Bard Ermentrout

• University of Pittsburgh

In order to forage for food, many animals regulate not only specific limb movements but the statistics of locomotor behavior, switching between long-range dispersal and local search depending on resource availability. How premotor circuits regulate locomotor statistics is not clear. Here, we analyze and model locomotor statistics and their modulati...

Cortical populations are in a broadly asynchronous state that is sporadically interrupted by brief epochs of coordinated population activity. Cortical models are at a loss to explain this combination of states. At one extreme are network models where recurrent inhibition dynamically stabilizes an asynchronous low activity state. While these network...

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 ac...

A fundamental challenge in neuroscience is explaining how widespread brain regions flexibly interact to support behaviors. We hypothesize that a mechanism of neural coordination is brain oscillations that propagate as traveling waves across the cortex in distinctive patterns that control when and where different regions interact. To test this hypot...

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 controll...

Oscillatory activity is commonly observed during the maintenance of information in short-term memory, but its role remains unclear. Non-oscillatory models of short-term memory storage are able to encode stimulus identity through their spatial patterns of activity, but are typically limited to either an all-or-none representation of stimulus amplitu...

Plane waves have commonly been observed in recordings of human brains. These waves take the form of spatial phase gradients in the oscillatory potentials picked up by implanted electrodes. We first show that long but finite chains of nearest-neighbor coupled phase oscillators can produce an almost constant phase gradient when the edge effects inter...

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 i...

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,...

Propagating waves of activity can be evoked and can occur spontaneously in vivo and in vitro . We examine the properties of these waves as inhibition varies in a cortical slice and then develop several computational models. We first show that in the slice, inhibition controls the velocity of propagation as well as the magnitude of the local field p...

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 dynam...

From the action potentials of neurons and cardiac cells to the amplification of calcium signals in oocytes, excitability is a hallmark of many biological signalling processes. In recent years, excitability in single cells has been related to multiple-timescale dynamics through canards, special solutions which determine the effective thresholds of t...

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 critic...

We used computer simulations of growth, mating and death of cephalopods and fishes to explore the effect of different life-history strategies on the relative prevalence of alternative male mating strategies. Specifically, we investigated the consequences of single or multiple matings per lifetime, mating strategy switching, cannibalism, resource st...

Computational models have great potential to accelerate bioscience, bioengineering, and medicine. However, it remains challenging to reproduce and reuse simulations, in part, because the numerous formats and methods for simulating various subsystems and scales remain siloed by different software tools. For example, each tool must be executed throug...

In primates, the dorsolateral prefrontal (DLPFC) and posterior parietal (PPC) cortices are critical nodes in the network mediating cognitive functions including attention and working memory. Notably, during working memory tasks, gamma oscillations, usually prominent in layer 3 (L3), are induced in both DLPFC and PPC but exhibit higher frequency in...

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 populationwide shared variability is unknown. In this work, w...

From the action potentials of neurons and cardiac cells to the amplification of calcium signals in oocytes, excitability is a hallmark of many biological signalling processes. In recent years, excitability in single cells has been related to multiple-timescale dynamics through canards, special solutions which determine the effective thresholds of t...

Computational models have great potential to accelerate bioscience, bioengineering, and medicine. However, it remains challenging to reproduce and reuse simulations, in part, because the numerous formats and methods for simulating various subsystems and scales remain siloed by different software tools. For example, each tool must be executed throug...

Fish escape from approaching threats via a stereotyped escape behavior. This behavior, and the underlying neural circuit organized around the Mauthner cell command neurons, have both been extensively investigated experimentally, mainly in two laboratory model organisms, the goldfish and the zebrafish. However, fish biodiversity is enormous, a numbe...

Respiratory viral infections pose a serious public health concern, from mild seasonal influenza to pandemics like those of SARS-CoV-2. Spatiotemporal dynamics of viral infection impact nearly all aspects of the progression of a viral infection, like the dependence of viral replication rates on the type of cell and pathogen, the strength of the immu...

Oscillatory activity is commonly observed during the maintenance of information in short-term memory, but its role remains unclear. Non-oscillatory models of short-term memory storage are able to encode stimulus identity through their spatial patterns of activity, but are typically limited to either an all-or-none representation of stimulus amplitu...

The pandemic outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has quickly spread worldwide, creating a serious health crisis. The virus is primarily associated with flu-like symptoms but can also lead to severe pathologies and death. We here present an ordinary differential equation model of the intrahost immune response to...

The unique fast spiking (FS) phenotype of cortical parvalbumin-positive (PV) neurons depends on the expression of multiple subtypes of voltage-gated potassium channels (Kv). PV neurons selectively express Kcns3, the gene encoding Kv9.3 subunits, suggesting that Kcns3 expression is critical for the FS phenotype. KCNS3 expression is lower in PV neuro...

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 t...

Respiratory viral infections pose a serious public health concern, from mild seasonal influenza to pandemics like those of SARS-CoV-2. Spatiotemporal dynamics of viral infection impact nearly all aspects of the progression of a viral infection, like the dependence of viral replication rates on the type of cell and pathogen, the strength of the immu...

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 wave...

Olfaction informs animal navigation for foraging, social interaction, and threat evasion. However, turbulent flow on the spatial scales of most animal navigation leads to intermittent odor information and presents a challenge to simple gradient-ascent navigation. Here we present two strategies for iterative gradient estimation and navigation via ol...

The majority of neurons in primary visual cortex respond selectively to bars of light that have a specific orientation and move in a specific direction. The spatial and temporal responses of such neurons are non-separable. How neurons accomplish that computational feat without resort to explicit time delays is unknown. We propose a novel neural mec...

The unique fast spiking (FS) phenotype of cortical parvalbumin-positive (PV) neurons depends on multiple subtypes of voltage-gated potassium channels (Kv). PV neurons selectively express Kcns3 , the gene encoding Kv9.3 subunits, suggesting that Kcns3 expression is critical for the FS phenotype. KCNS3 expression is lower in PV neurons in schizophren...

Animals use stereo sampling of odor concentration to localize sources and follow odor trails. We analyze the dynamics of a bilateral model that depends on the simultaneous comparison between odor concentrations detected by left and right sensors. The general model consists of three differential equations for the positions in the plane and the headi...

We study the nonlinear dynamics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show asynchronous activity, the network displays orderly, perfectly synchronized periodic responses at intermediate level...

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...

The majority of neurons in primary visual cortex respond selectively to bars of light that have a specific orientation and move in a specific direction. The spatial and temporal responses of such neurons are non-separable. How neurons accomplish that computational feat without resort to explicit time delays is unknown. We propose a novel neural mec...

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 behav...

Localization of odors is essential to animal survival, and thus animals are adept at odor navigation. In natural conditions animals encounter odor sources in which odor is carried by air flow varying in complexity. We sought to identify potential minimalist strategies that can effectively be used for odor-based navigation and asses their performanc...

The neural circuit linking the basal ganglia, the cerebellum and the cortex through the thalamus plays an essential role in motor and cognitive functions. However, how such functions are realized by multiple loop circuits with neurons of multiple types is still unknown. In order to investigate the dynamic nature of the whole-brain network, we built...

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 behav...

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...

Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only parameter that is allowed to change is the underlying network. While such a model was analyzed over the past...

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...

We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show asynchronous activity, the network displays orderly, perfectly synchronized periodic responses at intermediate leve...

Cross-frequency coupling (CFC) is thought to play an important role in communication across distant brain regions. However, neither the mechanism of its generation nor the influence on the underlying spiking dynamics is well understood. Here, we investigate the dynamics of two interacting distant neuronal modules coupled by inter-regional long-rang...

The demands on a sensory system depend not only on the statistics of its inputs but also on the task. In olfactory navigation, for example, the task is to find the plume source; allocation of sensory resources may therefore be driven by aspects of the plume that are informative about source location, rather than concentration per se. Here we explor...

We study the interaction of two bacterial pulses in a one-dimensional nutrient gradient. Simulations of the Keller-Segel chemotaxis model reveal two qualitatively distinct behaviors. As the two pulses approach one another, they either combine and move as a single pulse or, surprisingly, change direction and begin moving away from each other in the...

Navigating an odor landscape is a critical behavior for the survival of many species, including mice. One ethologically relevant mouse behavior is locating food using odor concentration gradients. To model this behavior, we use a naturalistic open field odor-based spot-finding task, examining navigation strategies as mice search for and approach an...

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 sho...

Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only parameter that is allowed to change is the underlying network. While such a model was analyzed over the past...

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...

The u, v, n system. (PDF)

Mean field model motivation and spiking network comparison. (PDF)

Weak coupling analysis. (PDF)

Change in OP and S dynamics with varying coupling strengths and synaptic timescales. (PDF)

Filamentous actin (F-actin) and non-muscle myosin II motors drive cell motility and cell shape changes that guide large scale tissue movements during embryonic morphogenesis. To gain a better understanding of the role of actomyosin in vivo, we have developed a two-dimensional (2D) computational model to study emergent phenomena of dynamic unbranche...

Quantitation of "No-Aster" cases beyond 1000 time steps. (DOCX)

10 different simulations for parameter switching of L = 0.5 μm to L = 1 μm (standard value). The first row is the morphology of filaments at T = 1000 of the shorter filament length of L = 0.5 μm. The initial orientation and distribution of filaments is random at T = 0. At T = 1001, the filament length has changed to 1 μm and plus-ends remain where...

Varying the percentage of cross-linkers and motors. Plots of filaments, cross linkers, and motors for simulations where the percentage of total motors (5,000) are designated as cross linkers. Aster formation is inhibited for 75% cross-linkers and 25% motors. (TIF)

Plots of the mean motor generated force over time for varying rates of filament turn over (p2). The end motor force decreases as polymerization rate decreases, the same conclusion (and the same shape of the force curve) as we found previously with our simple, 1D rotational model. However, there does seem to be a transition state between p2 = 0.3 an...

Accompanies Fig 1B. Time-lapse sequence of F-actin and myosin II in the basal cell cortex of Xenopus laevis dorsal mesoderm at gastrula stages. Video shows episodic actomyosin contractions. (AVI)

Accompanies Fig 8A. Simulated time-lapse sequence of filaments and motors where filaments are fixed to lower region of the domain. (AVI)

Accompanies S13 Fig. Vertical simulated time-lapse sequences of filaments, motors, and merged images of filaments and motors for standard filament turn over (p2 = 0.7), moderate turn over (p2 = 1.2) and high turnover (p2 = 5). (AVI)

Quantifying aster stability. (DOCX)

Mean motor generated force for 10 standard parameter cases. Between Figs 3 and 5 we ran 10 different examples of our standard parameter set. This plot shows the mean motor generated force for those 10 simulations. (TIF)

Color coded orientations of filaments. Filaments are color coded according to their orientation with the plus-end half of the filament shown in green, and the minus end half of the filament shown in red. This example is for no filament turn over (p2 = 0). (TIF)

Divergence map accompanying Fig 6. Divergence of filaments are shown on the heat map instead of plotting filament locations (Fig 6). Asters are located where the divergence is highlighted by a small cluster of dark pixels with neighboring light pixels. Panel (A) shows how a parameter switch from control to a higher or lower parameter disrupts the a...

Work-energy calculations over the course of simulations run at four conditions: Standard, high turnover, no turnover, and short filaments. Distinct quasi-static states are observed for each condition: For standard parameters ~ 33% motors are attached and maintain moderate low levels of potential elastic energy. Viscous losses are moderately low. Fo...

Determining if asters eventually emerge from T = 1000 cases where no aster was evident. We identified cases where simulations did not end in a central aster from Figs 4 to 5 (marked with an *) and ran those simulations for longer times (T = 3000 time steps) to determine if those parameter sets merely delayed aster formation. We have noticed that tw...

Accompanies Fig 3A. Simulated time-lapse sequence of filaments and motors for the standard parameter set. (AVI)

Accompanies Fig 7B. Simulated time-lapse sequence of filaments and motors for tethered motors. (AVI)

Accompanies S3 Fig. Side by side time-lapse sequences of smoothed divergence mapping for the standard simulation from Fig 3 with the hexagon mask created from the coarse-grained image analysis approach. (AVI)

Anchoring filaments and motors. (DOCX)

The organization of filaments and motors for increasing rates of filament turnover. When we look at the organization of filaments (red) and motors (green) at the end of the simulation (t = 10s), we see that motors are localized at the center of filament asters. Additionally, as the rate of filament turnover (p2) increases, motor localization loosen...

Accompanies Fig 1A. Time-lapse sequence of F-actin in the apical (left) and basal (right) cortex of cells within a Xenopus laevis animal cap explant at gastrula stage. Video shows differences of actin organization from the same tissue at the same time. (AVI)

Accompanies Fig 3G. The same video as S3 Video except that it shows the highlighted hexagons from the custom coarse-grained image analysis. (AVI)

Accompanies Fig 4. Simulated time-lapse sequence of filaments and motors for L = 0.25 μm. (AVI)

Accompanies Fig 6. Simulated time-lapse sequence of filaments and motors for parameter switching from L = 0.5 μm to L = 1 μm. Filament lengths for the first half of the movie are short then become longer for the last half of the simulation. (AVI)

Accompanies Fig 7A. Simulated time-lapse sequence of filaments and motors for fixed actin on a bar. (AVI)

1D motor-filament model. (DOCX)

Quantifying work-energy. (DOCX)

Further quantitation of asters in Figs 4 and 5. (DOCX)

Distribution plots of the mean motor generated force for the 100 simulations of the sparse filament network. The distributions are normal distributions and have been plotted on the same axes with the exception of the force plot for T = 0 where the motors are all not exerting force on the filaments yet. The mean force at T = 1000 is 0.0935 nN +/- 0....

Coarse-grained image analysis quantification of asters. We used the coarse-grained image analysis technique to quantify the actin aster evolution from simulated time-lapse sequences (S4 Video), and for the smoothed divergence images (S12 Video). “Actin with Hexs Highlighted” shows where hexagons with mean intensity 1.7-fold higher than the mean int...

Extended time analysis for the standard parameter set to T = 3000 time steps. (A) The mean motor generated force for a simulation with the standard parameter set shows a leveling off, or steady state, is reached by 1000 time steps, and remains steady for the duration of the 3000 time step simulation. (B) A kymograph shows that actin filaments quick...

Tracking filament plus-end recruitment into asters for motor stretch parameter, r. The percentage of filament plus-ends that are recruited into the steady state aster for motor stretch threshold value of r = 0.15 and r = 0.6. (TIF)

Anchored or localized actin filaments remodel and serve as attractors for asters in adjacent regions. (A) Time-evolution of asters under conditions where 10% of 1,000 filaments are fixed in place through their plus-ends. 100 filaments anchored to the bottom fourth of the hexagon (white) and 900 filaments are left free in the domain (red). Over time...