Biological Cybernetics

AO_SCPLOWBSTRACTC_SCPLOWMuscle efficiency decreases with increasing size, largely due to a relative decrease in its mechanical output. Muscle mechanical output depends on its activation, strain, and strain rate and thus varies between different muscles within a limb during locomotion. Distinct muscle coordination patterns are required for efficient cycling, and so we would expect that the coordination patterns for efficient cycling or indeed locomotion would change across animal sizes. We tested whether muscle coordination would change with muscle size using data derived from human cycling: this paradigm allowed for controlled changes in both crank torque and cadence, allowing the multifactorial problem of muscle power output to be decomposed. We used kinematic and pedal data from 12 cyclists undergoing steady pedalling at cadences from 80 to 140 r.p.m. and generated musculoskeletal simulations of their movements. We introduced novel multisegment muscle models in the simulation that incorporated the internal muscle mass and thus accounted for the scaling effects of muscle tissue inertia. We solved the simulations for the muscle activity that was required to minimise the metabolic cost during cycling for each condition. The masses of the muscle models were scaled across five orders of magnitude. The predicted muscle activations were classified by Principal Component analysis to identify whether the coordination of muscle activity was modulated across models with different sized muscles. Analysis of variance revealed significant changes in coordination at the large-scale factors. This study shows how the coordination of muscle activity during locomotion will likely change across a range of body sizes due to the non-linear effects of the inertial mass within the muscle tissues.

A motoneuron pool is often regarded as a rigid controller because the largely shared synaptic input across motoneurons leads to strongly correlated activity. However, brief deviations from this correlated behavior have been observed even in some constrained tasks, raising the question of whether these results reflect limitations of the rigid view of motoneuron pool control. Here we show that they do not. We developed a biophysical model of a motoneuron pool receiving shared excitatory and inhibitory synaptic inputs that also included the motoneuron-specific effects of neuromodulation; model parameters were tuned based on large-scale motoneuron recordings in humans. Simulations showed that the intrinsic differences in how motoneurons respond to neuromodulation are both necessary and sufficient to transiently decorrelate pairs of motoneurons receiving a shared synaptic input. Crucially, such transient decorrelation is only observed when motoneurons have different sensitivity to neuromodulation, consistent with experimental observations during volitional control in humans. Our model also explains how participants can improve their ability to transiently decorrelate the activity of motoneurons innervating the same muscle by leveraging refined behavioral strategies that exploit the differential response of motoneurons to neuromodulation, rather than through physiological changes. These results identify that heterogeneous sensitivity to neuromodulation enables brief flexibility in the otherwise rigid control of motoneurons enforced by a shared synaptic input, and show how practice allows participants to exploit latent flexibility within otherwise rigid constraints.

The phenomenon of splitting was originally observed in hamsters which, after prolonged exposure to constant light, exhibit two rest/wake cycles within a subjective day. Splitting is a consequence of the left and right suprachiasmatic nuclei (SCN) falling out of synchrony. While it is known that split activity is characterized by an antiphase relationship between the left and right SCN and between the core and shell within each hemisphere, the role of the commissural projections that connect the right and left SCN is not known. In the present study, we investigate the impact of the inter-hemispheric connections on the split and unsplit dynamics of a computational model of the bilateral SCN. Our model has 4 nodes corresponding to each right and left core and shell. We simulated our bilateral model under different lighting conditions and measured its period and the phase relationships among the 4 nodes. To further characterize the dynamics of the system, we performed a bifurcation analysis. We found that the bilateral model automatically splits unless entrained by bright light/dark cycles, or unless it has excitatory inter-hemispheric connections. This suggests that excitatory cross-connections may be important for freerunning behavior. We found that constant light of varying intensities transitions the model between split and unsplit activity only in very limited conditions, but the strength and polarity of the contralateral connections play a much greater role in this dynamical transition. These findings suggest that splitting may involve plasticity of the inter-hemispheric connections of the SCN.

Growing interest to describe the electrical behavior of glial cells, mainly astrocytes, in intact brain tissue poses more and more challenges to commonly accepted belief they only respond in a linear manner in uptake of the excess of extracellular potassium and maintenance of their network equipotentiality. Their highly conductive mutual interconnections via gap junction (GJ) connections introduce yet another class of nonlinear elements. As more studies report nonlinearities in membrane voltage Vm dependence of both, the membrane and junctional conductances, the need to formulate minimal dynamical models of their transient behavior is getting more acute. Since ODE models of coupled cells, even in simplest 1-d arrays, require simplified descriptions and small set of parameters, rare quantitative studies on glia makes the task even more difficult. This study attempts to qualify a self-coupled cell, or a glial cell coupled to fixed voltage as useful system for detecting the nature of instabilities and transitions coming from coupling. In a novel biophysical model of coupled astrocyte, we introduce nonlinear kinetics of deactivation for large junctional voltages for the first time. We found that N-shaped nonlinearities and corresponding fold structure in the vector field of isolated cell serves as a baseline on top of which coupling nonlinearities enrich the bifurcation picture. Numerical simulations of 1-d array of coupled astrocytes show that coupling increases the propensity of astrocytic Vm to bistability and front propagation. We believe that presented illustrations of possible effects of coupling nonlinearities will motivate neurobiologists to further explore their impact in disease. Significance statementTransient changes in membrane voltage of glial cells may produce significant transient voltage difference between directly coupled cells. Nonlinear steady-state conductance of their interconnection elements, the gap junctions, introduce nonlinear current profiles which are very difficult to measure and quantitate using the available methods due to marked permeability of the junctions and leakiness of glial membrane in general. We propose a minimal model of glial membrane extended with a self-coupled feedback loop, which under realistic simplifying assumptions could serve for qualitative analysis of the impact of coupling, on the stability of resting membrane voltage. Neuronal cells of the brain and spinal cord cannot exist and function without supportive and neuromodulatory functions of the diverse population of glial cells. This applies to virtually all physiological processes on cell level - from cell development, metabolic support, membrane signaling, slow molecular signal transduction, ion homeostasis, neurovascular coupling, myelination, to mention only a few, manifest neuro-glial interaction. Even though all glial cell types are interconnected, the most abundant ones, the astrocytes are massively interconnected by gap junctions to form ordered networks. Electrically, astrocytic networks display membrane voltage equipotentiality, which is considered system-wide resting state for given neuro-glial circuit or unit. With molecular and cellular substrates of glial connectivity being slowly elucidated, network science and dynamical modeling are slowly "invading" that area with many important issues left open. In this study using classical dynamical systems approaches we give indications how nonlinear intercellular coupling between astrocytes affects physiological resting state and its instabilities compared to isolated, uncoupled cell. We strongly believe the suggested minimal model could fill the gap in ODE modeling of neuro-glial circuits, within broadest scope of hypothesis-driven research in cell-level neuroscience.

The learning dynamics of biological brains and artificial neural networks are of interest to both neuroscience and machine learning. A key difference between them is that neural networks are often trained from a randomly initialized state whereas each brain is the product of generations of evolutionary optimization, yielding innate structures that enable few-shot learning and inbuilt reflexes. Artificial neural networks, by contrast, require non-ethological quantities of training data to attain comparable performance. To investigate the effect of evolutionary optimization on the learning dynamics of neural networks, we combined algorithms simulating natural selection and online learning to produce a method for evolutionarily conditioning artificial neural networks, and applied it to both reinforcement and supervised learning contexts. We found the evolutionary conditioning algorithm, by itself, performs comparably to an unoptimized baseline. However, evolutionarily conditioned networks show signs of unique and latent learning dynamics, and can be rapidly fine-tuned to optimal performance. These results suggest evolution constitutes an inductive bias that tunes neural systems to enable rapid learning.

Rhythm is a key building block of human music, speech and numerous other human activities. Understanding the computational substrates of rhythm perception requires models that bridge algorithmic function with biological implementation. We propose a physiologically grounded spiking neural network (SNN) framework to investigate the emergent representation and interpretation of auditory rhythms. Utilizing a recurrent SNN architecture trained on an auditory entrainment task, we characterize the networks latent dynamics through the analysis of firing rates and membrane potential fluctuations. Our results demonstrate that simulated neural populations exhibit phase-locking to the stimulus beat, with endogenous oscillations driven by rhythmic input. We further show that anticipatory dynamics--characterized by pre-stimulus depolarization--emerge naturally from the networks synaptic plasticity and temporal integration properties, rather than from explicitly defined oscillators. By treating network layers as functional analogs of cortical populations, this framework allows for the application of spectral and information-theoretic analyses typical of empirical electrophysiology. More in general, this approach establishes SNNs as robust exploratory tools for uncovering how predictive coding and rhythmic entrainment arise from the inherent constraints of biological neural computation.

Sympathetic preganglionic neurons (SPNs) distribute signals widely across paravertebral ganglia, yet the reliability of spike propagation along their predominantly unmyelinated axons remains poorly defined. We examined temperature- and activity-dependent modulation of SPN axonal conduction using an ex vivo adult mouse thoracic sympathetic chain preparation. Population compound action potentials (CAPs) were evoked by supramaximal stimulation of T10 ventral roots and recorded from branching axons in interganglionic compared to unbranching axons in the splanchnic nerve. At physiological temperature (36{degrees}C), scaled CAP magnitude was reduced by [~]50% relative to 22{degrees}C, with preferential loss of slower-conducting axonal components. These reductions are consistent with substantial temperature-dependent decreases in effective axonal recruitment, likely reflecting conduction failure in a large fraction of SPNs. Losses were more pronounced in interganglionic pathways, suggesting increased vulnerability in branching projections. To assess activity-dependent effects, stimuli were delivered at 1, 5, and 20 Hz with focus on 5 and 20 Hz stimulus trains (20s duration). The overall time-course of train-evoked depression was similar across temperatures; however, the underlying axonal populations differed. At 22{degrees}C, slower-conducting axons exhibited marked frequency-dependent depression, whereas at 36{degrees}C the remaining faster-conducting axons displayed facilitation, particularly at 20 Hz. Slower-conducting responses also showed post-train potentiation at physiological temperature. These findings indicate that SPN axonal conduction is not uniformly reliable and is strongly modulated by temperature and activation history. Preferential vulnerability of slow-conducting, likely small-diameter and branching axons identifies axonal conduction as a physiologically regulated site of gain control in sympathetic output.

The awake brain is known to display asynchronous (AS) states during periods of attention and arousal, but the responsiveness properties of such states remain unclear. Here, we investigate this question using computational models of spiking networks of excitatory and inhibitory neurons, mimicking recurrently-connected networks in layer 2/3 of the cerebral cortex. The networks can generate a continuum of AS states, but with different responsiveness characteristics. By using a mean-field model to infer the dynamic properties of the system, we find that there are two families of AS states, which we call "underdamped" (UD) and "overdamped" (OD). Responsiveness is maximised at the transition between OD and UD states, which identifies a "working point" that may present advantageous computational properties.

Mass is a fundamental aspect of muscle contractile function, yet the inertial effects of inactive muscle mass is generally neglected in modeling and not quantified in studies on small muscles or isolated fibers. However, during submaximal contractions, inactive muscle tissue may take longer to be accelerated by active fibers, and may be subject to prolonged deceleration, both of which may potentially reduce force development and work output. We sought to test if inactive tissue mass imposes an inertial penalty on muscle performance, using in situ sinusoidal work-loop experiments on rat plantaris muscles. Regional fascicle dynamics, measured across supramaximal and submaximal levels of activation, showed that decreasing activation significantly reduced fascicle strain and increased both shortening and lengthening latency. Contrary to our predictions, however, reductions in work, beyond those explained by decreased fascicle strain, were negligible. Normalized work did not decline disproportionately relative to force, suggesting no clear inertial penalty on work at this muscle size. Our findings suggest that while inactive muscle mass influences the dynamics of submaximal contractions, its impact on work during submaximal contractions at small muscle sizes is limited.

The routing of information across the brains structural network is central to its wide range of functional capabilities. However, the mechanisms underlying information routing in complex brain networks, particularly between regions that do not share a direct anatomical connection, remain poorly understood. Neural mass models (NMMs), a computational modelling framework capable of capturing complex neural dynamics across scales, can potentially be used to study the dynamical and network bases of these vital polysynaptic routing processes. In this study, we investigate polysynaptic signalling in three widely used NMMs, obeying Ornstein-Uhlenbeck, Stuart-Landau, and Jansen-Rit dynamics, by tracking the propagation of a discrete, focal, high-amplitude perturbation across the underlying network. We find that polysynaptic propagation emerges in all tested NMMs when configured within dynamical regimes that effectively enhance the persistence of perturbations. We also find distinct parameter domains that maximise signal propagation to directly connected regions and to those separated from the source by at least two hops. Finally, we benchmark in silico stimulus propagation in the brain network against an empirical dataset of direct electrical stimulation trials, to explore the relative capabilities of the NMMs in capturing signal propagation to connected versus unconnected regions. This analysis highlights the significance of dynamical repertoire in capturing stimulus propagation outcomes. Overall, this study provides insights into how dynamical and network features shape signal propagation over complex brain networks.

Calibration of closed-loop lumped-parameter cardiovascular models remains a major bottleneck for scalable digital-twin generation because inverse estimation is ill-conditioned and typically requires computationally expensive iterative forward simulation. This study investigates whether a supervised neural network (NN) can provide a fast inverse estimator for a paediatric sepsis cardiovascular ODE model by learning a direct mapping from prescribed haemodynamic target vectors to calibrated parameter sets. Training data are generated by sampling model parameters at random, forward-simulating the closed-loop system to steady state, and pairing the resulting target summaries with the corresponding parameters; the same target definitions and evaluation populations are used throughout for consistency. We evaluate NN inference by forward re-simulation to steady state and benchmark performance against a simulator-constrained calibration reference (Embedded Gradient Descent, EGD) using relative-error statistics, distributional similarity of achieved outputs and inferred parameters (median shift, IQR ratio, Wasserstein distance, KS statistic), and target-space localisation of parameter-space disparity (cosine distance). The NN reproduces the prescribed targets with predominantly small errors for most samples, while the largest discrepancies are confined to a well defined set of target configurations that also yield high residuals under the reference method, indicating feasibility limits of the target/model combination. Overall, NN-guided calibration provides a computationally efficient accelerator for virtual-twin generation and target-space screening, with simulator-based refinement and forward re-simulation retained to handle infeasible regimes and enforce mechanistic plausibility.

In previous studies by the author on binocular vision with the asymmetric eye (AE), which models a healthy human eye with misaligned optical components, the results were primarily presented in the Rodrigues vector (RV) framework and supported by simulations and 3D visualizations in GeoGebras dynamic geometry environment. In this paper, the novel geometric kinematics of the human eye, that is, the eye with misaligned optics, and simplified assumptions about the eye rotations (the eyes translational movements are disregarded), are developed within the framework of rigid-body rotations. The originality of the analysis lies in a precise geometric decomposition of a full rotation of the eyes posture into a torsion-free rotation (the geodesic part) and a torsional rotation (the non-geodesic extension of the geodesic part). This decomposition is extended to the corresponding decomposition of the angular velocity. A novel derivation of the eyes angular velocity from the RV formulation of the eye kinematics is proposed.

The ability of chemotactic populations to localize and track targets in fluctuating environments depends critically on the temporal structure of environmental signals. Using a minimal agent-based framework of non-interacting run-and-tumble cells implementing an E. coli-inspired temporal sensing strategy, populations are exposed to static and moving chemoattractant fields perturbed by noise with controlled temporal structure, spanning white, pink (1/f), and correlated Ornstein-Uhlenbeck processes. Chemotactic populations are found to act as temporal filters, robustly suppressing fast fluctuations while remaining highly sensitive to slowly varying perturbations. As a consequence, chemotactic performance is governed not by noise amplitude, but by its temporal correlations. By continuously varying the noise correlation time, a critical regime emerges at{tau} c [~]{tau} run, where aggregates lose stability, tracking errors increase sharply, and spatial dispersion rises. Power spectral analysis further shows that the low-frequency power fraction of the signal provides a strong predictor of failure, outperforming total signal variance and establishing a direct link between environmental noise spectra and collective behavior. Introducing external flow reveals that advective transport amplifies noise-induced destabilization when it overlaps the chemotactic capture region, defining a combined spatiotemporal constraint on robustness. Together, these results identify temporal correlations and spectral structure as fundamental control parameters for chemotactic organization and provide a quantitative framework for predicting and designing collective behavior in fluctuating environments.

Human goal pursuit is often marked by persistent activity toward achieving an objective, as well as flexibility in switching objectives based on environmental demands. How humans balance the stability and flexibility necessary for goal pursuit is the key question of this study. We propose that goal pursuit generates dynamic attractor modes in policy landscapes that produce stability in goal pursuit. The attractor properties are modulated through progress monitoring, allowing for the flexibility necessary to switch objectives in favor of alternative goals. Through simulations and behavioral cloning of human participants performing an extended goal selection task, we show how dynamic modes can develop in the latent spaces of recurrent neural networks trained with reinforcement learning. We develop metrics to quantitatively assess the attractor qualities of dynamic modes, validating them against synthetically generated dynamical systems, and use them to investigate the context modulation of attractor modes during goal pursuit. We then proceed to develop a circuit-level account of goal persistence incorporating self-excitation and cross-inhibition as motifs for fast, self-sustaining dynamics modulated by slow, progress-integrating momentum and context signals. Lastly, we show that the switching costs experienced while managing multiple goals are an emergent property of resistance to the intrinsic dynamics of goal pursuit, thereby contributing a fresh perspective on the dynamics of extended goal pursuit.

The acquisition of sensorimotor skills critically depends on basal ganglia (BG)-thalamo-cortical circuits. Prevailing theories propose that the BG optimize motor output through reinforcement learning (RL), using internal performance evaluations to approximate stochastic gradient ascent. However, this framework struggles in non-convex performance landscapes, where local optima hinder efficient learning. Songbirds provide a compelling biological example of robust sensorimotor learning, mastering complex vocalizations through trial-and-error within a specialized BG-thalamo-cortical architecture. Here, we present a computational model constrained by the anatomy, physiology, and developmental trajectory of the zebra finch song system. The model combines a BG-driven RL pathway with a parallel cortical motor pathway that progressively consolidates successful motor patterns via Hebbian plasticity. In addition, we incorporate synaptic volatility within the BG pathway, introducing structured variability across learning. Through simulations of vocal learning using both a biophysical syrinx model and synthetic performance landscapes, we demonstrate that this dual-pathway architecture reliably converges to global optima and outperforms standard and noise-annealed RL approaches. The model reproduces key experimental features of song learning, including non-monotonic learning trajectories, a gradual reduction in motor variability, and the developmental transfer of motor control from subcortical to cortical circuits. Mechanistically, delayed maturation of the cortical pathway provides an implicit regulation of the exploration-exploitation trade-off, while synaptic volatility enables escape from local optima. These results highlight the importance of neural circuit architecture and dynamics in efficient learning, and suggest biologically inspired design principles for improving the robustness and sample efficiency of artificial RL systems in complex sensorimotor domains.

Understanding intracranial pressure (ICP) dynamics is essential for interpreting clinical infusion tests used in the diagnosis of cerebrospinal fluid circulation disorders. However, the complex coupling between vascular pulsations, cerebrospinal fluid flow, and intracranial compliance makes quantitative interpretation of these tests challenging. Here, I present a patient specific simulation framework based on an extended electrical analog model that reproduces intracranial pressure dynamics observed during clinical infusion tests. The model integrates physiological inputs including arterial blood pressure, heart rate, respiratory rhythm, and resistance to cerebrospinal fluid outflow derived from clinical data. Built upon the classical Ursino framework, the model incorporates several modifications enabling realistic representation of physiological pulsations and infusion test conditions. The resulting system functions as a hybrid electrical-numerical simulation model representing a simplified digital electrical twin of intracranial hydrodynamics. The model was validated using data from 21 clinical infusion tests performed in patients with suspected normal pressure hydrocephalus. Simulated intracranial pressure recordings were compared with clinical measurements using regression and residual analysis. The simulations demonstrated strong agreement with measured data, with a mean correlation coefficient of r = 0.95 (95% CI 0.94 - 0.96), mean residual values within -1.71 to +1.68 mmHg, and a mean root mean square error (RMSE) of 2.07 mmHg. These results demonstrate that the proposed model accurately reproduces the dynamic behavior of intracranial pressure observed during clinical infusion tests. The framework provides a physiologically grounded computational tool for studying patient specific intracranial dynamics and may support improved interpretation of infusion test results in clinical practice.

Neuronal computation depends on the balance between excitation and inhibition, yet how this balance is implemented across the dendritic tree remains unclear. Classical views predict that inhibition should be most effective near the soma or along the path from excitation to output, but many interneuron subtypes preferentially target remote dendritic compartments. This apparent paradox is sharpened by active dendrites, where local NMDA spikes, calcium plateaus and backpropagating action potentials can make distal branches powerful contributors to somatic firing. Here we develop an analytical framework that extracts general principles of inhibition from biophysically detailed multi-compartment simulations. By reformulating the implicit voltage update of detailed neuron models as a matrix recursion, we derive exact voltage sensitivities to inhibitory synaptic perturbations. This leads to a unified {Phi}-a law: the somatic impact of inhibition factorizes into a global dendritic susceptibility term and a local synaptic perturbation term. Using this law to map inhibitory leverage and identify optimal inhibitory interventions, we show that active dendritic excitation can shift inhibitory hot zones from perisomatic regions toward distal or intermediate compartments. Across neocortical, hippocampal and striatal neuron models, the same response law explains convergent inhibitory strategies despite distinct cellular mechanisms. Our framework turns detailed numerical simulation into analytical theory, providing a general principle for how diverse dendritic inhibition controls active neurons.

Optogenetic defibrillation uses light-gated ion channels to terminate cardiac arrhythmias through targeted illumination. Previous studies assessed the feasibility of using either cation (e.g. ChR2) or anion (e.g. GtACR1) non-selective channels, both of which depolarise resting cardiomyocytes upon photoactivation. In contrast, recently identified light-gated K+-channels (e.g. WiChR) suppress cardiomyocyte activity while maintaining the membrane potential near its resting state. Here, we use biophysically detailed simulations to compare the defibrillation potential of ChR2, GtACR1, and WiChR. Single-cell simulations show that activation of ChR2 and GtACR1 markedly increase diastolic intracellular Ca2+ concentration (by 42.6% and 52.6%, respectively), whereas WiChR induces only minimal changes (4.0% increase), suggesting a lower pro-arrhythmogenic risk. WiChR activation, however, slightly increases intracellular Na+ levels (by 15.1% compared to 0.1% and 3.4% for ChR2 and GtACR), consistent with the residual Na+ permeability of all currently available K+-selective channelrhodopsins. Simulations of human ventricles and atria demonstrate that GtACR1 most effectively terminates re-entrant arrhythmias at low light intensities, while WiChR achieves comparable efficacy at light levels [≥]5 mW/mm2. Complementary tissue-scale simulations reveal that defibrillation is either based on depolarisation within the excitable gap, followed by fast Na+ channel inactivation (depolarising variants ChR2 and GtACR1), or based on a reduction in membrane resistance supporting arrhythmia termination at sufficiently high light levels (large-conductance ion channels GtACR1 and WiChR). Overall, our findings identify channelrhodopsin ion selectivity as a key determinant of both arrhythmia termination success and mechanisms underlying defibrillation. Key points summaryO_LIWe use computational simulations to compare non-selective cation (ChR2), anion (GtACR1), and K+-selective channelrhodopsins (WiChR) for optogenetic termination of re-entrant arrhythmia. C_LIO_LISingle-cardiomyocyte simulations suggest that ChR2 and GtACR1 activation can cause progressive accumulation of intracellular Ca2+, which is minimised when using WiChR. C_LIO_LISimulations of human left ventricles and atria indicate that GtACR1 is most effective in terminating re-entrant arrhythmia at low light intensities, while WiChR becomes similarly effective at higher intensities. C_LIO_LITissue-scale simulations indicate distinct defibrillation mechanisms: Excitable gap extinction by de-novo action potential initiation followed by inactivation of fast Na+ channels for depolarising channelrhodopsins (ChR2, GtACR1), and reduction in membrane resistance for the large-conductance channels (GtACR1, WiChR), effectively clamping the membrane potential at each channels reversal potential at high light levels. C_LI

Gait asymmetry is a common manifestation of walking impairment among clinical populations. We recently developed a novel treadmill walking approach called dynamic treadmill walking that can provide asymmetric gait training by changing the treadmill speed between fast and slow speeds within a single stride. Here, we studied the energy expenditure associated with a variety of dynamic treadmill walking conditions. We hypothesized that the metabolic power required for dynamic treadmill walking in all conditions would approximate the metabolic power associated with conventional walking at the mean of the fast and slow speeds employed in the task. Eleven young adults without gait impairment walked on an instrumented treadmill and breathed into a metabolic measurement system. During dynamic treadmill walking, the treadmill fluctuated between 0.75m/s and 1.50m/s, each for 50% of an individuals stride time. We used a metronome to synchronize participants right heel-strikes with four different timing conditions. Net metabolic power during dynamic treadmill walking was significantly greater than normal walking at the mean speed of the task (1.125m/s) and generally lower than walking at the fast speed (1.5m/s). We did not observe any significant associations between net metabolic power and several measures of gait asymmetry during dynamic treadmill walking. These findings establish dynamic treadmill walking as a promising technique for improving gait symmetry in individuals who cannot tolerate fast treadmill walking, a common gait rehabilitation approach. Future work will assess the feasibility, metabolic demands, and clinical efficacy of using dynamic treadmill walking to improve gait symmetry in clinical populations. Key Points SummaryO_LIDynamic treadmill walking (i.e., walking with oscillating treadmill speeds) has previously been shown to drive gait asymmetries, but little is known about the energy expenditure required to complete the task. C_LIO_LIOur hypothesis was that dynamic treadmill walking would have similar metabolic power requirements to normal walking at a speed that is intermediate between the two dynamic treadmill walking speeds. C_LIO_LIWe found that dynamic treadmill walking actually requires metabolic power that is greater than the average of the two belt speeds, but less than that used for fast walking. C_LIO_LIDynamic treadmill walking is a promising and clinically translatable technique for rehabilitating populations with gait asymmetries that is not more energetically costly than fast treadmill walking, a common gait rehabilitation approach. C_LI

Parameter estimation in nonlinear biological dynamical systems is a difficult inverse problem because the governing equations are often stiff or oscillatory, the data are sparse and noisy, and the objective landscape is non-convex. Physics-informed neural networks (PINNs) offer an alternative to purely simulation-based calibration by representing state trajectories with neural networks while penalizing violations of the governing equations. This paper studies the empirical reliability of PINNs for recovering the parameters of the repressilator, a synthetic genetic oscillator formed by three cyclically repressive genes. We use synthetic time-series generated from the standard ordinary differential equation model and train inverse PINNs to estimate the production parameter {beta} and the Hill coefficient n. The study varies observation noise, partial observation of repressors, sampling density, sensitivity to initial parameter guesses, and the difference between stable and oscillatory regimes. The results show that PINNs can reconstruct trajectories accurately when the model structure is correct and the three repressors are observed, but parameter recovery is more fragile than trajectory fitting. Noise, sparse sampling, unobserved variables, and unfavorable initial guesses increase the risk of biased estimates. The stable regime is easier to reconstruct, whereas the oscillatory regime provides richer information but also exposes optimization sensitivity. These findings support PINNs as a useful reverse-engineering tool for small gene-regulatory ODE models, while highlighting the need for repeated runs, uncertainty reporting, and experimental designs that improve identifiability.