Biological Cybernetics

Although many animals rely on visual information to navigate, optic flow is inherently ambiguous as it confounds information about motion speed and object distance. As a result, the visual feedback produced by a given motor command is context-dependent and requires an appropriately adapted response. Recent experiments have investigated how the fish Danionella cerebrum use visual cues to stabilize their position against simulated external currents. Logarithmic sensorimotor transformations have been proposed to enable adaptive responses to perturbations while preventing delay-induced instabilities. Here, we develop the theoretical framework introduced for continuous locomotion to show how logarithmic coding naturally gives rise to this adaptive behavior. The system is modeled by a nonlinear delay differential equation, which is analyzed using dynamical systems theory. We further analyze experimental data to uncover the mechanisms underlying swimming initiation and positional drift correction. Finally, we extend our framework to intermittent locomotion, resulting in a nonlinear difference equation, and show that it still produces robust adaptive behavior. This is motivated by the literature on zebrafish, where visuomotor stabilization has been extensively studied, but burst-and-coast swimming obscures the underlying adaptation mechanism. We show that our theory can reproduce the experimental results reported for motor adaptation in zebrafish without invoking internal models. Overall, our results highlight logarithmic coding as a unifying principle for visuomotor stability across continuous and intermittent locomotor regimes.

Paramecium is a large unicellular organism that swims in fresh water using cilia. When stimulated by various means (mechanically, chemically, optically, thermally), it often swims backward then turns and swims forward again in a new direction: this is called the avoiding reaction. This reaction is triggered by a calcium-based action potential. For this reason, several authors have called Paramecium the "swimming neuron". Here we present an empirically constrained model of its action potential based on electrophysiology experiments on live immobilized paramecia, together with simultaneous measurement of ciliary beating using particle image velocimetry. Using these measurements and additional behavioral measurements of free swimming, we extend the electrophysiological model by coupling calcium concentration to kinematic parameters, turning it into a swimming model. In this way, we obtain a model of autonomously behaving Paramecium. Finally, we demonstrate how the modeled organism interacts with an environment, can follow gradients and display collective behavior. This work provides a modeling basis for investigating the physiological basis of autonomous behavior of Paramecium in ecological environments. Author SummaryBehavior depends on a complex interaction between a variety of physiological processes, the body and the environment. We propose to examine this complex interaction in an organism consisting of a single excitable and motile cell, Paramecium. The behavior of Paramecium is based on trial and error: when it encounters an undesirable situation, it backs up and changes direction. This avoiding reaction is triggered by an action potential. Here we developed an empirically constrained biophysical model of Parameciums action potential, which we then coupled to its kinematics. We then demonstrate the potential of this model in investigating various types of autonomous behavior, such as obstacle avoidance, gradient-following and collective behavior.

Effective motor control requires sensory feedback but is seriously complicated by the sensorimotor delay (SMD), which is the time delay between the state of the body at feedback generation and the arrival in the bodys muscles of the feedback-informed motor command. I describe and evaluate three SMD compensation mechanisms: gain scaling, the convolution predictor, and the Smith predictor. These mechanisms are implemented using control theory results for linear dynamical systems, which are well motivated for balance control. These mechanisms are investigated theoretically and by simulations of balance control, both free standing and while riding a bicycle. I demonstrate that compensating for a SMD requires a convolution predictor, which involves a convolution over a memory buffer of efference copies and an initial condition obtained from a state observer that is based on a delayed-input forward model. The performance of a convolution predictor does not crucially depend on its exact computational implementation because a similar performance is obtained with an approximate convolution using a boxcar kernel. I also demonstrate that gain scaling is an effective SMD compensation mechanism but is not sufficient to compensate for a neurobiological SMD. Finally, I demonstrate that the Smith predictor is an ineffective and neurobiologically implausible SMD compensation mechanism for an unstable mechanical system.

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

Nonlinear mechanisms are at the heart of neuronal information processing, for example to fire an action potential, the membrane voltage must exceed a threshold nonlinearity. Even though, linear encoding schemes are commonly used and often successfully describe large parts of sensory encoding nonlinear mechanisms such as thresholds and saturations are well known to be crucial to encode behaviorally relevant features in the stimulus space not captured by linear methods. Here we analyze the role of bursts in p-type electroreceptor afferents (P-units) in the weakly electric fish Apteronotus leptorhynchus. It is long known that subpopulations of these cells fire bursts of action potentials while others do not. Previous research suggests, that the non-bursting cells are better at encoding the stimulus time-course while bursting neurons are better suited to encode special features in the stimulus. We here show, based on the analysis of experimental data and modeling, that bursts affect the linear as well as the nonlinear encoding. Theoretical work predicts that in simple leaky-integrate-and-fire model neurons, two periodic stimuli interact nonlinearly when the sum of the two frequencies matches the neurons baseline firing rate as quantified by the second-order susceptibility. Indeed, such nonlinear responses have been found in non-bursting P-units when stimulated by two beats simultaneously but only in those cells, that exhibit very low levels of intrinsic noise. In this study, we found that bursts strongly enhance these nonlinear responses which may play a critical role in the detection of weak intruder signals in the presence of a strong female signal, i.e. an electrosensory cocktail party.

In electrically coupled networks, the coupling coefficient (CC) quantifies the strength of the connectivity or the degree to which two participating nodes are coupled in response to an external input to one of them. The CC is measured by computing the relative responses of the indirectly activated (post-J) and the directly activated (pre-J) nodes. In response to time-dependent inputs, the CC is frequency-dependent and has two components capturing the contributions of the amplitude and phase frequency profiles of the participating nodes (quotient of the amplitudes and phase-difference, respectively). The properties and mechanisms of generation of the frequency-dependent CCs (FD-CCs) are largely unknown beyond electrically coupled passive cells and their electrical circuit equivalents. Being linear and 1D, the FD-CCs for passive cells are relatively simple, consisting of low-pass filters (amplitude) and positive and monotonically increasing phase-difference profiles. In linear systems, the FD-CCs depend on the properties of the pre-J cell and the connectivity and are independent of the properties of the post-J cell and the input amplitude. There is a gap in our understanding of the FD-CCs are shaped by (i) how the presence of intrinsic cellular positive and negative feedback currents and the resulting amplification and resonance phenomena, and (ii) the presence of cellular nonlinearities that incorporates the dependence of the FD-CC on the post-J node in addition to the pre-J one. In this paper we address these issues by using biophysically plausible (conductance-based) mathematical modeling, numerical simulations, analytical calculations and dynamical systems tools. We conduct a systematic analysis of the properties of the FD-CC in networks of two electrically connected nodes receiving oscillatory inputs, which is the minimal network architecture that allows for a systematic study of the biophysical and dynamic mechanisms that shape the FD-CC profiles. The participating neurons are either passive cells (low-pass filters) or resonators (band-pass filter) and exhibit lagging or mixed leading-lagging phase-shift responses as the input frequency increases. The formalism and tools we develop and use in this paper can be extended to larger networks with an arbitrary number of nodes, to spatially extended multicompartment neuronal models, and to neurons having a variety of ionic currents. The principles that emerge from our study are directly applicable to these scenarios. Our results make experimentally testable predictions and have implications for the understanding of spike transmission, synchronized firing and coincidence detection in electrically coupled networks in the presence of oscillatory inputs. For clarity, the paper includes an extensive supplementary material section.

Hydra is a non-senescent animal with a relatively small number of cell types and overall low structural complexity, but a surprisingly rich behavioral repertoire. The main drivers of Hydra s behavior are neurons that are arranged in two nerve nets comprising several distinct neuronal populations. Among these populations is the ectodermal nerve net N3 which is located throughout the animal. It has been shown that N3 is necessary and sufficient for the complex behavior of somersaulting and is also involved in Hydra feeding behavior. Despite being a behavioral jack-of-all-trades, there is insufficient knowledge on the coupling structure of neurons in N3, its connectome, and its role in activity propagation and function. We construct a model connectome for the part of N3 located on the body column. Using experimental data on the placement of neuronal somata and the spatial dimensions of the body column, we show that a generative network model combining non-random placement of neuronal somata and the preferred orientation of primary neurites yields good agreement with experimentally observed distributions of connection distances, connection angles, and the number of primary neurites per neuron. Having validated the N3 connectome model in this fashion, we place a simple excitable dynamical model on each node of the body column network and show that it generates directed, short-lived, fast propagating patterns of activity. In addition, by slightly changing the parameters of the dynamical model, the same structural network can also generate persistent activity. Finally, we use a neuromorphic circuit based on the Morris-Lecar model to show that the same structural connectome can, in addition to through-conductance with biologically plausible time scales, also host a dynamical pattern related to the complex behavioral pattern of somersaulting. We speculate that such different dynamical regimes act as dynamical substrates for the different functional roles of N3, allowing Hydra to exhibit behavioral complexity with a relatively simple nervous system that does not possess modules or hubs.

Multiple studies have experimentally observed common fluctuations in the discharge rates of spinal motor neurons, which have been classically interpreted as generated by correlated synaptic inputs. However, so far it has not been possible to identify the number of inputs, nor their relative strength, received by each motor neuron. This information would reveal the distribution of inputs and dimensionality of the neural control of movement at the motor neuron level. Here, we propose a method that generates networks of correlation between motor neuron outputs to estimate the number of common inputs to motor neurons and their relative strengths. The method is based on force-directed graphs, the hierarchical clustering of motor neurons in the graphs, and the estimation of input strengths based on the graph structure. To evaluate the accuracy and robustness of the method, we simulated 100 motor neurons driven by a known number of inputs with fixed weights. The simulation results showed that 99.2 {+/-} 0.6%, 94.3 {+/-} 2.2 %, and 95.1 {+/-} 2.7 % of the motor neurons were accurately assigned to the input source with the highest weight for simulations with 2, 3, and 4 inputs, respectively. Moreover, the normalised weigths (range 0 to 1) with which each input was transmitted to individual motor neurons were estimated with a root-mean-squared error of 0.11, 0.18, and 0.28 for simulations with 2, 3, and 4 inputs, respectively. These results were robust to errors introduced in the discharge times (as they may occur due to errors by decomposition algorithms), with up to 5% of missing spikes or false positives. We finally applied this method on various experimental datasets to demonstrate typical case scenario when studying the neural control of movement. Overall, these results show that the proposed graph-based method accurately describes the distribution of inputs across motor neurons. Authors summaryAn important characteristics for our understanding of the neural control of natural behaviors if the dimensionality in neural control signals to the musculoskeletal system. This dimensionality in turn depends on the number of synaptic inputs transmitted to the elementary units of this control, i.e., the spinal motor neurons, and on their correlation. We propose a graph-based approach applied to the discharge times of motor neurons to estimate the number of inputs and associated strength transmitted to each motor neuron. For this purpose, we first calculated the correlation between motor neuron smoothed discharge rates, assuming that correlated discharge rates result from the reception of a correlated inputs. Then, we derived networks/graphs in which each node represented a motor neuron and where the nodes were positioned close to each or further apart, depending on the level of correlated activities of the corresponding motor neurons. Using simulations of motor neuron behaviour, we showed that the spatial information embedded in the proposed graphs can be used to accurately estimate the number and the relative strengths of the inputs received by each motor neurons. This method allows to reconstruct the distribution of synaptic inputs to motor neurons from the observed motor neuron activity.

Accurate navigation often requires the maintenance of a robust internal estimate of heading relative to external surroundings. We propose a novel model for angular velocity integration to update the representation of heading in the central complex of the desert locust. In contrast to similar models proposed for the fruit fly, this circuit model uses a single 360{degrees} heading direction representation and is updated by neuromodulatory angular velocity inputs. Our computational model was implemented using steady-state firing rate neurons with dynamical synapses. The circuit connectivity was constrained by biological data and remaining degrees of freedom were optimised with a machine learning approach to yield physiologically plausible neuron activities. We demonstrate that the integration of heading and angular velocity in this circuit is robust to noise. The heading signal can be effectively used as input to an existing insect goal-directed steering circuit, adapted for outbound locomotion in a steady direction that resembles locust migration. Our study supports the possibility that similar computations for orientation may be implemented differently in the neural hardware of the fruit fly and the locust. Author summaryIn both fruit flies and locusts, a specific brain region has been observed to have an activity pattern that resembles a compass, with an activity peak moving across an array of neurons as the animal rotates through 360 degrees. However, some apparent differences in the properties of this pattern between the two species suggest there may be differences in how this internal compass is implemented. Here we focus on the locust brain, building a computational model that is based on observed neural connections and using machine learning to tune the system. Turning by the simulated locust provides modulatory input to the neural circuit that keeps activity in the array aligned to its heading direction. We simulate a migrating locust that tries to keep the same heading despite perturbances and show this circuit can steer it back on course. Our model differs from existing models of the fruit fly compass, showing how similar computations could have different implementations in different species. O_TBL View this table: org.highwire.dtl.DTLVardef@109a8b3org.highwire.dtl.DTLVardef@12298eborg.highwire.dtl.DTLVardef@65a654org.highwire.dtl.DTLVardef@18ae048org.highwire.dtl.DTLVardef@8ace20_HPS_FORMAT_FIGEXP M_TBL O_FLOATNOTable 1.C_FLOATNO O_TABLECAPTIONAbbreviations for neuron types and brain regions in the desert locust (Schistocerca gregaria) and homologues in the fruit fly (Drosophila melanogaster). C_TABLECAPTION C_TBL

Animals rely on both feedforward and feedback control for perturbation responses. When comparing animals of different sizes, we find that several features that affect perturbation responses change--larger animals have longer sensorimotor time delays, heavier body segments and proportionally weaker muscles. We used simple computational models to compare fast perturbation response times under feedforward and feedback control, as a function of animal size. We developed two tasks representing common perturbation response scenarios in animal locomotion: a distributed mass pendulum approximating swing limb repositioning (swing task), and an inverted pendulum approximating whole body posture recovery (posture task). First, we used a normalized feedback control system to show how feedback response times can either be limited by the force generation capacity of muscles (force-limited), or by sensorimotor delays which constrain the maximum feedback gains that can be used to produce stable responses (delay-limited). Next, we used more detailed scaled models which represent the full-size range of terrestrial mammals and parameterized the sensorimotor delays, maximum muscle forces, and inertial properties using published scaling relationships from literature. Across animal size and in both tasks, we found that feedback control was primarily delay-limited--the fastest responses used a fraction of the available muscle force capacity. Feedforward control, which is able to fully activate muscles and produce faster responses--was about four times faster than feedback control in the smallest animals, and around two times faster in the largest animals. For rapid perturbation responses, feedback control appears ineffective for terrestrial mammals of all sizes, as the fastest response times exceeded available movement times, while feedforward control did not. Thus, feedforward control is more effective for reacting quickly to sudden and large perturbations in animals of all sizes.

The stomatogastric ganglion (STG) is a group of about 30 neurons that resides on the stomach in decapod crustaceans. Its two central pattern generators (CPGs) control the chewing action of the gastric mill and the peristaltic movement of food through the pylorus to the gut. The STG has been studied extensively because it has properties that are common to all nervous systems and because of the small number of neurons and other features that make it convenient to study. So many details are known that the STG is considered a classic test case in neuroscience for the reductionist strategy of explaining the emergence of macro-level phenomena from micro-level data. In spite of the intense scrutiny the STG has received, how it generates its rhythmic patterns of bursts remains unknown. The explicit neural networks proposed here model the pyloric CPG of the American lobster (Homarus americanus). The models share enough significant features with the lobsters CPG that they may be considered first approximations, or perhaps simplified versions, of STG architecture. The similarities include 1) mostly inhibitory synapses; 2) pairs of cells with reciprocal inhibitory inputs, complementary outputs that are approximately 180 degrees out of phase, and state changes occurring with the high output changing first; 3) cells that have reciprocal, inhibitory inputs with more than one other cell; and 4) six cells that produce coordinated oscillations with the same period, four phases distributed approximately uniformly over the period, and half of the burst durations approximately 1/4 of the period and the other half 3/8. Each models connectivity is explicit, and its operation depends only on minimal neuron capabilities of excitation and inhibition. One model performs a function that fills a gap in standard ring oscillators. It is apparently new to engineering, making it an example of neuroscience and logic circuit design informing each other. Some models are derived from standard circuit designs by moving each negation symbol from one end of a connection to the other. This does not change the logic of the network, but it changes each logic gate to one that can be implemented with a single neuron.

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.

Two simple models - vaulting over stiff legs and rebounding over compliant legs - are employed to describe the mechanics of legged locomotion. It is agreed that compliant legs are necessary for describing running and that legs are compliant while walking. Despite this agreement, stiff legs continue to be employed to model walking under the assumption that the compliance of the leg during walking is high enough to be considered stiff. Here we study gait choice and walk-to-run transition in a biped with compliance and show that the principles underlying gait choice and transition are completely different from stiff legs. Two findings underpin our conclusions: First, at the same speed, step length, and stance duration, multiple gaits that differ in the number of leg contraction cycles are possible. Among them, humans and other animals choose the (normal) gait with M-shaped vertical ground reaction forces (vGRF) not just because of energy considerations but also constraints from forces. Second, the transition from walking to running occurs because of three factors: vGRF minimum at mid-stance characteristic of normal walking, synchronization of horizontal and vertical motions during single support, and velocity redirection during the double support. The insight above required an analytical approximation of the double spring-loaded pendulum (DSLIP) model describing the intricate oscillatory dynamics that relate single and double support phases. Additionally, we also examined DSLIP as a quantitative model for locomotion and conclude that DSLIP speed-range is limited. However, insights gleaned from the analytical treatment of DSLIP are general and will inform the construction of more accurate models of walking.

In the present work, we propose a new integrated mathematical model for the neuromuscular activation of a motor unit, describing the four consecutive processes, leading to muscle contraction--neural impulse propagation, acetylcholine transport in the neuromuscular junction, calcium release in the muscle cell, and force generation. We connect in an appropriate way models of the respective processes, known from the literature, and validate the resulting model by showing that it can reproduce with high accuracy experimental data for two motor unit twitches on a rat medial gastrocnemius muscle and can numerically restore the sequence of events that result in force generation. Sensitivity analysis for some of the model parameters is further performed to study their effect on the model solutions and to show that they can be related to known malfunctions or treatments of the neuromuscular system.

Inhibitory synapses can control a neurons firing rate and also control supralinear dendritic integration. It is not known how inhibitory synapses can learn to perform these functions using only signals available locally at the synaptic site. We study an inhibitory plasticity rule based on the Bienenstock-Cooper-Munro theory in multicompartment models of striatal projection neurons, and show that it can perform these two functions. The rule uses local voltage-gated calcium concentration in the dendrites to regulate inhibitory synaptic strength. We show that, for rate-coded inputs, the rule can achieve precise control of neuronal firing rate after changes in excitatory input rate or excitatory synaptic strength. Additionally, for sparsely-coded inputs that activate localized synaptic clusters in dendrites, the rule can either allow or inhibit the supralinear dendritic response evoked by the clustered excitatory synapses, or equalize the dendritic response arising from different clusters. Finally, we demonstrate the use of learning to inhibit supralinear dendritic integration for solving the nonlinear feature binding problem (NFBP), in tandem with a simple excitatory plasticity rule. We conclude by discussing why the collateral inhibitory synapses between striatal projection neurons could contribute to solving the NFBP with this plasticity rule. Author summaryNeurons are the main cells in the nervous system that process information. They receive signals from the bodys senses--both external and internal--and use them to guide actions such as muscle movement and the regulation of bodily functions. A neuron becomes active when incoming signals excite it strongly enough. But for neurons to work timely, precisely, and reliably, their activity needs to be shaped, modified and controlled. This is done by inhibition, which comes from specialized inhibitory neurons. In this article we study how inhibition can learn to do two of its most basic roles in the nervous system. The first is to help neurons stay responsive across a wide range of input strengths--from very weak to very strong stimulation. For example, neurons in the retina allow vision both in dim starlight and in bright sunlight, even though these conditions differ in brightness by a trillion-fold. Inhibition contributes to handling this huge range by preventing overstimulation of the neurons in bright light. The second role of inhibition is to control strong, local excitations that occur on specific dendritic branches of a neuron. These local excitations can suddenly push a neuron into activity, and inhibition controls whether such excitations are allowed or suppressed. We use a learning mechanism that is already known to exist for excitatory synapses, but here we apply it to inhibition to explore what it could achieve. The results show that if inhibitory synapses used this same learning rule, they could support the two fundamental roles of inhibition in the nervous system described above.

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 general, control of movement is considered to be either cortical, spinal, or purely biomechanical and is studied separately at these levels. To achieve this separation when studying a particular level, variations that may be introduced by the other levels are generally either ignored or restricted. This restriction misrepresents the way movements occur in realistic scenarios and limits the ability to model movements in a biologically inspired manner. In this work, we propose a heuristic model for motor control that conceptually and mathematically accounts for the entire motor process, from target to endpoint. It simulates human arm motion and is able to represent functionally different motion properties by flexibly choosing more or less complex motion paths without built-in optimization or joint constraints. With a novel implementation of hierarchical control, this model successfully overcomes the problem of degrees of freedom in robotics. It can serve as a template for neurocomputational work that currently uses control architectures that do not mirror the human motor control process. The model itself also suggests a maximum threshold for delays in position feedback for effective movement, and that the primary role of position feedback in movement is to overcome the effects of environmental perturbations at the joint level. These findings can inform future efforts to develop biologically inspired motor control techniques for prosthetic devices.

Since its introduction by Briat, Gupta and Khammash, the antithetic feedback controller design has attracted considerable attention in both theoretical and experimental systems biology. The case in which the plant is a two-dimensional linear system (making the closed-loop system a nonlinear four-dimensional system) has been analyzed in much detail. This system has a unique equilibrium but, depending on parameters, it may exhibit periodic orbits. An interesting open question is whether other dynamical behaviors, such as chaotic attractors, might be possible for some parameter choices. This note shows that, for any parameter choices, every bounded trajectory satisfies a Poincare-Bendixson property. The analysis is based on the recently introduced notion of k-cooperative dynamical systems. It is shown that the model is a strongly 2-cooperative system, implying that the dynamics in the omega-limit set of any precompact solution is conjugate to the dynamics in a compact invariant subset of a two-dimensional Lipschitz dynamical system, thus precluding chaotic and other strange attractors.

In sensory systems, stimuli are represented through the diverse firing responses and receptive fields of neurons. These features emerge from the interaction between excitatory (E) and inhibitory (I) neuron populations within the network. Changes in sensory inputs alter this balance, leading to shifts in firing patterns and the input-output properties of individual neurons and the network. While these phenomena have been studied extensively with experiments and theory, the underlying principles for combining E and I inputs are still unclear. Here, the rules for probabilistically combining E and I inputs are derived that describe how neurons in a feedforward inhibitory circuit respond to stimuli. This simple model is broadly applicable, capturing a wide range of response features that would otherwise require multiple separate models and offers insights into the cellular and network mechanisms influencing the input-output properties of neurons, gain modulation, and the emergence of diverse temporal firing patterns. Author SummarySensory stimuli activate a broad network of excitatory and inhibitory neurons. The response of individual neurons is often complex and influenced by the animals state--such as whether it is resting, moving, or attending to a specific environmental cue. To understand how stimulus features are encoded and modulated, it is essential to examine how synaptic inputs are integrated within individual neurons and across neural networks. In this manuscript, I propose a set of rules for combining excitatory and inhibitory synaptic inputs in neural circuits. This simple, general model captures key features of sensory-driven responses.

Nonlinear feedback controllers are ubiquitous features of biological systems at different scales. A key motif arising in these systems is a sequestration-based feedback. As a physiological example of this type of feedback architecture, platelets (specialized cells involved in blood clotting) differentiate from stem cells, and this process is activated by a protein called Thrombopoietin (TPO). Platelets actively sequester and degrade TPO, creating negative feedback whereby any depletion of platelets increases the levels of freely available TPO that upregulates platelet production. We show similar examples of sequestration-based feedback in intracellular biomolecular circuits involved in heat-shock response and microRNA regulation. Our systematic analysis of this feedback motif reveals that platelets induced degradation of TPO is critical in enhancing system robustness to external disturbances. In contrast, reversible sequestration of TPO without degradation results in poor robustness to disturbances. We develop exact analytical results quantifying the limits to which the sensitivity to disturbances can be attenuated by sequestration-based feedback. Next, we consider the stochastic formulation of the circuit that takes into account low-copy number fluctuations in feedback components. Interestingly, our results show that the extent of random fluctuations are enhanced with increasing feedback strength, but can exhibit local maxima and minima across parameter regimes. In summary, our systematic analysis highlights design principles for enhancing the robustness of sequestration-based feedback mechanisms to external disturbances and inherent noise in molecular counts.