Biological Cybernetics

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 bifurcations, the approach focuses on the geometry of membrane potential trajectories. The changes in concavity during the upstroke of an action potential can be directly obtained from a time series of voltages. The concavity criterion is then extended to models based on autonomous dynamical systems where the changes in concavity can be obtained analytically from a curve of inflection points in phase space. The inflection point manifold defines a region required for excitability: all the orbits that cross it contain action potentials, and all the trajectories that contain action potentials are in it. This analytical principle can then be used to define excitability in a dynamical system, and also a measure of excitability that enables quantification and comparisons of excitability across dynamical system. The measure provides a way to compare the excitabilities of systems that model neurons with different electrophysiological phenotypes and consider different stimulus conditions. The traditionally vague physiological concept of electrical excitability is transformed into a rigorous analytical description by considering the time-dependent curvature of the membrane potential. The criterion is robust across smooth, single compartment models of electrical excitability and can be can be extended to single compartment models in higher dimensions, and multicompartment models as well.

Animals use long-range signals, such as hormones and neural signals, to coordinate the actions of distant organs. There is no precise, quantitative framework that explains the problems these control systems must solve and thus predicts their behavior under varied conditions. We consider this problem in the context of blood glucose regulation by the hormone insulin, the failure of which produces diabetes. We show that existing mathematical models of glucose regulation admit equivalent control strategies with no hormones at all, and thus cannot explain the need for hormonal regulation. We therefore introduce a minimal model of inter-organ variations in local glucose, and show that control strategies based on local glucose measurements face severe trade-offs between different control objectives. In contrast, we show that hormonal control signals from the pancreas can overcome these limitations. By exposing the benefits of hormonal control, our work paves the way to a detailed understanding of physiological design principles, with possible implications for the engineering of an artificial pancreas.

Pacemaking neurons, often found in mammalian nervous systems, integrate their inputs differently than quiescent neurons. Rhythmic single-spike pacemaking that is robust to noise can be achieved with a slow process that enforces a "resting potential" at each point along a ramp-like interspike interval (ISI) coupled with a fast restorative component. To demonstrate this phenomenon, we modeled previously identified distinct subpopulations of midbrain dopamine neurons that differed in projection target and in the regularity of their pacemaking. In the model of the more regularly-firing subpopulation projecting to the dorsomedial striatum, KV4 current was recruited by a deep after-hyperpolarizing potential (AHP) mediated by the SK channel. In the model of the less regularly-firing subpopulation projecting to the medial shell of the nucleus accumbens, the AHP was too shallow to recruit the KV4 current. In the more regularly firing population, the trajectory in the phase space of membrane potential and slow inactivation of KV4 was confined to move slowly through a narrow channel during the ramp-like portion of the ISI. Noisy perturbations from this channel were quickly damped by fast activation of KV4. In contrast, the smaller AHP in the model of the subpopulation projecting to the medial shell of the nucleus accumbens failed to recruit Kv4-mediated current, therefore the narrow channel was never entered, greatly decreasing the regularity in the presence of noise. This mechanism may be broadly applicable to single-spike pacemakers and explains how slow pacemaking with small net currents can be robust to fluctuations in single channel openings. Author SummaryPacemaking cells spike at regular intervals without the need for external input. There are numerous examples of pacemaking cells in the nervous system. We show that a process with slow dynamics relative to the individual spikes can make regular pacemaking robust to the noise that is always present in biological systems.

This study presents improvements to the Hodgkin-Huxley (HH) models of ionic conductance and action potential generation. Sodium and potassium conductances are expressed by a single analytical formula describing the impulse response of a convolution of exponential distributions within a short-memory integration space. Treating transmembrane ion transit duration as a random variable, conductance profiles are interpreted as realizations of the probability density functions governing ionic movements. Applying the central limit theorem, the lognormal distribution emerges as the asymptotic profile of ionic conductances, constituting a fundamental primitive for such biosignals. A temporal state-transition paradigm describes the action potential waveform through four successive membrane potential transitions. Applied to electrophysiological recordings from lamprey reticulospinal neurons, this framework enables indirect estimation of key physiological quantities, including depolarization threshold, Nernst potentials, and net ion fluxes across the membrane. These advances open new perspectives for parameter estimation from experimental data and neuronal network simulation.

With 302 neurons and a rigorously characterized connectome, the nematode Caenorhabditis elegans represents a powerful model organism to study the fundamental roles of neuronal circuits in behavior. However, despite the breadth of research, many questions remain unanswered regarding how these organisms are able to successfully navigate their environment. Here, we present a biologically grounded dynamical circuit model for the investigation of sensory-guided behavior during C. elegans chemotaxis. Our mathematical model consists of the chemosensory neuron AWA, interneurons RIM and RIA, motor neurons, including SMDs and RMDs, and body wall muscles that provide proprioceptive feedback through stretch receptors. After optimization with an evolutionary algorithm, the model locomotes effectively toward a chemical attractant, realistically capturing nematode chemotactic behavior. Chemotaxis is ensured by sharp turns, which resemble the omega turns of living nematodes, as a key emergent property of the model. The sharp turning behavior is triggered by decreases in the concentration of the attractant. These result in reduced AWA activity, which in turn triggers disinhibition of RIM and subsequent changes in RIA oscillations. The ensuing coordinated changes in downstream motor neurons activity patterns produce sharp turns, which correct the nematodes path, so that the model worm heads toward the attractant, and remains at its proximity, after it reaches the gradient peak. The proposed framework, along with its emergent dynamics, provides new insights into the minimum requirements for C. elegans circuitry to display major features of its chemotactic behavior, including omega turns. In parallel, it generates experimentally testable hypotheses with respect to the participating neuronal elements.

Neural temporal point processes (NTPPs) are powerful tools for modeling sequences of timestamped events with statistical temporal structure. Density-based NTPPs, in particular, are an interesting opportunity to merge the universal function approximation capability of neural networks with a defined statistical model in a way that has many potential applications. We demonstrate one such application to heartbeat dynamics, a physiologic point process. We specifically apply a lognormal mixture NTPP to compute instantaneous estimates of the mean and standard deviation of beat-to-beat intervals. We compare our results to the state of art (Barbieri et al.) point process model for heartbeat dynamics, which uses a more physiologically rigorous inverse Gaussian model. We find that the NTPP model maintains reasonable accuracy while improving upon robustness to noise.

This paper introduces a sensorimotor learning framework for a corticocerebellar network, grounded in the perspective of population dynamics. Using an optimal control theory approach, the cerebellum model enhances preparatory activity through premotor input, allowing the motor cortex to reach the desired initial conditions for movement more efficiently. Unlike traditional motor learning approaches that focus on acquiring new skills, this paradigm emphasizes automatization of already executable behaviors through repetition driven by intrinsic motivation. The proposed model is evaluated using a center-out reaching task, demonstrating that the role of the cerebellum is to shorten the preparatory period required for the successful execution of the movement. These findings suggest that corticocerebellar interactions play a crucial role in optimizing motor preparation, offering insight into the neural mechanisms underlying movement efficiency.

Classical neurogeometric models describe the primary visual cortex as a fibered structure in which retinal position and local orientation are coupled through the geometry of the roto-translation group. We extend this approach to the visuomotor cortex by modeling it as an assemblage of visual and motor cortical geometries. The model combines orientation-selective representations, analogous to those of the primary visual cortex, with movement-direction-selective representations, analogous to those of the primary motor cortex, in order to describe the mixed visual and motor selectivity observed in the visuomotor cortex. We introduce a coupled visuomotor structure in which visual orientation and motor direction coexist over a common spatial plane and interact through a relative-orientation constraint. Neural responses are modeled by orientation- and direction-dependent profile functions, and preference maps are obtained from vectorized population responses. Numerical simulations generate visual, motor, and mixed visuomotor response maps. A competition rule between visual and motor responses produces incidence ratios close to experimental observations in macaque visuomotor cortex. This framework provides a first neurogeometric approximation of visuomotor functional architecture and a mathematical setting for studying visually guided action.

Action-selection is determined by a combination of goal-directed and habitual processes. Habits are defined as the reward-independent, stimulus-response relationships which form when an action is regularly executed in the same context, regardless of outcome. An influential computational model proposes that habit formation is driven by action prediction errors which occur when non-habitual actions are taken. It has been further suggested that action prediction errors are encoded in activity of specific dopamine neurons, and it has been recently observed that dopamine activity in the tail of the striatum follows a pattern consistent with the action prediction errors. However, the original models capture changes in habits across trials, but do not describe the time-course of action prediction errors within trials, hence it is difficult to directly compare them with dopamine activity. We begin by outlining the temporal-difference action learning algorithm, which uses biologically-plausible mechanisms to determine how dynamic changes in action intensity influence the resultant prediction errors across near-continuous time. We then demonstrate that dopaminergic data recently collected from the tail of the striatum is better represented by action prediction errors than reward prediction errors. Overall, our results support the existence of value-free action prediction errors and associated habitual behaviour in dopaminergic signals. Author summaryWhenever we choose one action over another, there are two ways that the selection can be made. We could take the time to consider what we want to achieve, calculate which action is the most likely to give us that outcome and balance it against the possible negative consequences. These goal-directed calculations are very time-consuming and our brains could not possibly do it for every choice. Instead, we often rely on the second method, habits, which learn to copy the actions that were most often chosen in the past. In this paper, we present a new model of learning that is based on biologically plausible brain networks and applies action prediction errors to update our habits across continuous time. Using simulations, we reveal testable predictions that are specific to our temporal-difference action learning model and build an intuition for its behaviour. Finally, this model is tested against real dopaminergic data from the tail of the striatum, and we show that our model provides better explanation for these data, than classic reward-based reinforcement learning models.

Biological neurons can perform nonlinear computations within their dendrites and support branch-localized plasticity. This raises the possibility that single cells can store memories more efficiently and with less interference by confining synaptic modifications to specific dendrites. We study a parallel-dendrite model performing online familiarity detection and compare three dendrite-update rules during learning: (i) independent thresholding, (ii) an interacting rule that adapts the target local dendritic activation per item, and (iii) an interacting n-winners-take-all (WTA) rule that constrains the number of updated branches per item. The interacting rules substantially improve capacity by limiting variance in memory responses and decorrelating weights across branches -- even when inputs are strongly correlated. These results suggest that competition among dendrites, consistent with resource-limited plasticity mechanisms, can enhance single-cell memory beyond non-interacting schemes.

Determining the amount of information a neuron receives per unit of time is key to understanding brain connectivity and how neural networks encode and transmit information. In particular, estimating this information flow by distinguishing between excitatory and inhibitory synaptic contributions is critical to understanding neural network function, as maintaining the excitation-inhibition (E/I) balance regulates neuronal excitability and circuit stability, whereas its disruption can lead to a plethora of brain disorders, including neurodegenerative and psychiatric conditions. However, because synaptic conductances cannot be measured directly, inverse methods are required to infer them from the membrane potential --a readily measurable quantity. Although partial solutions have been proposed, accurately estimating these conductances remains a significant challenge due to the complexity and diversity of the inputs. This is particularly true in the spiking regime, where neurons actively fire. In this work, we introduce a novel computational strategy that combines two critical metrics extracted from the time course of the membrane potential recording: the amplitude of the spike and the interspike interval. By using these quantities, the proposed method enables the accurate separation of excitatory and inhibitory contributions, yielding highly favorable results in the spiking regime. Author summaryQuantifying the continuous stream of inputs a neuron receives is key to understanding brain connectivity. Inside the brain, individual cells must maintain a tight balance between excitation and inhibition (E/I) to process information correctly, as any disruption in this equilibrium can impair its functionality. However, directly measuring the underlying excitatory and inhibitory synaptic conductances is technically challenging, and existing mathematical tools often fail when neurons enter their active firing regime. In this work, we introduce a novel computational strategy designed to extract and separate these time-varying conductances directly from the neurons spiking activity. By dynamically tracking just two accessible metrics - the amplitude of the spikes and the time intervals between them - our algorithm estimates both conductance profiles with high precision. Furthermore, we demonstrate that this procedure is highly robust against realistic experimental noise and data variability, providing an accessible framework that does not require complex hardware or an unfeasible number of repetitive experimental trials. By tracking changes in the E/I ratio of the synaptic input, this method provides an efficient approach to detecting pathological imbalances and understanding how local connectivity shapes cellular functionality.

Scaling laws help determine the optimal data size for training large models but are established in domains where the target is deterministic. Physiological signals are different: heartbeat sequences are stochastic, so part of the error is irreducible even with large amounts of data. Metrics such as MAE do not account for non-deterministic behavior, and therefore assessing scaling requires evaluating distributional calibration (measuring how well predicted probability densities capture true conditional characteristics). We formulate a scaling law metric(n) = E + A n- and evaluate it with five metrics: accuracy (MAE, RMSE), distributional calibration (KS distance, goodness-of-fit), and training objective (negative log loss) using a neural temporal point process trained on a cohort of four-ECG datasets. The law fits all five metrics. While point accuracy is near saturation at n = 183, KS distance and goodness-of-fit improve by 6% and 12% respectively when extrapolated to 10,000 subjects, showing that scaling decisions in stochastic domains must be guided by distributional calibration rather than point accuracy.

Motor systems controlling locomotion must generate repetitive rhythmic activity, while also still retaining the ability to generate a diverse range of outputs. How motor systems monitor, regulate, and promote diversity of their own outputs is not well understood. Here, we perform single-step, variable-order and hidden-state Markov modelling (HSMM) on spontaneous fictive locomotor activity in the isolated Drosophila larval nervous system to examine how a motor system balances constraint and promotion of diversity amongst competing motor programs. We show that spontaneous fictive activity is structured by interacting mechanisms operating at multiple levels of sequence organisation. Analysis of one-step transition rules revealed a bias in activity towards activity states underlying exploration that in turn, promote transition to diverse outputs. In contrast, higher-order Markov, N-gram, and HSMM analysis indicated a memory biased towards revisiting recently executed motor programs. These mechanisms together suggest that the Drosophila larval locomotor system maintains a dynamic repertoire of possible motor outputs by monitoring recent activity and biasing future transitions accordingly. In this sense, fictive rhythmogenesis reflects a diversity-generating process: the larval locomotor network does not simply repeat a fixed motor programme or randomly transition from one state to another, but rather continually regulates access to rhythmic states based on recent experience. Together, these findings suggest that fictive locomotor dynamics are consistent with adaptive winner-takes-all competition between central pattern generating (CPG) modules that balance constraint and promotion of motor program diversity.

When sensory modalities yield conflicting information, animals must rapidly reassess stimuli to select their actions. We induced auditory-visual conflict in free-flying echolocating Egyptian fruit bats, by fitting animals with prisms that shifted the perceived visual location of a landing perch while echoes returned from its veridical location. Bats that course-corrected within a single goal-directed flight did so by decoupling sonar gaze from steering, to enable rapid reweighting of visual and auditory cues. We designed artificial agents that used Bayesian inference to construct estimates of goal locations in their environment. When competing estimates directed active-sensing behaviors distinctly from steering, agents course-corrected more rapidly. Consistent with this idea, when bats were fit with prisms and earplugs that attenuated auditory localization cues, they were unable to course-correct. Removing prisms produced no systematic after-effects. Our framework suggests that instead of correcting their behavior after failure, animals could efficiently employ active sensing to resolve sensory conflict before failure occurs. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=178 SRC="FIGDIR/small/743555v1_ufig1.gif" ALT="Figure 1"> View larger version (41K): org.highwire.dtl.DTLVardef@16262edorg.highwire.dtl.DTLVardef@4cd82aorg.highwire.dtl.DTLVardef@103e6fforg.highwire.dtl.DTLVardef@13292bf_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOCover figure.C_FLOATNO Bat wearing helmet with clear-glasses and tracking markers. Photograph (C) 2026 Nikita M. Finger / Moss Laboratory. C_FIG

Humans often collaborate under asymmetric information, for example when two people carry a table and only one knows the destination. They coordinate without speech using cues from movement kinematics, interaction forces, and object states. Characterizing this sensorimotor communication is difficult because these signals both execute the task and convey information, whose meaning is context-dependent. Here, we investigated a virtual table-carrying task where one partner knew the target while the other inferred it from visuo-haptic feedback. Participants flexibly adapted kinematic and haptic cues across contexts to convey intention. We introduce an explainable machine-learning framework that decodes intent from ongoing multimodal signals and quantifies where individual features are informative. Incorporating the decoded signals into a drift-diffusion model accurately predicted the uninformed partner's target choices and decision times. Together, our framework explains how humans communicate through action and offers principles for collaborative robots to infer and express intent through physical interaction.

Animals must generalize from limited experience, yet behavioral experiments in the laboratory setting rarely assess whether or how rapidly they generalize. This contrasts with machine learning systems, where generalization is considered a fundamental test of learning, and emphasizes performance evaluation with new in-distribution or out-of-distribution examples. Here, we used an olfactory categorization task to investigate rules of generalization versus memorization in mice. We trained mice to discriminate between two target odorants mixed with a variable number (0-13) of background odors. There are 32766 possible mixture stimuli to be classified, yet mice learn to generalize from as few as 8 unique mixtures. This generalization is not due to limited memory capacity: mice successfully learned to group the same set of mixtures when category labels were randomly shuffled. Analysis of individual variability revealed features in learning dynamics during training that predict performance in the generalization phase. A linear supervised learning algorithm could describe the generalization from few exemplars well, whereas nonlinear classifiers were necessary to explain memorization. Our experiments suggest that mice have an inductive bias towards generalization, consistent with a preference for simple rules, and will memorize only when forced to do so.

Flexibly recombining computational modules is essential for biological and artificial neural networks to rapidly adapt to changing environments. This requires modules to be shared across tasks rather than rigidly segregated, yet what determines this organization remains unknown. Previous work suggests that weight initialization shapes whether networks learn task-specific or generic representations, but it is unclear whether this extends to recurrent networks and, more importantly, to network connectivity. Here, we systematically vary the initial weight variance of recurrent neural networks and study them using a framework that allows us to identify the functionally relevant connectivity subspaces for each computational module. We find that networks with low initial weight variance converge to solutions in which different subtasks rely on largely overlapping weight subspaces, whereas high-variance networks implement subtasks in higher-dimensional, more segregated weight subspaces. Our results also provide mechanistic insights with implications for interpreting biological neural circuits and for designing efficient recurrent architectures.

PurposeThe neural representation of pitch and timbre in complex sounds has previously been studied using synthetic, controlled stimuli to investigate underlying encoding mechanisms. These studies provide information about how single attributes of sound are represented in the inferior colliculus (IC), a critical hub of the auditory pathway where neurons are sensitive to stimulus periodicity and spectral shape, giving rise to representations of pitch and timbre, respectively. However, there is a gap in understanding how natural sounds with both pitch and timbre attributes, such as instrument sounds, are represented in the IC. MethodsIn this study, extracellular recordings were made in the IC of awake rabbits in response to natural instrument stimuli varying in fundamental frequency (F0) to determine how instrument identity (timbre) and F0 (pitch) are represented in IC neurons. ResultsUsing decoding models for instrument identification, we found that instrument identity was redundantly encoded in a population of neurons with diverse rate and timing characteristics. F0 identification using decoding models trained on single-neuron rate responses was poor, but the population of rate responses contained enough information to identify F0 reliably. F0 information was also encoded in single-neuron temporal responses up to 196 Hz. F0 identification from a population of temporal responses was accurate up to approximately 900 Hz, but accuracy decreased at high F0s. For the task in which F0 was identified based on responses to both oboe and bassoon stimuli that had overlapping F0s, performance decreased compared to F0 identification based on responses to a single instrument. ConclusionThis result supports the hypothesis that pitch and timbre information are encoded jointly in the IC.

Decision formation is commonly described as the accumulation of noisy evidence in a low-dimensional decision variable, but it remains unclear how this latent computation is implemented by heterogeneous neural responses. Here, we propose that ramping and sequentially firing neurons form complementary population codes for the same decision variable. Inspired by Laplace-domain neural representations of time, exponential receptive fields in a ramping population give rise to a translatable edge-like activity profile; localized receptive fields in a sequential population give rise to an aligned bump-like profile. We construct a continuous attractor neural network that dynamically maintains these complementary representations while implementing evidence accumulation along a shared latent manifold. At the behavioral level, simulations show that the circuit closely reproduces the single-trial trajectories, choice probabilities, and reaction-time statistics of a standard diffusion decision model while generating heterogeneous ramping and sequential neural responses. Our framework connects latent behavioral dynamics, population geometry, and recurrent circuit mechanisms. More broadly, it provides a circuit-level realization of computation in the Laplace domain that may support the representation and updating of continuous cognitive variables across decision making, timing, memory, and spatial cognition.

Every movement unfolds with a simple question: Where is my body? The nervous system answers through proprioception - the sense of limb position (static position sense) and movement (dynamic proprioception). Although position sense has been well characterized, dynamic proprioception has remained difficult to isolate and measure. Here we introduce a continuous proprioceptive tracking paradigm, coupled with computational modelling, that captures dynamic proprioception in real time. We first establish that this approach is sensitive, reliable and efficient. Leveraging this method, we then show that dynamic proprioception provides faster and more faithful estimates of limb state than vision, dominates multisensory state estimation when vision is also available, and is not correlated with conventional measures of position sense. Together, these findings provide a new quantitative framework for characterizing dynamic proprioception in health and disease.