Neuroscience, Statistical and Nonlinear Physics, Artificial Intelligence, Developmental Neuroscience
14
Scopus Publications
622
Scholar Citations
10
Scholar h-index
11
Scholar i10-index
Scopus Publications
How heterogeneity shapes dynamics and computation in the brain David Dahmen, Axel Hutt, Giacomo Indiveri, Ann Kennedy, Jeremie Lefebvre, Luca Mazzucato, Adilson E. Motter, Rishikesh Narayanan, Melika Payvand, Henrike Planert, Richard Gast Neuron, 2026 Much effort has been spent clustering neurons into transcriptomic or functional cell types and characterizing the differences between them. Beyond subdividing neurons into categories, we must recognize that no two neurons are identical and that graded physiological or transcriptomic properties exist within cells of a given type. This often overlooked "within-type" heterogeneity is a specific neuronal implementation of what statistical physics refers to as "disorder" and exhibits rich computational properties, the identification of which may shed crucial insights into theories of brain function. In this perspective article, we address this gap by highlighting theoretical frameworks for the study of neural tissue heterogeneity and discussing the benefits and implications of within-type heterogeneity for neural network dynamics, computation, and self-organization.
Direct and Retrograde Wave Propagation in Unidirectionally Coupled Wilson-Cowan Oscillators Guy Elisha, Richard Gast, Sourav Halder, Sara A. Solla, Peter J. Kahrilas, John E. Pandolfino, Neelesh A. Patankar Physical Review Letters, 2025 Some biological systems exhibit both direct and retrograde propagating signal waves despite unidirectional coupling. To explain this phenomenon, we study a chain of unidirectionally coupled Wilson-Cowan oscillators. Surprisingly, we find that changes in the homogeneous global input to the chain suffice to reverse the wave propagation direction. To obtain insights, we analyze the frequencies and bifurcations of the limit cycle solutions of the chain as a function of the global input. Specifically, we determine that the directionality of wave propagation is controlled by differences in the intrinsic frequencies of oscillators caused by the differential proximity of the oscillators to a homoclinic bifurcation.
Neural heterogeneity controls computations in spiking neural networks Richard Gast, Sara A. Solla, Ann Kennedy Proceedings of the National Academy of Sciences of the United States of America, 2024 The brain is composed of complex networks of interacting neurons that express considerable heterogeneity in their physiology and spiking characteristics. How does this neural heterogeneity influence macroscopic neural dynamics, and how might it contribute to neural computation? In this work, we use a mean-field model to investigate computation in heterogeneous neural networks, by studying how the heterogeneity of cell spiking thresholds affects three key computational functions of a neural population: the gating, encoding, and decoding of neural signals. Our results suggest that heterogeneity serves different computational functions in different cell types. In inhibitory interneurons, varying the degree of spike threshold heterogeneity allows them to gate the propagation of neural signals in a reciprocally coupled excitatory population. Whereas homogeneous interneurons impose synchronized dynamics that narrow the dynamic repertoire of the excitatory neurons, heterogeneous interneurons act as an inhibitory offset while preserving excitatory neuron function. Spike threshold heterogeneity also controls the entrainment properties of neural networks to periodic input, thus affecting the temporal gating of synaptic inputs. Among excitatory neurons, heterogeneity increases the dimensionality of neural dynamics, improving the network’s capacity to perform decoding tasks. Conversely, homogeneous networks suffer in their capacity for function generation, but excel at encoding signals via multistable dynamic regimes. Drawing from these findings, we propose intra-cell-type heterogeneity as a mechanism for sculpting the computational properties of local circuits of excitatory and inhibitory spiking neurons, permitting the same canonical microcircuit to be tuned for diverse computational tasks.
PyRates-A code-generation tool for modeling dynamical systems in biology and beyond Richard Gast, Thomas R. Knösche, Ann Kennedy Plos Computational Biology, 2023 The mathematical study of real-world dynamical systems relies on models composed of differential equations. Numerical methods for solving and analyzing differential equation systems are essential when complex biological problems have to be studied, such as the spreading of a virus, the evolution of competing species in an ecosystem, or the dynamics of neurons in the brain. Here we present PyRates, a Python-based software for modeling and analyzing differential equation systems via numerical methods. PyRates is specifically designed to account for the inherent complexity of biological systems. It provides a new language for defining models that mirrors the modular organization of real-world dynamical systems and thus simplifies the implementation of complex networks of interacting dynamic entities. Furthermore, PyRates provides extensive support for the various forms of interaction delays that can be observed in biological systems. The core of PyRates is a versatile code-generation system that translates user-defined models into “backend” implementations in various languages, including Python, Fortran, Matlab, and Julia. This allows users to apply a wide range of analysis methods for dynamical systems, eliminating the need for manual translation between code bases. PyRates may also be used as a model definition interface for the creation of custom dynamical systems tools. To demonstrate this, we developed two extensions of PyRates for common analyses of dynamic models of biological systems: PyCoBi for bifurcation analysis and RectiPy for parameter fitting. We demonstrate in a series of example models how PyRates can be used in combination with PyCoBi and RectiPy for model analysis and fitting. Together, these tools offer a versatile framework for applying computational modeling and numerical analysis methods to dynamical systems in biology and beyond.
Macroscopic dynamics of neural networks with heterogeneous spiking thresholds Richard Gast, Sara A. Solla, Ann Kennedy Physical Review E, 2023 Mean-field theory links the physiological properties of individual neurons to the emergent dynamics of neural population activity. These models provide an essential tool for studying brain function at different scales; however, for their application to neural populations on large scale, they need to account for differences between distinct neuron types. The Izhikevich single neuron model can account for a broad range of different neuron types and spiking patterns, thus rendering it an optimal candidate for a mean-field theoretic treatment of brain dynamics in heterogeneous networks. Here we derive the mean-field equations for networks of all-to-all coupled Izhikevich neurons with heterogeneous spiking thresholds. Using methods from bifurcation theory, we examine the conditions under which the mean-field theory accurately predicts the dynamics of the Izhikevich neuron network. To this end, we focus on three important features of the Izhikevich model that are subject here to simplifying assumptions: (i) spike-frequency adaptation, (ii) the spike reset conditions, and (iii) the distribution of single-cell spike thresholds across neurons. Our results indicate that, while the mean-field model is not an exact model of the Izhikevich network dynamics, it faithfully captures its different dynamic regimes and phase transitions. We thus present a mean-field model that can represent different neuron types and spiking dynamics. The model comprises biophysical state variables and parameters, incorporates realistic spike resetting conditions, and accounts for heterogeneity in neural spiking thresholds. These features allow for a broad applicability of the model as well as for a direct comparison to experimental data.
Mean-field approximations of networks of spiking neurons with short-term synaptic plasticity Richard Gast, Thomas R. Knösche, Helmut Schmidt Physical Review E, 2021 In Parkinson's disease (PD), large parts of the brain transition into states of enhanced neural synchronization. These phase transitions have been associated with the death of dopaminergic neurons as well as with impaired motor function. In this thesis, we address the much-debated question of how parkinsonian synchronization depends on dopamine depletion in the basal ganglia (BG). To this end, we develop spiking neural network (SNN) models of BG circuits and study them via bifurcation analysis. First, we derive mean-field models that allow to account for various forms of short-term plasticity in SNNs. We show that such short-term plasticity mechanisms can lead to highly synchronous, periodic bursting dynamics and discuss the relevance of this bursting regime for PD. Second, we find that the external pallidum, an important part of the BG, cannot cause parkinsonian oscillations autonomously. However, our results suggest that the external pallidum may contribute to the emergence of cross-frequency coupling that has been reported for parkinsonian oscillations. Finally, we describe an open-source Python toolbox that we developed to implement and analyze mean-field models of neural dynamics. Together, this thesis provides insight into BG synchronization processes as well as the mathematical basis and software for future studies of neural synchronization.:1 Introduction 1.1 A complex systems perspective of the brain 1.2 Brain function and the phase transition to synchronized neural activity 1.3 Low-dimensional manifolds of synchronized neural activity 1.4 Phase transitions to synchronized neural activity in Parkinson’s disease 1.5 Thesis overview 2 Mathematical Models and Methods 2.1 A non-linear oscillator model of neural activity 2.2 Dynamical systems methods for the study of neural network models 2.3 Dynamics of a single QIF neuron 3 Low-Dimensional Dynamics in Spiking Neural Networks 3.1 Mean-field approaches in neuroscience 3.2 Dynamics of QIF networks with post-synaptic STP 3.3 Dynamics of QIF networks with spike-frequency adaptation 3.4 Mean-field dynamics of QIF networks with pre-synaptic STP 3.5 Discussion 4 Phase Transitions and Neural Synchronization in the External Pallidum 4.1 A new perspective on GPe structure and function 4.2 GPe model definition and analysis 4.3 Phase transitions in the GPe under static and periodic input 4.4 Discussion 5. Modeling of Neural Mean-Field Dynamics Via PyRates 5.1 Computational modeling in neuroscience 5.2 The Framework 5.3 Pre-implemented methods for neural modeling workflows 5.4 Results 5.5 Discussion 6. Conclusion and Outlook
On the role of arkypallidal and prototypical neurons for phase transitions in the external pallidum Richard Gast, Ruxue Gong, Helmut Schmidt, Hil G.E. Meijer, Thomas R. Knösche Journal of Neuroscience, 2021 The external pallidum (globus pallidus pars externa [GPe]) plays a central role for basal ganglia functions and dynamics and, consequently, has been included in most computational studies of the basal ganglia. These studies considered the GPe as a homogeneous neural population. However, experimental studies have shown that the GPe contains at least two distinct cell types (prototypical and arkypallidal cells). In this work, we provide in silico insight into how pallidal heterogeneity modulates dynamic regimes inside the GPe and how they affect the GPe response to oscillatory input. We derive a mean-field model of the GPe system from a microscopic spiking neural network of recurrently coupled prototypical and arkypallidal neurons. Using bifurcation analysis, we examine the influence of dopamine-dependent changes of intrapallidal connectivity on the GPe dynamics. We find that increased self-inhibition of prototypical cells can induce oscillations, whereas increased inhibition of prototypical cells by arkypallidal cells leads to the emergence of a bistable regime. Furthermore, we show that oscillatory input to the GPe, arriving from striatum, leads to characteristic patterns of cross-frequency coupling observed at the GPe. Based on these findings, we propose two different hypotheses of how dopamine depletion at the GPe may lead to phase-amplitude coupling between the parkinsonian beta rhythm and a GPe-intrinsic c rhythm. Finally, we show that these findings generalize to realistic spiking neural networks of sparsely coupled Type I excitable GPe neurons.
Spatiotemporal features of β-γphase-Amplitude coupling in Parkinson's disease derived from scalp EEG Ruxue Gong, Mirko Wegscheider, Christoph Mühlberg, Richard Gast, Christopher Fricke, Jost-Julian Rumpf, Vadim V Nikulin, Thomas R Knösche, Joseph Classen Brain, 2021 Abnormal phase-amplitude coupling between β and broadband-γ activities has been identified in recordings from the cortex or scalp of patients with Parkinson’s disease. While enhanced phase-amplitude coupling has been proposed as a biomarker of Parkinson’s disease, the neuronal mechanisms underlying the abnormal coupling and its relationship to motor impairments in Parkinson’s disease remain unclear. To address these issues, we performed an in-depth analysis of high-density EEG recordings at rest in 19 patients with Parkinson’s disease and 20 age- and sex-matched healthy control subjects. EEG signals were projected onto the individual cortical surfaces using source reconstruction techniques and separated into spatiotemporal components using independent component analysis. Compared to healthy controls, phase-amplitude coupling of Parkinson’s disease patients was enhanced in dorsolateral prefrontal cortex, premotor cortex, primary motor cortex and somatosensory cortex, the difference being statistically significant in the hemisphere contralateral to the clinically more affected side. β and γ signals involved in generating abnormal phase-amplitude coupling were not strictly phase-phase coupled, ruling out that phase-amplitude coupling merely reflects the abnormal activity of a single oscillator in a recurrent network. We found important differences for couplings between the β and γ signals from identical components as opposed to those from different components (originating from distinct spatial locations). While both couplings were abnormally enhanced in patients, only the latter were correlated with clinical motor severity as indexed by part III of the Movement Disorder Society Unified Parkinson’s Disease Rating Scale. Correlations with parkinsonian motor symptoms of such inter-component couplings were found in premotor, primary motor and somatosensory cortex, but not in dorsolateral prefrontal cortex, suggesting motor domain specificity. The topography of phase-amplitude coupling demonstrated profound differences in patients compared to controls. These findings suggest, first, that enhanced phase-amplitude coupling in Parkinson’s disease patients originates from the coupling between distinct neural networks in several brain regions involved in motor control. Because these regions included the somatosensory cortex, abnormal phase-amplitude coupling is not exclusively tied to the hyperdirect tract connecting cortical regions monosynaptically with the subthalamic nucleus. Second, only the coupling between β and γ signals from different components appears to have pathophysiological significance, suggesting that therapeutic approaches breaking the abnormal lateral coupling between neuronal circuits may be more promising than targeting phase-amplitude coupling per se.
Amean-field description of bursting dynamics in spiking neural networks with short-term adaptation Richard Gast, Helmut Schmidt, Thomas R. Knösche Neural Computation, 2020 Bursting plays an important role in neural communication. At the population level, macroscopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of phase transitions between bursting and non-bursting states, mean-field descriptions of macroscopic bursting behavior are a valuable tool. In this article, we derive mean-field descriptions of populations of spiking neurons and examine whether states of collective bursting behavior can arise from short-term adaptation mechanisms. Specifically, we consider synaptic depression and spike-frequency adaptation in networks of quadratic integrate-and-fire neurons. Analyzing the mean-field model via bifurcation analysis, we find that bursting behavior emerges for both types of short-term adaptation. This bursting behavior can coexist with steady-state behavior, providing a bistable regime that allows for transient switches between synchronized and nonsynchronized states of population dynamics. For all of these findings, we demonstrate a close correspondence between the spiking neural network and the mean-field model. Although the mean-field model has been derived under the assumptions of an infinite population size and all-to-all coupling inside the population, we show that this correspondence holds even for small, sparsely coupled networks. In summary, we provide mechanistic descriptions of phase transitions between bursting and steady-state population dynamics, which play important roles in both healthy neural communication and neurological disorders.
Pygpc: A sensitivity and uncertainty analysis toolbox for Python Konstantin Weise, Lucas Poßner, Erik Müller, Richard Gast, Thomas R. Knösche Softwarex, 2020 We present a novel Python package for the uncertainty and sensitivity analysis of computational models. The mathematical background is based on the non-intrusive generalized polynomial chaos method allowing one to treat the investigated models as black box systems, without interfering with their legacy code. Pygpc is optimized to analyze models with complex and possibly discontinuous transfer functions that are computationally costly to evaluate. The toolbox determines the uncertainty of multiple quantities of interest in parallel, given the uncertainties of the system parameters and inputs. It also yields gradient-based sensitivity measures and Sobol indices to reveal the relative importance of model parameters.
How heterogeneity shapes dynamics and computation in the brain D Dahmen, A Hutt, G Indiveri, A Kennedy, J Lefebvre, L Mazzucato, ... Neuron 114 (5), 804-819 , 2026 2026 Citations: 15
Reversal of Wave Direction in Unidirectionally Coupled Oscillator Chains R Gast, G Elisha, SA Solla, NA Patankar JOURNAL OF COMPUTATIONAL NEUROSCIENCE 54 (SUPPL 1) , 2026 2026
Direct and retrograde wave propagation in unidirectionally coupled wilson-cowan oscillators G Elisha, R Gast, S Halder, SA Solla, PJ Kahrilas, JE Pandolfino, ... Physical review letters 134 (5), 058401 , 2025 2025 Citations: 2
Effects of Neural Heterogeneity on the Low-Dimensional Dynamics of Spiking Neural Networks R Gast, SA Solla, A Kennedy JOURNAL OF COMPUTATIONAL NEUROSCIENCE 52, S68-S68 , 2024 2024
Neural heterogeneity controls computations in spiking neural networks R Gast, SA Solla, A Kennedy Proceedings of the National Academy of Sciences 121 (3), e2311885121 , 2024 2024 Citations: 102
PyRates—A code-generation tool for modeling dynamical systems in biology and beyond R Gast, TR Knösche, A Kennedy PLOS Computational Biology 19 (12), e1011761 , 2023 2023 Citations: 7
Macroscopic dynamics of neural networks with heterogeneous spiking thresholds R Gast, SA Solla, A Kennedy Physical Review E 107 (2), 024306 , 2023 2023 Citations: 44
pyrates-neuroscience/PyCoBi: v0. 8.5: New method for creating ODESystem instances R Gast Zenodo , 2023 2023 Citations: 1
pyrates-neuroscience/PyRates: v1. 0.4: Dropped support for Python 3.6 and added support for Python 3.10 R Gast, DF Rose Zenodo , 2023 2023 Citations: 1
30th Annual Computational Neuroscience Meeting: CNS*2021–Meeting Abstracts W Singer, W Bialek, D Basset, et al. Journal of Computational Neuroscience 49, 3-208 , 2021 2021 Citations: 1
Mean-field approximations of networks of spiking neurons with short-term synaptic plasticity R Gast, K Thomas R, H Schmidt Physical Review E 104 (4), 044310 , 2021 2021 Citations: 33
On the Role of Arkypallidal and Prototypical Neurons for Phase Transitions in the External Pallidum R Gast, R Gong, H Schmidt, HGE Meijer, TR Knösche Journal of Neuroscience 41 (31), 6673-6683 , 2021 2021 Citations: 21
Low-dimensional dynamics of spiking neural networks with short-term plasticity R Gast 30th Annual Computational Neuroscience Meeting (CNS) , 2021 2021
On the role of arkypallidal and prototypical neurons for neural synchronization in the basal ganglia R Gast 30th Annual Computational Neuroscience Meeting (CNS) , 2021 2021
A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation (vol 32, pg 1615, 2020) R Gast, H Schmidt, TR Knosche NEURAL COMPUTATION 33 (6), 1717-1717 , 2021 2021
Spatiotemporal features of β-γ phase-amplitude coupling in Parkinson’s disease derived from scalp EEG R Gong, M Wegscheider, C Mühlberg, R Gast, C Fricke, JJ Rumpf, ... Brain 144 (2), 487-503 , 2021 2021 Citations: 82
Phase transitions between asynchronous and synchronous neural dynamics: Theoretical insight into the mechanisms behind neural oscillations in Parkinson's disease R Gast University of Leipzig , 2021 2021
Increased phase-amplitude coupling in Parkinson’s disease: Evidence from source localized electroencephalography R Gong, M Wegscheider, C Mühlberg, R Gast, C Fricke, JJ Rumpf, ... 7th International Conference on Non-invasive Brain Stimulation , 2020 2020
Dynamic regimes of spiking neural networks with short-term adaptation: Phase transitions of low-dimensional manifolds between asynchronous, synchronized and chaotic regimes R Gast, H Schmidt, TR Knösche Bernstein Conference 2020 , 2020 2020
MOST CITED SCHOLAR PUBLICATIONS
Using virtual reality to assess ethical decisions in road traffic scenarios: applicability of value-of-life-based models and influences of time pressure LR Sütfeld, R Gast, P König, G Pipa Frontiers in behavioral neuroscience 11, 122 , 2017 2017 Citations: 158
Neural heterogeneity controls computations in spiking neural networks R Gast, SA Solla, A Kennedy Proceedings of the National Academy of Sciences 121 (3), e2311885121 , 2024 2024 Citations: 102
Spatiotemporal features of β-γ phase-amplitude coupling in Parkinson’s disease derived from scalp EEG R Gong, M Wegscheider, C Mühlberg, R Gast, C Fricke, JJ Rumpf, ... Brain 144 (2), 487-503 , 2021 2021 Citations: 82
A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation R Gast, H Schmidt, TR Knösche Neural Computation 32 (9), 1615-1634 , 2020 2020 Citations: 67
Macroscopic dynamics of neural networks with heterogeneous spiking thresholds R Gast, SA Solla, A Kennedy Physical Review E 107 (2), 024306 , 2023 2023 Citations: 44
Pygpc: A sensitivity and uncertainty analysis toolbox for Python K Weise, L Poßner, E Müller, R Gast, TR Knösche SoftwareX 11, 100450 , 2020 2020 Citations: 36
Mean-field approximations of networks of spiking neurons with short-term synaptic plasticity R Gast, K Thomas R, H Schmidt Physical Review E 104 (4), 044310 , 2021 2021 Citations: 33
PyRates—A Python framework for rate-based neural simulations R Gast, D Rose, C Salomon, HE Möller, N Weiskopf, TR Knösche PLoS ONE 14 (12), e0225900 , 2019 2019 Citations: 30
On the Role of Arkypallidal and Prototypical Neurons for Phase Transitions in the External Pallidum R Gast, R Gong, H Schmidt, HGE Meijer, TR Knösche Journal of Neuroscience 41 (31), 6673-6683 , 2021 2021 Citations: 21
How heterogeneity shapes dynamics and computation in the brain D Dahmen, A Hutt, G Indiveri, A Kennedy, J Lefebvre, L Mazzucato, ... Neuron 114 (5), 804-819 , 2026 2026 Citations: 15
Probing neural networks for dynamic switches of communication pathways H Finger, R Gast, C Gerloff, AK Engel, P König PLoS Comput Biol 15 (12), e1007551 , 2019 2019 Citations: 10
PyRates—A code-generation tool for modeling dynamical systems in biology and beyond R Gast, TR Knösche, A Kennedy PLOS Computational Biology 19 (12), e1011761 , 2023 2023 Citations: 7
Encoding and decoding dynamic sensory signals with recurrent neural networks: An application of conceptors to birdsongs R Gast, P Faion, K Standvoss, A Suckro, B Lewis, G Pipa bioRxiv, 131052 , 2017 2017 Citations: 6
Response: Commentary: Using virtual reality to assess ethical decisions in road traffic scenarios: Applicability of value-of-life-based models and influences of time pressure LR Sütfeld, R Gast, P König, G Pipa Frontiers in behavioral neuroscience 12, 128 , 2018 2018 Citations: 3
Direct and retrograde wave propagation in unidirectionally coupled wilson-cowan oscillators G Elisha, R Gast, S Halder, SA Solla, PJ Kahrilas, JE Pandolfino, ... Physical review letters 134 (5), 058401 , 2025 2025 Citations: 2
pyrates-neuroscience/PyCoBi: v0. 8.5: New method for creating ODESystem instances R Gast Zenodo , 2023 2023 Citations: 1
pyrates-neuroscience/PyRates: v1. 0.4: Dropped support for Python 3.6 and added support for Python 3.10 R Gast, DF Rose Zenodo , 2023 2023 Citations: 1
30th Annual Computational Neuroscience Meeting: CNS*2021–Meeting Abstracts W Singer, W Bialek, D Basset, et al. Journal of Computational Neuroscience 49, 3-208 , 2021 2021 Citations: 1
Representing predictability of sequence patterns in a random network with short-term plasticity VSC Chien, R Gast, B Maess, TR Knösche BMC Neurosci 21, P101 , 2020 2020 Citations: 1
