show that when faced with multiple tasks which share subcomponents, models learn a low-dimensional representation that captures how subcomponents are reused across the task set. These low-dimensional spaces encode the structure that governs how modules should be recombined. Restricting learning to these subspaces greatly reduces the amount of experience needed to acquire a novel task, even when learning from reinforcement on single trials. In some cases, we can leverage the geometric regularities of these representations to reduce learning to a form of hypothesis testing over a small set of discrete points. Finally, we use this theory to model both behavioral and neural data from non-human primates performing a compositional task, and show that key features in this data are consistent with a model in which exploration during learning is restricted to these low-dimensional spaces. Overall, this work shows that the advantages of modularity in neural systems can be greatly improved upon when models represent the structure of module reuse. Both these features working in tandem lead to learning on timescales similar to biological intelligences, and hence provide a model for how such fast, adaptable behavior can emerge from systems of neurons.

The phenomenon of splitting was originally observed in hamsters which, after prolonged exposure to constant light, exhibit two rest/wake cycles within a subjective day. Splitting is a consequence of the left and right suprachiasmatic nuclei (SCN) falling out of synchrony. While it is known that split activity is characterized by an antiphase relationship between the left and right SCN and between the core and shell within each hemisphere, the role of the commissural projections that connect the right and left SCN is not known. In the present study, we investigate the impact of the inter-hemispheric connections on the split and unsplit dynamics of a computational model of the bilateral SCN. Our model has 4 nodes corresponding to each right and left core and shell. We simulated our bilateral model under different lighting conditions and measured its period and the phase relationships among the 4 nodes. To further characterize the dynamics of the system, we performed a bifurcation analysis. We found that the bilateral model automatically splits unless entrained by bright light/dark cycles, or unless it has excitatory inter-hemispheric connections. This suggests that excitatory cross-connections may be important for freerunning behavior. We found that constant light of varying intensities transitions the model between split and unsplit activity only in very limited conditions, but the strength and polarity of the contralateral connections play a much greater role in this dynamical transition. These findings suggest that splitting may involve plasticity of the inter-hemispheric connections of the SCN.

Strongly interconnected neuronal populations, called assemblies, dynamically form through synaptic plasticity mechanisms and are thought to be a substrate for memories in the brain. Many assembly formation models use Hebbian excitatory-to-excitatory plasticity, where coordinated activity strengthens recurrent structure. However, these models typically yield binary assembly outcomes: networks with either weak (no assembly) or maximally strong (assembly) connectivity. We consider networks with a combination of Hebbian excitatory-to-excitatory plasticity and inhibitory-to-excitatory synapses with plasticity that homeostatically stabilizes excitatory neuron firing at a target value. When we set excitatory-to-excitatory plasticity to be homeostatically compliant, in that potentiation and depression are balanced at the homeostatic target firing rate, we find a stable continuum of synaptic strengths, and assembly structure is no longer binary. We use a recurrent network of spiking neuron models and an associated mean-field theory to identify this continuum as a line attractor in synaptic weight space. While along the attractor, homeostasis ensures that neuronal firing rates are invariant, the dynamical response properties of the network are quite malleable, with strongly coupled networks having high gain and longer timescale responses. Using our mean-field theory we show how correlated stochastic spiking activity among the excitatory neurons can destroy the line attractor, yet this can be mitigated when correlated inputs are shared across the excitatory and inhibitory neurons. Altogether, we provide a learning framework based on homeostasis, where a tunable and flexible assembly structure is possible.

Neuronal computation depends on the balance between excitation and inhibition, yet how this balance is implemented across the dendritic tree remains unclear. Classical views predict that inhibition should be most effective near the soma or along the path from excitation to output, but many interneuron subtypes preferentially target remote dendritic compartments. This apparent paradox is sharpened by active dendrites, where local NMDA spikes, calcium plateaus and backpropagating action potentials can make distal branches powerful contributors to somatic firing. Here we develop an analytical framework that extracts general principles of inhibition from biophysically detailed multi-compartment simulations. By reformulating the implicit voltage update of detailed neuron models as a matrix recursion, we derive exact voltage sensitivities to inhibitory synaptic perturbations. This leads to a unified {Phi}-a law: the somatic impact of inhibition factorizes into a global dendritic susceptibility term and a local synaptic perturbation term. Using this law to map inhibitory leverage and identify optimal inhibitory interventions, we show that active dendritic excitation can shift inhibitory hot zones from perisomatic regions toward distal or intermediate compartments. Across neocortical, hippocampal and striatal neuron models, the same response law explains convergent inhibitory strategies despite distinct cellular mechanisms. Our framework turns detailed numerical simulation into analytical theory, providing a general principle for how diverse dendritic inhibition controls active neurons.