Biological Cybernetics

AO_SCPLOWBSTRACTC_SCPLOWRespiration and swallowing are vital orofacial motor behaviours that require the coordination of the activity of two brainstem central pattern generators (r-CPG, sw-CPG). Here, we use computational modelling to further elucidate the neural substrate for breathing-swallowing coordination. We progressively construct several computational models of the breathing-swallowing circuit, starting from two interacting half-centre oscillators for each CPG. The models are based exclusively on neuronal nodes with spike-frequency adaptation, having a parsimonious description of intrinsic properties. These basic models undergo a stepwise integration of synaptic connectivity between central sensory relay, sw- and r-CPG neuron populations to match experimental data obtained in a perfused brainstem preparation. In the model, stimulation of the superior laryngeal nerve (SLN, 10s) reliably triggers sequential swallowing with concomitant glottal closure and suppression of inspiratory activity, consistent with the motor pattern in experimental data. Short SLN stimulation (100ms) evokes single swallows and respiratory phase resetting yielding similar experimental and computational phase response curves. Subsequent phase space analysis of model dynamics provides further understanding of SLN-mediated respiratory phase resetting. Consistent with experiments, numerical circuit-busting simulations show that deletion of ponto-medullary synaptic interactions triggers apneusis and eliminates glottal closure during sequential swallowing. Additionally, systematic variations of the synaptic strengths of distinct network connections predict vulnerable network connections that can mediate clinically relevant breathing-swallowing disorders observed in the elderly and patients with neurodegenerative disease. Thus, the present model provides novel insights that can guide future experiments and the development of efficient treatments for prevalent breathing-swallowing disorders. KO_SCPLOWEYC_SCPLOWO_SCPCAP C_SCPCAPO_SCPLOWPOINTSC_SCPLOWO_LIThe coordination of breathing and swallowing depends on synaptic interactions between two functionally distinct central pattern generators (CPGs) in the dorsal and ventral brainstem. C_LIO_LIWe model both CPGs as half-centre oscillators with spike-frequency adaptation to identify the minimal connectivity sufficient to mediate physiologic breathing-swallowing interactions. C_LIO_LIThe resultant computational model(s) can generate sequential swallowing patterns including concomitant glottal closure during simulated 10s stimulation of the superior laryngeal nerve (SLN) consistent with experimental data. C_LIO_LIIn silico, short (100 ms) SLN stimulation triggers a single swallow which modulates the respiratory cycle duration consistent with experimental recordings. C_LIO_LIBy varying the synaptic connectivity strengths between the two CPGs and the sensory relay neurons, and by inhibiting specific nodes of the network, the model predicts vulnerable network connections that may mediate clinically relevant breathing-swallowing disorders. C_LI

The stability of rhythmic activity in neural networks is an important aspect in the study of central pattern generators (CPGs). Different from other physiological rhythms, the activity of CPGs has not been fully characterized in terms of its stability, especially using quantitative methods. We propose a method that takes advantage of the natural noise present in CPGs to quantify the stability of the rhythmic activity. Furthermore, we used the stationary bootstrap method to define confidence intervals of the results. We applied this method to study the influence of a synaptic modification on the pyloric CPG circuit, using artificial synapses implemented in dynamic clamp software. We show that even after removing one of its strongest synapses, the CPG stability remains unaltered. This analysis suggests that CPGs are designed to be strongly stable regardless of the parameter perturbations they undergo.

Motor outputs are generated by the spinal cord in response to de-scending inputs from the brain. While particular descending commands generate specific outputs, how descending inputs interact with spinal cord circuitry to generate these outputs remains unclear. Here, we suggest that during development particular motor programmes are stored in premotor spinal circuitry, and that these can subsequently be retrieved when the associated descending input is received. We propose that different motor patterns are not stored in the spinal cord as a library of separate programmes, but that the spinal cord orthogonalises and normalises the various inputs, identifies the similarities and differences between them, and stores only the differences: similarities between patterns are recognised and used as a common basis that subsequent input patterns are built upon. By removing redundancy this can greatly increase the storage capacity of a system composed of a finite number of processing units, thus overcoming the problems associated with the storage limits of conventional artificial networks (e.g. catastrophic interference). Where possible we relate the various stages of the processing to the known circuitry and synaptic properties of spinal cord locomotor networks, and suggest experimental approaches that could test unknown aspects.

An inhibition-stabilized network (ISN) is a network of excitatory and inhibitory cells at a stable fixed point of firing rates for a given input, for which the excitatory subnetwork would be unstable if inhibitory rates were frozen at their fixed point values. It has been shown that in a low-dimensional model (one unit per neuronal subtype) of an ISN with a single excitatory and single inhibitory cell type, the inhibitory unit shows a "paradoxical" response, lowering (raising) its steady-state firing rate in response to addition to it of excitatory (inhibitory) input. This has been generalized to an ISN with multiple inhibitory cell types: if input is given only to inhibitory cells, the steady-state inhibition received by excitatory cells changes paradoxically, that is, it decreases (increases) if the steady-state excitatory firing rates decrease (increase). We generalize these analyses of paradoxical effects to low-dimensional networks with multiple cell types of both excitatory and inhibitory neurons. The analysis depends on the connectivity matrix of the network linearized about a given fixed point, and its eigenvectors or "modes". We show the following: (1) A given cell type shows a paradoxical change in steady-state rate in response to input it receives, if and only if the network with that cell type omitted has an odd number of unstable modes. Excitatory neurons can show paradoxical responses when there are two or more inhibitory subtypes. (2) More generally, if the cell types are divided into two nonoverlapping subsets A and B, then subset B has an odd (even) number of modes that show paradoxical response if and only if subset A has an odd (even) number of unstable modes. (3) The net steady-state inhibition received by any unstable mode of the excitatory subnetwork will change paradoxically, i.e. in the same direction as the change in amplitude of that mode. In particular, this means that a sufficient condition to determine that a network is an ISN is if, in response to an input only to inhibitory cells, the firing rates of and inhibition received by all excitatory cell types all change in the same direction. This in turn will be true if all E cells and all inhibitory cell types that connect to E cells change their firing rates in the same direction.

The preBotzinger complex of the lower brainstem generates two breathing-related rhythms: one for inspiration on a timescale of seconds, and another that produces larger amplitude sighs on the order of minutes. We hypothesize that these two disparate rhythms emerge in tandem wherein recurrent excitation gives rise to the inspiratory rhythm while a calcium oscillator generates sighs; distinct neuronal populations are not required. We present several mathematical models that instantiate our working hypothesis including: (1) an activity (firing rate) model and (2) a minimal spiking network model. Both modeling frameworks corroborate the single-population rhythmogenic hypothesis.

Excitable cells exhibit different electrophysiological profiles while responding to current stimulation in current-clamp experiments. In theory, the differences could be explained by changes in the expression of proteins mediating transmembrane ion transport. Experimental verification by performing systematic, controlled variations in the expression of proteins of the same type (e.g. voltage-dependent, noninactivating Kv2.1 channels) is difficult to achieve in the absence of other changes. However, biophysical models enable this possibility and allows us to assess and characterise the electrophysiological phenotypes associated to different levels of expression of non-inactivating voltage-dependent K-channels of type Kv2.1. To do so, we use a 2-dimensional biophysical model of neuronal membrane potential and study the phase plane geometry and bifurcation structures associated with different levels of Kv2.1 expression with the input current as bifurcation parameter. We find that increasing the expression of Kv2.1 channels reduces the size of the region of the phase plane from which action potentials can be initiated. The changes in expression can also be related to different transitions between rest and repetitive firing in current clamp experiments. For instance, increasing the number of Kv2.1 channels shifts the rheobase current to higher levels, but also expands the dynamic range in which excitatory external current produces repetitive spiking. Our analysis shows that changes in the responses to increasing input currents can be associated to different sequences of fixed point bifurcations. In general, the fixed points are attracting, then repulsive, and later become attracting again as the input current increases, but the bifurcation sequences also include changes in fixed point type, and change qualitatively with the expression of Kv2.1 channels. In the non-repetitive spiking regime with low current stimulation, low expression of Kv2.1 channels yields bifurcation sequences that include transitions between 3 and 1 fixed points, and repetitive firing starts with delays that decrease with increasing current (aggregation). For higher expression of Kv2.1 channels there is only one fixed point that changes in type and attractivity as the input current increases, convergence to rest tends to be oscillatory (resonance), and repetitive spiking starts without noticeable delays. Our models explain how the same neuron is theoretically be capable of including both aggregating and resonant modes of integration for synaptic input, as shown in current clamp experiments.

In insect locomotion, the transmission of energy from muscles to motion is a process within which there are many sources of dissipation. One significant but understudied source is the structural damping within the insect exoskeleton itself: the thorax and limbs. Experimental evidence suggests that exoskeletal damping shows frequency (or, rate) independence, but investigation into its nature and implications has been hampered by a lack methods for simulating the time-domain behaviour of this damping. Here, synergising and extending results across applied mathematics and seismic analysis, we provide these methods. We show that existing models of exoskeletal rate-independent damping are equivalent to an important singular integral in time: the Hilbert transform. However, these models are strongly noncausal, violating the directionality of time. We derive the unique causal analogue of these existing exoskeletal damping models, as well as an accessible approximation to them, as Hadamard finite-part integrals in time, and provide methods for simulating them. These methods are demonstrated on several current problems in insect biomechanics. Finally, we demonstrate, for the first time, that existing rate-independent damping models are not strictly dissipative: in certain circumstances they are capable of generating negative power without apparently storing energy, likely violating conservation of energy. This work resolves a key methodological impasse in the understanding of insect exoskeletal dynamics and offers new insights into the micro-structural origins of rate-independent damping as well as the directions required in order to resolve violations of causality and the conservation of energy in existing models.

Rhythmic neural activity underlies essential biological functions such as locomotion, breathing, and feeding. Computational models are widely used to study how such rhythms emerge from interactions between neuron-level and circuit-level dynamics. Intrinsically bursting neurons are key components of many central pattern generators (CPGs), yet existing models span a tradeoff between biological realism and practical usability. Biophysical models involve many parameters that are difficult to tune, whereas abstract models often integrate poorly into neural circuit simulations. We propose a simplified model of intrinsically bursting neurons derived from a reduced non-spiking biophysical formulation. The model integrates readily into neural circuits while enabling direct and independent control of bursting characteristics, including duration, amplitude, and shape. We show that the model reproduces single-unit biophysical responses to diverse stimuli as well as circuit-level activity patterns from crustacean and mammalian CPGs. This model provides a practical tool for studying rhythm generation in neural circuits.

Using an information criterion to evaluate models fitted to spike train data from chinchilla semicircular canal afferent neurons, we found that the superficially complex functional organization of the canal nerve branch can be accurately quantified in an elegant mathematical model with only three free parameters. Spontaneous spike trains are samples from stationary renewal processes whose interval distributions are Exwald distributions, convolutions of Inverse Gaussian and Exponential distributions. We show that a neuronal membrane compartment is a natural computer for calculating parameter likelihoods given samples from a point process with such a distribution, which may facilitate fast, accurate, efficient Bayesian neural computation for estimating the kinematic state of the head. The model suggests that Bayesian neural computation is an aspect of a more general principle that has driven the evolution of nervous system design, the energy efficiency of biological information processing. Significance StatementNervous systems ought to have evolved to be Bayesian, because Bayesian inference allows statistically optimal evidence-based decisions and actions. A variety of circumstantial evidence suggests that animal nervous systems are indeed capable of Bayesian inference, but it is unclear how they could do this. We have identified a simple, accurate generative model of vestibular semicircular canal afferent neuron spike trains. If the brain is a Bayesian observer and a Bayes-optimal decision maker, then the initial stage of processing vestibular information must be to compute the posterior density of head kinematic state given sense data of this form. The model suggests how neurons could do this. Head kinematic state estimation given point-process inertial data is a well-defined dynamical inference problem whose solution formed a foundation for vertebrate brain evolution. The new model provides a foundation for developing realistic, testable spiking neuron models of dynamical state estimation in the vestibulo-cerebellum, and other parts of the Bayesian brain.

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

AO_SCPLOWBSTRACTC_SCPLOWGrand efforts in neuroscience are working toward mapping the connectomes of many new species, including the near completion of the Drosophila melanogaster. It is important to ask whether these models could benefit artificial intelligence. In this work we ask two fundamental questions: (1) where and when biological connectomes can provide use in machine learning, (2) which design principles are necessary for extracting a good representation of the connectome. Toward this end, we translate the motor circuit of the C. Elegans nematode into artificial neu-ral networks at varying levels of biophysical realism and evaluate the outcome of training these networks on motor and non-motor behavioral tasks. We demonstrate that biophysical realism need not be upheld to attain the advantages of using biological circuits. We also establish that, even if the exact wiring diagram is not retained, the architectural statistics provide a valuable prior. Finally, we show that while the C. Elegans locomotion circuit provides a powerful inductive bias on locomotion problems, its structure may hinder performance on tasks unrelated to locomotion such as visual classification problems.

Neural circuits are remarkably robust to perturbations that threaten their function. Activity-dependent homeostatic plasticity (ADHP) is a stabilizing mechanism that supports robustness by tuning neuronal ion conductances to combat chronic over- or under-activity. Its restorative capacity has been demonstrated in the pyloric circuit of the crustacean stomatogastric ganglion, whose neurons must burst in a specific order to coordinate digestive muscles. After disruption by physical and pharmacological manipulations, this circuit reliably recovers not only the activity levels of constituent neurons, but also the proper burst order. But how could ADHP, operating only on local information about each neurons average activity, maintain higher-order circuit properties? We explored this question in a computational model of the pyloric pattern generator. We first optimized a set of pyloric-like networks, then optimized ADHP mechanisms for each network to restore its pyloric character after parametric perturbations. This was possible for some networks and impossible for others, so we aimed to explain this disparity. We found that successful homeostatic regulators target average neural activity levels which happen to occur only among pyloric circuits and not among non-pyloric ones, within the set of reachable circuit configurations. Therefore, in subsets of parameter space where such dissociation is possible, activity carries indirect information about burst order, which ADHP can exploit to maintain pyloricness. Other subsets, whose pyloric averages are inseparable from non-pyloric ones, cannot be perfectly regulated. This separability property may explain differences in recovery capacity across perturbations and across individuals.

A model for the joint motion of the basilar membrane (BM) and the outer hair cells (OHC) in the cochlea is presented. The model consists of two one-dimensional mass distributions, one along the OHC and outer hair bundle (OHB) interface, and one along the BM. The motion of these masses is driven by the forces exerted on them by the elastic bodies connecting them and by the pressure difference in the fluids separated by the BM. The model includes a nonlinear motility of the OHC and its coupling with the vibrations of the BM. The model implies a Hopf bifurcation for the dynamical system governing the two coupled distributed oscillators. It is shown that when the system operates near the bifurcation point the BM motion is amplified up to a saturation level. The model provides very sharp frequency decomposition of the incident audio signal according to the place principle. It also acts as a powerful filter that distinguishes pure tones even in the presence of louder noisy background. In addition to simulations of the model, the unusual role played by the OHC friction is studied. Energy estimates are derived for the model functions.

1The brain consists of many interconnected networks with time-varying activity. There are multiple sources of noise and variation yet activity has to eventually converge to a stable state for its computations to make sense. We approached this from a control-theory perspective by applying contraction analysis to recurrent neural networks. This allowed us to find mechanisms for achieving stability in multiple connected networks with biologically realistic dynamics, including synaptic plasticity and time-varying inputs. These mechanisms included anti-Hebbian plasticity, synaptic sparsity and excitatory-inhibitory balance. We leveraged these findings to construct networks that could perform functionally relevant computations in the presence of noise and disturbance. Our work provides a blueprint for how to construct stable plastic and distributed networks.

The cell is the power station of life. Surprisingly, to date there is still no metabolic scaling theory that links cellular respiration to organismal metabolism and predicts the mouse-to-elephant curve, also known as Kleibers law, in an approach that is consistent with physicochemical principles. This paper shows that for a consistent model, the novel concept of the optimised Metabolic Module (MM) is the missing link between cell and organism. It is shown how evolutionary selection under resource scarcity optimises the MM towards (a) lightweight design and (b) resource efficiency. Thus, Darwins evolution by natural selection is simulated by model-based optimisation. The final general model presented is complete (for the entire mass range of the organism of different taxonomic classes), concise (it uses only five scale-invariant physicochemical constants), clear (it predicts all metabolic rates within the uncertainty range of a scale model observed in measurements) and consistent with Murrays law of capillary blood flow and cell metabolism. The model features observed asymptotes for both small protists and large endotherms. It predicts the mass-dependent metabolic rate of protists, planarians, ectotherms and endotherms with the usual uncertainty of any scaling theory. It finally turns out that Kleibers law is an asymptote of the derived general model, namely for the case of diffusion-limited cell metabolism.

Motivated by previous research suggesting that mesoscopic collective activity has the defining characteristics of a turbulent system, we postulate a thermodynamic model based on the fundamental assumption that the activity of a neuron is characterized by two distinct stages: a sub-threshold stage, described by the value of mean membrane potential, and a transitional stage, corresponding to the firing event. We therefore distinguish between two types of energy: the potential energy released during a spike, and the internal kinetic energy that triggers a spike. Formalizing these assumptions produces a system of integro-differential equations that generalizes existing models [Wilson and Cowan, 1973, Amari, 1977], with the advantage of providing explicit equations for the evolution of state variables. The linear analysis of the system shows that it supports single- or triple-point equilibria, with the refractoriness property playing a crucial role in the generation of oscillatory behavior. In single-type (excitatory) systems this derives from the natural refractory state of a neuron, producing "refractory oscillations" with periods on the order of the neuron refractory period. In dual-type systems, the inhibitory component can provide this functionality even if neuron refractory period is ignored, supporting mesoscopic-scale oscillations at much lower activity levels. Assuming that the model has any relevance for the interpretation of LFP measurements, it provides insight into mesocale dynamics. As an external forcing, theta may play a major role in modulating key parameters of the system: internal energy and excitability (refractoriness) levels, and thus in maintaining equilibrium states, and providing the increased activity necessary to sustain mesoscopic collective action. Linear analysis suggest that gamma oscillations are associated with the theta trough because it corresponds to higher levels of forced activity that decreases the stability of the equilibrium state, facilitating mesoscopic oscillations.

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

Activity-dependent modifications of synaptic efficacies are a cellular substrate of learning and memory. Current theories propose that the long-term maintenance of synaptic efficacies and memory is accomplished via a positive-feedback loop at the level of production of a protein species or a protein state. Here we propose a qualitatively different theoretical framework based on negative feedback at the level of protein elimination. This theory is motivated by recent experimental findings regarding the binding of PKM{zeta} and KI-BRA, two synaptic proteins involved in maintenance of memory, and on how this binding downregulates the proteins degradation. We demonstrate this theoretical framework with two different models. First, a simple abstract model to explore generic features of the negative-feedback process. Second, a biophysical model based on PKM{zeta}-KIBRA dimers that cooperatively form larger complexes at active synapses. These larger complexes have slower degradation and diffusion, allowing for bistability of potentiated and unpotentiated synaptic states. The results of these models are qualitatively consistent with existing experiments showing reversal of long-term potentiation and erasure of long-term memory by inhibition of KIBRA-PKM{zeta} interactions. The theory generates novel predictions that could be experimentally tested to further validate or reject the negative-feedback theory.

Traditional models of neural excitability, such as the Hodgkin-Huxley framework, treat the action potential as a purely electrical phenomenon. While its thermodynamic footprint--including heat and entropy generation--is experimentally known, it is typically regarded as a passive consequence of signal propagation. This work explores the hypothesis that this thermodynamic output is not passive, but instead plays an active role in modulating neural function. To investigate this, we developed a novel, fully coupled electro-thermo-entropic model where the entropy generated by an action potential directly feeds back to influence the kinetics of ion channels. Our simulations demonstrate a profound consequence of this coupling: the action potential undergoes progressive self-amplification, driven by a massive acceleration of its underlying kinetics. As the signal propagates, its peak amplitude grows significantly while its temporal duration remains remarkably stable. Furthermore, a statistical analysis reveals that this mechanism relies on the system operating as a robust thermodynamic switch, transitioning between a low-entropy quiescent state and a high-dissipation active state. Finally, we show that achieving this high-performance, amplifying state requires a disproportionately high energetic cost, a finding we term the Intelligence Premium. These results suggest that the action potential is a coupled electro-thermodynamic process that actively enhances its own strength and reliability. Our model offers a candidate mechanism for how waste energy is repurposed into a functional signal, providing a physical explanation for the brains high energy consumption and opening new perspectives on the link between thermodynamics and computation.

The Kolliker-Fuse nucleus (KF), which is part of the parabrachial complex, participates in the generation of eupnea under resting conditions and the control of active abdominal expiration when increased ventilation is required. Moreover, dysfunctions in KF neuronal activity are believed to play a role in the emergence of respiratory abnormalities seen in Rett syndrome (RTT), a progressive neurodevelopmental disorder associated with an irregular breathing pattern and frequent apneas. Relatively little is known, however, about the intrinsic dynamics of neurons within the KF and how their synaptic connections affect breathing pattern control and contribute to breathing irregularities. In this study, we use a reduced computational model to consider several dynamical regimes of KF activity paired with different input sources to determine which combinations are compatible with known experimental observations. We further build on these findings to identify possible interactions between the KF and other components of the respiratory neural circuitry. Specifically, we present two models that both simulate eupneic as well as RTT-like breathing phenotypes. Using nullcline analysis, we identify the types of inhibitory inputs to the KF leading to RTT-like respiratory patterns and suggest possible KF local circuit organizations. When the identified properties are present, the two models also exhibit quantal acceleration of late-expiratory activity, a hallmark of active expiration featuring forced exhalation, with increasing inhibition to KF, as reported experimentally. Hence, these models instantiate plausible hypotheses about possible KF dynamics and forms of local network interactions, thus providing a general framework as well as specific predictions for future experimental testing. Key pointsThe Kolliker-Fuse nucleus (KF), a part of the parabrachial complex, is involved in regulating normal breathing and controlling active abdominal expiration during increased ventilation. Dysfunction in KF neuronal activity is thought to contribute to respiratory abnormalities seen in Rett syndrome (RTT). This study utilizes computational modeling to explore different dynamical regimes of KF activity and their compatibility with experimental observations. By analyzing different model configurations, the study identifies inhibitory inputs to the KF that lead to RTT-like respiratory patterns and proposes potential KF local circuit organizations. Two models are presented that simulate both normal breathing and RTT-like breathing patterns. These models provide plausible hypotheses and specific predictions for future experimental investigations, offering a general framework for understanding KF dynamics and potential network interactions.