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Two simple algorithms based on combining odor concentration differences across time and space along with information on the flow direction are tested for their ability to locate an odor source in four different odor landscapes. Image data taken from air plumes in three different regimes and a water plume are used as test environments for a bilateral ("stereo sampling") algorithm using concentration differences across two sensors and a "casting" algorithm that uses successive samples to decide orientation. Agents are started at random locations and orientations in the landscape and allowed to move until they reach the source of the odor (success) or leave the imaged area (failure). Parameters for the algorithm are chosen to optimize success and to minimize path length to the source. Success rates over 90% are consistently obtained with path lengths that can be as low as twice the starting distance from the source in air and four times the distance in the highly turbulent water plumes. We find that parameters that optimize success often lead to more exploratory pathways to the source. Information about the direction from which the odor is coming is necessary for successful navigation in the water plume and reduces the path length in the three tested air plumes.

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In order to forage for food, many animals regulate not only specific limb movements but the statistics of locomotor behavior over time, for example switching between long-range dispersal behaviors and more localized search depending on the availability of resources. How pre-motor circuits regulate such locomotor statistics is not clear. Here we took advantage of the robust changes in locomotor statistics evoked by attractive odors in walking Drosophila to investigate their neural control. We began by analyzing the statistics of ground speed and angular velocity during three well-defined motor regimes: baseline walking, upwind running during odor, and search behavior following odor offset. We find that during search behavior, flies adopt higher angular velocities and slower ground speeds, and tend to turn for longer periods of time in one direction. We further find that flies spontaneously adopt periods of different mean ground speed, and that these changes in state influence the length of odor-evoked runs. We next developed a simple physiologically-inspired computational model of locomotor control that can recapitulate these statistical features of fly locomotion. Our model suggests that contralateral inhibition plays a key role both in regulating the difference between baseline and search behavior, and in modulating the response to odor with ground speed. As the fly connectome predicts decussating inhibitory neurons in the lateral accessory lobe (LAL), a pre-motor structure, we generated genetic tools to target these neurons and test their role in behavior. Consistent with our model, we found that activation of neurons labeled in one line increased curvature. In a second line labeling distinct neurons, activation and inactivation strongly and reciprocally regulated ground speed and altered the length of the odor-evoked run. Additional targeted light activation experiments argue that these effects arise from the brain rather than from neurons in the ventral nerve cord, while sparse activation experiments argue that speed control in the second line arises from both LAL neurons and a population of neurons in the dorsal superior medial protocerebrum (SMP). Together, our work develops a biologically plausible computational architecture that captures the statistical features of fly locomotion across behavioral states and identifies potential neural substrates of these computations.

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To support a range of behaviours, the brain must flexibly coordinate neural activity across widespread brain regions. One potential mechanism for this coordination is a travelling wave, in which a neural oscillation propagates across the brain while organizing the order and timing of activity across regions. Although travelling waves are present across the brain in various species, their potential functional relevance has remained unknown. Here, using rare direct human brain recordings, we demonstrate a distinct functional role for travelling waves of theta- and alpha-band (2-13 Hz) oscillations in the cortex. Travelling waves propagate in different directions during separate cognitive processes. In episodic memory, travelling waves tended to propagate in a posterior-to-anterior direction during successful memory encoding and in an anterior-to-posterior direction during recall. Because travelling waves of oscillations correspond to local neuronal spiking, these patterns indicate that rhythmic pulses of activity move across the brain in different directions for separate behaviours. More broadly, our results suggest a fundamental role for travelling waves and oscillations in dynamically coordinating neural connectivity, by flexibly organizing the timing and directionality of network interactions across the cortex to support cognition and behaviour.

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Propagating waves of activity can be evoked and can occur spontaneously in vivo and in vitro in cerebral cortex. These waves are thought to be instrumental in the propagation of information across cortical regions and as a means to modulate the sensitivity of neurons to subsequent stimuli. In normal tissue, the waves are sparse and tightly controlled by inhibition and other negative feedback processes. However, alterations of this balance between excitation and inhibition can lead to pathological behavior such as seizure-type dynamics (with low inhibition) or failure to propagate (with high inhibition). We develop a spiking one-dimensional network of neurons to explore the reliability and control of evoked waves and compare this to a cortical slice preparation where the excitability can be pharmacologically manipulated. We show that the waves enhance sensitivity of the cortical network to stimuli in specific spatial and temporal ways. To gain further insight into the mechanisms of propagation and transitions to pathological behavior, we derive a mean-field model for the synaptic activity. We analyze the mean-field model and a piece-wise constant approximation of it and study the stability of the propagating waves as spatial and temporal properties of the inhibition are altered. We show that that the transition to seizure-like activity is gradual but that the loss of propagation is abrupt and can occur via either the loss of existence of the wave or through a loss of stability leading to complex patterns of propagation.

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In primates, the dorsolateral prefrontal (DLPFC) and posterior parietal (PPC) cortices are key nodes in the working memory network. The working memory-related gamma oscillations induced in these areas, predominantly in layer 3, exhibit higher frequency in DLPFC. Although these regional differences in oscillation frequency are likely essential for information transfer between DLPFC and PPC, the mechanisms underlying these differences remain poorly understood. We investigated, in rhesus monkey, the DLPFC and PPC layer 3 pyramidal neuron (L3PN) properties that might regulate oscillation frequency and assessed the effects of these properties simulating oscillations in computational models. We found that GABAAR-mediated synaptic inhibition synchronizes L3PNs in both areas, but analysis of GABAAR mRNA levels and inhibitory synaptic currents suggested similar mechanisms of inhibition-mediated synchrony in DLPFC and PPC. Basal dendrite spine density and AMPAR/NMDAR mRNA levels were higher in DLPFC L3PNs, whereas excitatory synaptic currents were similar between areas. Therefore, synaptically evoked excitation might be stronger in DLPFC L3PNs due to a greater quantity of synapses in basal dendrites, a main target of recurrent excitation. Simulations in computational networks showed that oscillation frequency and power increased with increasing recurrent excitation, suggesting a mechanism by which the DLPFC-PPC differences in oscillation properties are generated.

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Neural activity in the cortex is highly variable in response to repeated stimuli. Population recordings across the cortex demonstrate that the variability of neuronal responses is shared among large groups of neurons and concentrates in a low dimensional space. However, the source of the population-wide shared variability is unknown. In this work, we analyzed the dynamical regimes of spatially distributed networks of excitatory and inhibitory neurons. We found chaotic spatiotemporal dynamics in networks with similar excitatory and inhibitory projection widths, an anatomical feature of the cortex. The chaotic solutions contain broadband frequency power in rate variability and have distance-dependent and low-dimensional correlations, in agreement with experimental findings. In addition, rate chaos can be induced by globally correlated noisy inputs. These results suggest that spatiotemporal chaos in cortical networks can explain the shared variability observed in neuronal population responses.

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Recent empirical investigations have characterized the synchronized flashing behaviours of male Photinus carolinus fireflies in their natural habitat in Great Smoky Mountain National Park as well as in controlled environments. We develop a model for the flash dynamics of an individual firefly based on a canonical elliptic burster, a slow-fast dynamical system that produces a repeating pattern of multiple flashes followed by a quiescent period. We show that a small amount of noise renders that oscillation very irregular, but when multiple model fireflies interact through their flashes, the behaviour becomes much more periodic. We show that the aggregate behaviour is qualitatively similar to the experimental findings. We next distribute the fireflies in a two-dimensional spatial domain and vary the interaction range. In addition to synchronization, various spatio-temporal patterns involving propagation of activity emerge spontaneously. Finally, we allow a certain number of fireflies to move and demonstrate how their speed affects the rate and degree of synchronization.

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Age-induced dysregulation of the immune response is a major contributor to the morbidity and mortality related to influenza a virus infections. Experimental data have shown substantial changes to the activation and maintenance of the immune response will occur with age, but it remains unclear which of these many interrelated changes are most critical to controlling the survival of the host during infection. To ascertain which mechanisms are predominantly responsible for the increased morbidity in elderly hosts, we developed an ordinary differential equation model to simulate the immune response to pandemic H1N1 infection. We fit this model to experimental data measured in young and old macaques. We determined that the severity of the infection in the elderly hosts is caused by a dysregulation in the innate immune response. We also simulated CD8+ T cell exhaustion, a common consequence of chronic and extensive infections. Our simulations indicate that while T cell exhaustion is possible in both age groups, its effects are more severe in the elderly population, as their dysregulated immune response cannot easily compensate for the exhausted T cells. Finally, we explore a therapeutic approach to reversing T cell exhaustion through an inflammatory stimulus. A controlled increase in inflammatory signals can lead to a higher chance of surviving the infection, but excess inflammation will likely lead to septic death. These results indicate that our model captures distinctions in the predominant mechanisms controlling the immune response in younger and older hosts and allows for simulations of clinically relevant therapeutic strategies post-infection.

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Entrainment of a nonlinear oscillator by a periodic external force is a much studied problem in nonlinear dynamics and characterized by the well-known Arnold tongues. The circle map is the simplest such system allowing for stable N:M entrainment where the oscillator produces N cycles for every M stimulus cycles. There are a number of experiments that suggest that entrainment to external stimuli can involve both a shift in the phase and an adjustment of the intrinsic period of the oscillator. Motivated by a recent model of Loehr et al. [J. Exp. Psychol.: Hum. Percept. Perform. 37, 1292 (2011)], we explore a two-dimensional map in which the phase and the period are allowed to update as a function of the phase of the stimulus. We characterize the number and stability of fixed points for different N:M-locking regions, specifically, 1:1, 1:2, 2:3, and their reciprocals, as a function of the sensitivities of the phase and period to the stimulus as well as the degree that the oscillator has a preferred period. We find that even in the limited number of locking regimes explored, there is a great deal of multi-stability of locking modes, and the basins of attraction can be complex and riddled. We also show that when the forcing period changes between a starting and final period, the rate of this change determines, in a complex way, the final locking pattern.

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Traveling phase waves are commonly observed in recordings of the cerebral cortex and are believed to organize behavior across different areas of the brain. We use this as motivation to analyze a one-dimensional network of phase oscillators that are nonlocally coupled via the phase response curve (PRC) and the Dirac delta function. Existence of waves is proven and the dispersion relation is computed. Using the theory of distributions enables us to write and solve an associated stability problem. First and second order perturbation theory is applied to get analytic insight and we show that long waves are stable while short waves are unstable. We apply the results to PRCs that come from mitral neurons. We extend the results to smooth pulse-like coupling by reducing the nonlocal equation to a local one and solving the associated boundary value problem.

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Navigating an odor landscape is a critical behavior for the survival of many species, including mice. An ethologically relevant mouse behavior is locating food using information about odor concentration. To approximate this behavior, we used an open field odor-based spot-finding task indoors with little wind, examining navigation strategies as mice search for and approach an odor source. After mice were trained to navigate to odor sources paired with food reward, we observed behavioral changes consistent with localization 10-45 cm away from the source. These behaviors included orientation toward the source, decreased velocity, and increased exploration time. We also found that the amplitude of 'casting,' which we define as lateral back and forth movement of the nose, increased with proximity to the source. Based on these observations, we created a concentration-sensitive agent-based model to simulate mouse behavior. This model provided evidence for a binaral-sniffing strategy (inter-nostril comparison of concentration in a single sniff) and a serial-sniffing strategy (sampling concentration, moving in space, and then sampling again). Serial-sniffing may be accomplished at farther distances by moving the body and at closer distances by moving the head (casting). Together, these results elucidate components of behavioral strategies for odor-based navigation.

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We use the theory of isostable reduction to incorporate higher order effects that are lost in the first order phase reduction of coupled oscillators. We apply this theory to weakly coupled complex Ginzburg-Landau equations, a pair of conductance-based neural models, and finally to a short derivation of the Kuramoto-Sivashinsky equations. Numerical and analytical examples illustrate bifurcations occurring in coupled oscillator networks that can cause standard phase-reduction methods to fail.

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We review the theory of weakly coupled oscillators for smooth systems. We then examine situations where application of the standard theory falls short and illustrate how it can be extended. Specific examples are given to non-smooth systems with applications to the Izhikevich neuron. We then introduce the idea of isostable reduction to explore behaviours that the weak coupling paradigm cannot explain. In an additional example, we show how bifurcations that change the stability of phase-locked solutions in a pair of identical coupled neurons can be understood using the notion of isostable reduction. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

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In this paper, we study pairs of oscillators that are indirectly coupled via active (excitable) cells. We introduce a scalar phase model for coupled oscillators and excitable cells. We first show that one excitable and one oscillatory cell will exhibit phase locking at a variety of m:n patterns. We next introduce a second oscillatory cell and show that the only attractor is synchrony between the oscillators. We will also study the robustness to heterogeneity when the excitable cell fires or is quiescent. We next examine the dynamics when the oscillators are coupled via two excitable cells. In this case, the dynamics are very complicated with many forms of bistability and, in some cases, chaotic behavior. We also apply weak-coupling analysis to this case and explain some of the degeneracies observed in the bifurcation diagram. Further, we look at pairs of oscillators coupled via long chains of excitable cells and show that small differences in the frequency of the oscillators makes their locking more robust. Finally, we demonstrate many of the same phenomena seen in the phase model for a gap-junction coupled system of Morris-Lecar neurons.

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Neural oscillations have been recorded and implicated in many different basic brain and cognitive processes. For example, oscillatory neural activity has been suggested to play a role in binding and in the maintenance of information in working memory. With respect to the latter, the majority of work has focused primarily on oscillations in terms of providing a "code" in working memory. However, oscillations may additionally play a fundamental role by enabling or facilitating essential properties and behaviors that neuronal networks must exhibit in order to produce functional working memory and the processes it supports, such as combining items in memory into bound objects or separating bound objects into distinct items. In the present work, we present a biologically plausible working memory model and demonstrate that specific types of stable oscillatory dynamics that arise may play critical roles in providing mechanisms for working memory and the cognitive functions that it supports. Specifically, these roles include (1) enabling a range of different types of binding, (2) both enabling and limiting capacities of bound and distinct items held active in working memory, and (3) facilitating transitions between active working memory states as required in cognitive function. Several key results arise within the examinations, such as the occurrence of different network capacities for working memory and binding, differences in processing times for transitions in working memory states, and the emergence of a combinatorially rich and complex range of oscillatory states that are sufficient to map onto a wide range of cognitive operations supported by working memory, such as variable binding, reasoning, and language. In particular, we show that these oscillatory states and their transitions can provide a specific instantiation of current established connectionist models in representing these functions. Finally, we further characterize the dependence of the relevant oscillatory solutions on certain critical parameters, including mutual inhibition and synaptic timescales.

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The applicability of phase models is generally limited by the constraint that the dynamics of a perturbed oscillator must stay near its underlying periodic orbit. Consequently, external perturbations must be sufficiently weak so that these assumptions remain valid. Using the notion of isostables of periodic orbits to provide a simplified coordinate system from which to understand the dynamics transverse to a periodic orbit, we devise a strategy to correct for changing phase dynamics for locations away from the limit cycle. Consequently, these corrected phase dynamics allow for perturbations of larger magnitude without invalidating the underlying assumptions of the reduction. The proposed reduction strategy yields a closed set of equations and can be applied to periodic orbits embedded in arbitrarily high dimensional spaces. We illustrate the utility of this strategy in two models with biological relevance. In the first application, we find that an optimal control strategy for modifying the period of oscillation can be improved with the corrected phase reduction. In the second, the corrected phase reduced dynamics are used to understand adaptation and memory effects resulting from past perturbations.

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Depressed heart rate variability is a well-established risk factor for sudden cardiac death in survivors of acute myocardial infarction and for those with congestive heart failure. Although measurements of heart rate variability provide a valuable prognostic tool, it is unclear whether reduced heart rate variability itself is proarrhythmic or if it simply correlates with the severity of autonomic nervous system dysfunction. In this work, we investigate a possible mechanism by which heart rate variability could protect against cardiac arrhythmia. Specifically, in numerical simulations, we observe an inverse relationship between the variance of stochastic pacing and the occurrence of spatially discordant alternans, an arrhythmia that is widely believed to facilitate the development of cardiac fibrillation. By analyzing the effects of conduction velocity restitution, cellular dynamics, electrotonic coupling, and stochastic pacing on the nodal dynamics of spatially discordant alternans, we provide intuition for this observed behavior and propose control strategies to inhibit discordant alternans.

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Abnormal Ca2+ handling is well-established as the trigger of cardiac arrhythmia in catecholaminergic polymorphic ventricular tachycardia and digoxin toxicity, but its role remains controversial in Torsade de Pointes (TdP), the arrhythmia associated with the long QT syndrome (LQTS). Recent experimental results show that early afterdepolarizations (EADs) that initiate TdP are caused by spontaneous (non-voltage-triggered) Ca2+ release from Ca2+-overloaded sarcoplasmic reticulum (SR) rather than the activation of the L-type Ca2+-channel window current. In bradycardia and long QT type 2 (LQT2), a second, non-voltage triggered cytosolic Ca2+ elevation increases gradually in amplitude, occurs before overt voltage instability, and then precedes the rise of EADs. Here, we used a modified Shannon-Puglisi-Bers model of rabbit ventricular myocytes to reproduce experimental Ca2+ dynamics in bradycardia and LQT2. Abnormal systolic Ca2+-oscillations and EADs caused by SR Ca2+-release are reproduced in a modified 0-dimensional model, where 3 gates in series control the ryanodine receptor (RyR2) conductance. Two gates control RyR2 activation and inactivation and sense cytosolic Ca2+ while a third gate senses luminal junctional SR Ca2+. The model predicts EADs in bradycardia and low extracellular [K+] and cessation of SR Ca2+-release terminate salvos of EADs. Ca2+-waves, systolic cell-synchronous Ca2+-release, and multifocal diastolic Ca2+ release seen in subcellular Ca2+-mapping experiments are observed in the 2-dimensional version of the model. These results support the role of SR Ca2+-overload, abnormal SR Ca2+-release, and the subsequent activation of the electrogenic Na+/Ca2+-exchanger as the mechanism of TdP. The model offers new insights into the genesis of cardiac arrhythmia and new therapeutic strategies.

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Sculpting organism shape requires that cells produce forces with proper directionality. Thus, it is critical to understand how cells orient the cytoskeleton to produce forces that deform tissues. During Drosophila gastrulation, actomyosin contraction in ventral cells generates a long, narrow epithelial furrow, termed the ventral furrow, in which actomyosin fibres and tension are directed along the length of the furrow. Using a combination of genetic and mechanical perturbations that alter tissue shape, we demonstrate that geometrical and mechanical constraints act as cues to orient the cytoskeleton and tension during ventral furrow formation. We developed an in silico model of two-dimensional actomyosin meshwork contraction, demonstrating that actomyosin meshworks exhibit an inherent force orienting mechanism in response to mechanical constraints. Together, our in vivo and in silico data provide a framework for understanding how cells orient force generation, establishing a role for geometrical and mechanical patterning of force production in tissues.

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