Journal of Computational Neuroscience

Fly compound eyes pool signals from photoreceptors that sample the same region of visual space through neural superposition in the lamina. The optical axes of photoreceptors projecting to a single lamina cartridge are not perfectly parallel, but instead converge at a point a few millimeters in front of the eye. At short viewing distances (1-10 mm) this leads to distance-dependent differences in receptive field overlap. We explored whether it was possible that flies could sense depth in this "personal space" purely from the geometry of neural superposition. To this end, we combined a computational model of fly eye optics with a disparity-tuned lamina model originally developed for stereoscopic prey capture in praying mantises, and simulated the responses of lamina monopolar cells to moving stimuli at different distances. Across variations in stimulus parameters and lamina models, we found that lamina neuron responses indeed contain a distance-dependent component, which can overall be summarised as an enhanced response due to temporally overlapping receptor responses at a critical distance of 3-4 mm, the convergence distance of photoreceptor axes. Depending on the lamina model and stimulus size, either response amplitude or onset gradient, or both, exhibited this peak. We further show that changes in eye size systematically shift this preferred distance, such that larger flies had a peak response at a greater distance. Our results demonstrate that lamina cell responses may contain a robust, geometry-derived component that is specific to object distance and invariant to other stimulus properties. This suggests that neural superposition, beyond improving sensitivity, may function analogously to a light-field camera system that is effectively "focused" on a behaviorally relevant distance. Author summaryIn this study, we explored how neural superposition in fly compound eyes may lead to an enhanced response to objects at a behaviorally relevant distance. The optical axis of neurally pooled photoreceptors, from neighbouring ommatidia, are not parallel, but converge at a point a few millimeters in front of the eye, which should lead to the strongest correlation of their signals at that distance. This idea was tested by combining a geometric model of the fly eye optics with a computational model of how the lamina cells process the responses of photoreceptors, and evaluating the output for a moving bright dot at different distances. We found that the simulated lamina cell has its fastest response, as measured by the onset gradient, to a stimulus at the distance where the photoreceptors converge (3-4 mm). This distance scales with the simulated eye size and corresponds to behaviorally relevant distances for fly behavior. This suggests that neural superposition may act to enhance the response to objects at a critical distance in the early visual processing of flies.

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.

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.

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.

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.

Locusts possess a collision-sensitive pathway in their visual system culminating in a neuron, the lobula giant movement detector (LGMD), which preferentially responds to looming stimuli. The LGMD is also notable for its reduced or absent response to other stimuli, such as translating objects, wide-field motion, and incoherent images of looming objects. While experimental and modelling work have both shed light on the various mechanisms underpinning these properties, broad examinations of how these mechanisms interact with each other and with diverse stimulus types have been limited. To address this, we developed a model incorporating mechanisms from recent literature, and subjected to an array of looming stimuli with varying size-to-speed ratio, polarity (OFF and ON), and coherence; wide-field background motion, translating stimuli, and trajectory changes were also examined. The model showed quantitative and qualitative fidelity to biological data in its replication of a wide variety of stimulus responses, with its preference for incoherent visual stimuli being a notable exception. Based on investigations with various inhibition types removed, it was shown that lateral inhibition predominantly suppressed wide-field motion responses. Global inhibition both normalized growing excitation over the course of looming, and improved recognition of looming stimuli against moving backgrounds. Feedforward inhibition was found to have diverse roles, including shaping peak response time and its variability, and improving coherence selectivity. The success of the model in replicating multiple stimuli also showed the plausibility of several underlying assumptions, including sharing of input between the LGMD and multiple other neuron types.

Emerging research on desynchronization reveals strong relations to memory formation and recollection with much of the evidence originating from studies of the hippocampus, a brain region central to memory processing. However, growing evidence emphasizing the role of desynchronization is accompanied by challenges, most notably the synchronization/desynchronization conundrum. The conundrum arises from an apparent contradiction between learning and Shannon's information theory: spike-timing-dependent plasticity (STDP) acquires information via synchronized populational activity whereas information theory suggests that information channel is encoded through higher variability. Both frameworks are well-founded. Learning is widely accepted as the mathematical abstraction of STDP while Shannon's information theory showcases its power ubiquitously across fields from communication systems to neuroscience. Here, we propose that learning and Shannon's information theory are not necessarily opposing principles. Rather, learning plays a critical role in the process of synchronization and desynchronization. To justify our claim, we conduct computational simulations based on a Hodgkin-Huxley neuronal model coupled with NMDA, AMPA, and GABA synapses with inputs of biologically realistic spiking data. Our results show that enabling STDP significantly influences synchronization and desynchronization dynamics. Specifically, we find that STDP and desynchronization form a regulatory loop, in which STDP regulates the level of synchrony, and synchrony regulates subsequent learning strength. Further study reveals STDP is capable of switching neurons from synchronization to desynchronization. This framework mitigates the synchronization/desynchronization conundrum by clarifying the relationship between desynchronization and learning, and offers a new perspective on how synchrony contributes to memory formation and recollection.

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.

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.

We have studied the emergence of slow relaxation oscillations in next generation neural mass models with spike frequency adaptation. Relaxation oscillations connect low firing state (Down state) to high firing state (Up state) via the slow adaptation. In the examined cases, the orbit relaxes towards the Up State via a sequence of collective damped oscillations (peaks of activity), thus revealing population bursting dynamics. The slower is the adaptation time scale the higher is the complexity (number of peaks) displayed by the relaxation oscillations. In particular, a chaos-induced spike-adding mechanism regulates the increase in the number of peaks. In analogy to what found in the Hidmarsh-Rose neuron model, two different types of chaotic behaviors have been identified: Population Spiking and Population Bursting Chaos. The increase of the adaptation strength leads to shorter (longer) Up (Down) state durations somehow mimicking the effect of charbachol in in vitro experiments, where spontaneous slow waves are observed. Indeed, the scenario depicted in [1], where an increase of the concentration of carbachol induces a transition from anesthesia-like to sleep-like dynamics is consistent with our results based on the variation of the adaptation strength. HighlightsO_LISpike Frequency Adaptation (SFA) promotes the emergence of Slow Relaxation Oscillations C_LIO_LISpike-adding mechanisms, controlled by SFA, lead to Relaxation Oscillations of increasing complexity C_LIO_LITwo types of chaotic behaviours: Population Spiking and Population Bursting Chaos C_LIO_LISFA regulates Up and Down States durations and their correlation C_LI

The retina encodes visual information through parallel pathways formed by distinct retinal ganglion (RGC) types. Current understanding of how each cell type contributes to downstream visual processing and perception is limited by a lack of tools for selectively manipulating the activities of individual RGC types. Here, we introduce a computational framework called STORM (SpatioTemporal Orthogonal Response Modulation) that creates visual stimuli that aim to selectively modulate the activities of specific RGC types while minimally affecting the activities of nearby RGCs of non-targeted types. To illustrate the approach, demonstrate its flexibility, and identify conditions under which each simulated RGC type could be selectively manipulated, we first applied this framework to simplified models of RGC function, such as Linear-Nonlinear-Poisson (LNP) and LN-LN cascade models. We also deployed this approach on more complex (and more accurate) models of RGC responses, based on convolutional neural networks. We demonstrate that differences in spatial receptive fields, temporal dynamics, response polarities, and nonlinearities can provide sufficient degrees of freedom for designing stimuli that selectively manipulate individual RGC types. We also generalize this approach to conditions where the receptive field locations are unknown for in vivo and clinical applications.

Hippocampal area CA3 is widely believed to serve a core memory function: retrieving distributed patterns of neural activity that were previously stored in the recurrent connections between neurons. However, it remains unknown how the physiological properties of individual neurons contribute to this function. Here, we present a mathematical analysis of a canonical recurrent neural network model of CA3. Our analysis provides three main, experimentally testable predictions for recurrent circuits performing stable memory recall. Two of these predictions, that pyramidal cells should be characterized by elevated intrinsic excitability and by inhibition-dominated recurrent connections, are consistent with previous experimental findings. We thus focused on testing the third prediction: that neuronal activation functions have an exponent slightly above $1$. For this, we performed \textit{in vivo} intracellular recordings of 49 pyramidal neurons from the CA3 area of behaving mice. Fitting a range of parametric models to these voltage traces and performing statistical model comparison revealed an average neural activation exponent slightly above $1$, confirming our theoretical predictions, with substantial heterogeneity across cells, which remains to be accounted for by the theory. An analysis of 133 further cells from two other previous studies provided neural activation exponent estimates highly consistent with those we found in our data. Our results suggest that the properties of hippocampal CA3 area are tuned to support reliable memory recall even at the level of single neurons.

Recent studies have reached conflicting conclusions about the statistical significance of lesion network mapping (LNM), especially regarding the impact of regional node strength on lesion-associated network detection. Here, we present a statistical framework that clarifies the origin of these apparently conflicting findings. Based on the simplified formulation of LNM introduced by van den Heuvel et al. (2026), we propose alternative, permutation-based null models corresponding to the sensitivity and specificity tests used in standard LNM analysis. We derive analytical expressions for both the proposed null models and the node-strength-constrained approach recently introduced by Zalesky and Cash (2026), thereby providing a computationally efficient alternative to permutation-based significance testing. Using synthetic lesion and connectivity matrices, as well as clinical datasets, we compare the outcome of the proposed null models with the standard LNM analysis and demonstrate how the choice of null models influences statistical inference and the resulting lesion network maps. Our framework shows that the apparent disagreements in the recent LNM literature can be understood as a consequence of different statistical null models rather than to conflicting conclusions about LNM itself.

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.

Neural encoding of sensory information becomes more efficient when distinct stimuli evoke uncorrelated activity patterns. Spatial frequency (SF) information becomes decorrelated early in visual processing in a manner that involves both temporal differentiation in the dorsal lateral geniculate nucleus (dLGN) and firing rate differentiation in the primary visual cortex (V1). However, the specific functional circuit configurations that enable this synergy are not fully understood. To address this gap, we developed a geniculocortical subunit model to identify functional circuit configurations capable of producing a decorrelated V1 population response. We found that decorrelation could be explained by the combined activity of two complementary circuit configurations with distinct functional organization. The first circuit was characterized by temporally organized, late-onset dLGN inputs coupled to weak and delayed intracortical inhibition, whereas the second was characterized by less temporally constrained, early-onset dLGN inputs coupled to strong and early intracortical inhibition. Eliminating SF selectivity in upstream dLGN subunits did not affect SF decorrelation in the modeled V1 population response, indicating that decorrelation tolerates weak SF selectivity and is primarily driven by temporal organization. Together, these results suggest that biologically plausible circuit configurations are likely to produce SF decorrelation in the cortex through the temporal organization of feedforward inputs and intracortical inhibition.

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.

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.

In this study, we develop a mathematical model of the hypothalamic pituitary adrenal (HPA) axis and systematically investigate the model complexity required to reproduce observed hormone dynamics. The model is fitted to ACTH and cortisol measurements from five healthy volunteers reported in the literature. We show that simultaneous reproduction of both hormone profiles requires a delay differential equation model with at least five state variables among the model architectures considered. Following fitting the volunteer data, we investigate the response of the model to sustained stress using bifurcation analysis. The coupled system exhibits bifurcations over a range of stress intensities. This analysis reveals bifurcations whose critical stress thresholds depend strongly on the modulatory state of the system. These results provide a mathematical framework for investigating transitions between physiological and dysregulated HPA axis dynamics, which may be related to states of health and disease.

In biological neural circuits, the dynamics of neurons and synapses are tightly coupled. We study the consequences of this coupling and show that it enables a novel form of working memory. In recurrent neural network models with ongoing Hebbian plasticity, we find that following oscillatory stimulation, neurons continue to oscillate long after the input is removed. This creates a dynamic form of memory that has no explicit storage or retrieval phases and that requires no prior knowledge of the input. We trace the mechanism of these "persistent oscillations" to an interaction between neurons and synapses that creates complex outlier eigenvalues of the connectivity matrix. This is shown both in simulation and analytically. We leverage this mechanistic understanding to generate persistent oscillations with prespecified dynamics, creating a dynamic analog of a classical Hopfield network. Our work demonstrates that coupling neuronal and synaptic dynamics enables novel forms of computation.

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.