Biological Cybernetics

We present a network model that enables a navigating agent to shape the spatial and temporal structure of its paths through its environment. The model is inspired by the insect fan-shaped body. In it, a recurrent neural network receives an input that encodes an agent's velocity vector. Meanwhile, network activity determines the setpoint of a control loop that influences this velocity vector through motor outputs. The network thus guides future movement using memory of past movement. We illustrate how the network's dynamics determine the trajectory features it extracts to produce the setpoint. We then relate the joint dynamics of network activity and the agent's velocity vector to the structure of the resulting paths. This network can produce paths suitable for different forms of exploration. It can also stabilize movements initiated by lower-level systems. Our analyses illustrate how recurrent neural dynamics and memory can shape behavior when embedded in closed loops.

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.

Most animals move intermittently. Of these, animals that fly and swim move in two stages: during active propulsion, when they beat their wings or swing their tails, and right after, when they glide or coast through the air or water. The kinematics of active movements are typically well studied, but the coasting period afterwards is less understood. We used larval zebrafish as a model of intermittent locomotion. Larval zebrafish swim in discrete bouts lasting ~200 ms, coast for short durations and distances, and then are largely stationary for ~800 ms. We find that larval zebrafish do not coast like a passive object. While they coast for distances that are correlated with the prior swim's strength, as expected from physics, they seem to be able to modulate the mechanics of their coasting: the time constant is not a constant, but varies from coast-to-coast. Furthermore, the time constant is correlated with the duration of the interval between swim bouts. This suggests that larval zebrafish can either shorten or extend their coasting duration, and that coasting inhibits the initiation of the next swim. Finally, the time constant changes quickly, while other swimming kinematics (e.g., distance swum) are autocorrelated over the course of at least several seconds. Altogether, this suggests that fish, and perhaps other animals that move intermittently, actively modulate their post-propulsion movement, possibly to gather sensory feedback in the absence of blurry visual feedback associated with fast locomotion.

Sensory integration within antennal lobe (AL) is thought to play a role in the guidance of odor tracking, though while responses to olfactory input within the AL have been well-studied, responses to mechanosensory stimuli, in the form of wind speed, have received less scrutiny. Recent experimental work has systematically characterized mechanosensory responses of individual neurons within the AL, showing four distinct response patterns, labeled as sustained, transient, biphasic, and offset types; furthermore, these experiments have demonstrated that the distribution of response patterns, as well as the response type of a fixed neuron, can vary with stimulus intensity (wind speed). In this work, we develop a realistic biophysical model of the AL and, using this model, we show that internal AL dynamics are capable of generating the response patterns observed experimentally - namely, we find that response type is determined by the interplay of slow synaptic inhibition, an intrinsic calcium dependent potassium (SK) current, and stimulus strength, and hence that a heterogeneous distribution of slow inhibition and SK current strength across the AL can lead to the emergence of all four types at a fixed wind speed. Moreover, similar to experiment, we find that the distribution of response patterns across the AL changes with wind speed. Finally, we examine the distribution of response types in the presence of a simulated odor stimulus as well as odor separation by the AL in the presence versus absence of a strong mechanosensory signal.

Parvalbumin-expressing interneurons (PVINs) in the spinal dorsal horn play a key role in preventing touch inputs from engaging nociceptive pathways through fast inhibitory control. Although most PVINs are typically quiescent and require external input to fire, a subset of these neurons exhibits spontaneous activity, including isolated spikes and bursts. The mechanisms underlying this behavior in spontaneously active PVINs (spPVINs) remain unclear. To address this, we developed a stochastic two-compartment Hodgkin-Huxley (HH) type model, consisting of a soma and an axon initial segment (AIS), to investigate the effects of synaptic noise and intrinsic electrical properties of spPVINs in driving their spontaneous firing. The model incorporates two subthreshold currents: the M-type K+ current (Im) and the hyperpolarization-activated current (Ih). The model revealed that, in the presence of Ornstein-Uhlenbeck noise, Ih promotes spontaneous firing by enhancing noise-driven depolarizations. Model simulations closely reproduced the firing patterns of spPVINs observed experimentally, including irregular spiking and bursting. Bifurcation analysis showed that varying the applied current can lead to transitions between quiescent, tonic, and elliptic bursting regimes, allowing stochastic fluctuations to switch between these states, which gives rise to irregular spontaneous activity. Reducing the conductance of Im and increasing the conductance of the fast Na+ current (INa) both enlarge the elliptic bursting regime, thereby enabling noise to promote bursting. Interestingly, when the model was incorporated into a circuit, the downstream inhibitory effects of spPVINs were enhanced by the expression of Ih. Taken together, these results demonstrate how intrinsic electrical properties of spPVINs shape their firing dynamics and circuit activity.

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.

Behaviors and thoughts are driven by a multitude of nested neuronal circuitry loops. They cause complex brain activity dynamics that remain poorly understood. We show that closed-loop neuronal network operation results in an activity state space that can be best understood as a vector field with an attractor point, which controls the activity dynamics across the neuronal population. We show that brain activity in vivo, however, indicates the attractor point is continually moving along a trajectory, which requires the presence of dynamic sensory input or independent activity generation within neurons. Using a spinal network model receiving sensory feedback from a dynamical biomechanical system, we show how these two independent dynamical systems mutually drive each others activity trajectories to generate behavior. Similarly, independent self-generated activity within each thalamic neuron, in closed loop with cortical subpopulations, results in a multitude of dynamical subnetworks that shape each others activity trajectories to control cortical populations. Although the attractor trajectories reflect emergent stability, we show them to be susceptible to criticality effects where minor changes in synaptic inputs can cause the attractor trajectory to switch to cause alternative behaviors. This renders the mutual perturbations between neural and biomechanical dynamics, and between subnetworks within the CNS, an effective operational mode to achieve behavioral flexibility and to simplify learning of apparently complex behaviors. We illustrate how this mode of operation necessitates anticipatory control, thoughts, by the cortex and discuss how it can encompass also the other CNS structures involved in somatic sensorimotor control.

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.

Songbirds, in particular zebra finches (Taeniopygia guttata), provide a powerful model for investigating the neural mechanisms of learned vocal behavior. Researchers typically rely on the acoustic structure of birdsong to quantify vocal behavior. As a more direct measure of motor control, we present VIBE: Vocal acoustic Inversion to Biomechanical Estimates, an open-source pipeline that recovers the biomechanical control parameters of song production directly from the acoustic waveform. Biomechanical models of the songbird syrinx describe vocal production with two continuously varying parameters: and {beta}, representing subsyringeal air sac pressure and syringeal muscle tension, respectively. Recovering these parameters from song acoustics provides a motor-based coordinate system against which neural activity or other dependent variables can be directly compared. Because and {beta} are the coupled control parameters of a nonlinear oscillator, their joint recovery is non-trivial. VIBE addresses this through iterative optimization of the governing normal-form equations. We validate VIBE against recorded air sac pressure across 44 songs from twelve birds, showing that the recovered corresponds to empirically measured air sac pressure. Pairing VIBE with Neuropixels recordings from RA in five birds, we find that RA activity is well predicted by the recovered parameters, and that and {beta} add predictive power beyond the acoustic features of song. By recovering biomechanical control parameters from the acoustic signal, VIBE makes the biomechanical coordinate system of song production accessible to the broader songbird research community. New & NoteworthyVIBE provides a novel, fully automated pipeline to recover the biomechanical control parameters of the avian vocal organ, and {beta}, as continuously varying quantities from the raw acoustic waveform, making the full biomechanical model of song production accessible at the scale of modern datasets.

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 potentials are brief electrical impulses that form the mechanistic basis for how neurons communicate. While it is well known that the shape of action potentials can differ across neurons, one fundamental assumption is that the complex voltage waveforms of action potentials within a given neuron are reducible to binary spikes. This assumption has constrained our conception of possible neural codes to those amenable to binary signaling, such as rate, temporal, and population codes. Here, we show that action potential waveform variability is not random, but is, instead, state dependent. To show this, we parameterize action potential waveforms in a set of very high temporal resolution (200 kHz) intracellular action potential recordings. We show that an action potential is not a digital '1', but is instead a rich signal whose fine-scale features influence the shape and timing of the next action potential and whose waveform is systematically biased by input drive. We then show that intracellular action potential waveforms can vary as a function of the extracellular local field potential, but do so heterogeneously, as a function of the field potential amplitude and standard deviation. Our results have profound implications for systems and computational neuroscience, especially regarding the development of next-generation, biologically-inspired artificial neural networks that incorporate waveform dynamics. Non-binary action potentials point to a broader landscape of possible neural codes, whereby neurons communicate not just via binary spikes, but through their state-dependent waveform features.

The results in this article demonstrate that the central nervous system CNS plans trajectories in the vertical plane by minimizing a Generalized Dynamic Jerk GJerk cost function, which we have proposed as an advancement of the traditional Minimum Jerk cost function. While the traditional Jerk cost function generates smooth trajectories by minimizing the third derivative of joint angle over time, it neglects real dynamic constraints most notably the effect of gravity. According to our engineering interpretation, the arm functions as a constrained manipulator where gravity acts as a non-linear, state-dependent bias; thus, the asymmetry in velocity profiles is not an anomaly but an optimal adaptation to the gravitational field. Consequently, it predicts mathematically symmetrical upward and downward movements, even in contexts where gravitational forces play a decisive role. The proposed GJerk cost function extends the classical framework by incorporating position-dependent dynamic coefficients into the cost function, thereby embedding gravitational effects directly within the planning process. As a result, the generated movements are not only smooth in a mathematical sense but also physically and mechanically consistent with the actual torque and energy demands imposed by the musculoskeletal system. The GJerk cost function reduces angular change in high-gravitational-torque regions because it makes the joint configuration with the highest gravitational torque more expensive within the cost function, prompting the planner to choose a slower and more conservative movement. This does not physically dissipate energy, but it acts as a behavioral damping mechanism, similar to how humans naturally slow down when approaching a high load or potentially dangerous configuration. In this way, the GJerk cost function reduces abrupt changes in joint kinetic energy and prevents sudden jumps in acceleration, ultimately producing a smoother and more stable trajectory that aligns with both biomechanical reality and observed human behavior. Within this framework, upward movements become inherently more costly than downward ones, penalizing configurations that require large torques to counteract gravity. This induces a biomechanically meaningful asymmetry, ensuring the resulting trajectories reflect the body's true mechanical constraints rather than mere geometric smoothness. Our empirical results demonstrate that the GJerk cost function provides a more realistic and physiologically grounded account of motor planning in the vertical plane, linking smoothness optimization with genuine dynamic requirements and offering a closer approximation to biological motor behavior

The dentate gyrus' principal neuron, the granule cell (GC), plays a key role in pattern separation, transforming similar inputs into dissimilar outputs. We used a new measure based on information theory to evaluate this transformation in an experimentally derived in silico GC model with realistic ion channel distributions across its dendrites. We found that model performance aligned well with current-clamp recordings from mouse brain slices. However, it was also possible to find artificial parameter combinations in the model that functionally outperformed the recorded cells while matching their action potential shapes. Rather than maximising computational power, the biologically realistic GC model balanced energy efficiency against increased functionality in a Pareto optimal way: No possible parameter combination was found to improve one of the objectives without impairing the other. Interestingly, immature GCs adopted a different weighted trade-off with a stronger emphasis on energy efficiency than pattern separation, but they remained Pareto optimal over their putative developmental trajectory. Our results support the idea that evolution favours neurons that can satisfy functional and energetic demands simultaneously.

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.

Predictive coding is a powerful normative framework for understanding cortical computation, but it is still an open question how biologically plausible networks with local plasticity support predictive inference and representation learning. In this work we show that a recurrent excitatory-inhibitory circuit with purely local plasticity can perform predictive inference without explicit error representations. We establish a direct analytic link that shows that learning in these circuits requires the weights to remain on a consistency manifold where recurrent inhibition matches the inhibition required by the predictive coding objective. Using a closed-form derivation of the consistency condition, we derive a plasticity rule that maintains it exactly under a Gaussian prior. Under a non-Gaussian prior, we find the rule supports learning sparse, factorized features, such as edge detectors from natural images. We show empirically that a BCM-like rule with an activity-dependent threshold approximates this well, while other Hebbian-like rules tend to learn less accurate solutions because they keep the weights too far from this manifold. With recurrent excitation the networks acquire spatiotemporal features like direction selectivity, and the ability to complete partially observed sequences. Time-continuous learning then leads to the development of low-dimensional attractor-like structures and noise-driven replay. Overall, these results link predictive coding to local circuit plasticity, show it does not require an explicit prediction error representation, and suggest a normative role for BCM-like plasticity in excitatory synapses.

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.