Principles of Computational Modelling in Neuroscience
Abstract
The nervous system is made up of a large number of interacting elements. To understand how such a complex system functions requires the construction and analysis of computational models at many different levels. This book provides a step-by-step account of how to model the neuron and neural circuitry to understand the nervous system at all levels, from ion channels to networks. Starting with a simple model of the neuron as an electrical circuit, gradually more details are added to include the effects of neuronal morphology, synapses, ion channels and intracellular signalling. The principle of abstraction is explained through chapters on simplifying models, and how simplified models can be used in networks. This theme is continued in a final chapter on modelling the development of the nervous system. Requiring an elementary background in neuroscience and some high school mathematics, this textbook is an ideal basis for a course on computational neuroscience.
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Reduced-scale models of large networks with realistic single cell electrophysiological properties remain silent unless synaptic strengths or numbers are arbitrarily increased beyond biologically relevant levels.
“smaller models of large networks with realistic single cell electrophysiological properties (e.g., input resistance and resting membrane potential) remain silent unless synaptic strengths or numbers are arbitrarily increased beyond the biologically relevant levels to compensate for fewer inputs to their model cells”
From Interneuronal mechanisms of hippocampal theta oscillations in a full-scale model of the rodent CA1 circuit (2016) · cites this paper as Sterratt et al., 2011
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Stochastic phase-change neurons
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“DOI: 10.7554/eLife.18566 1 of 106 for fewer inputs to their model cells (e.g., [Dyhrfjeld-Johnsen et al., 2007; Sterratt et al., 2011]).”
BackgroundInfluentialThe Scientific Case for Brain Simulations
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“Starting with the seminal work of Hodgkin andHuxley (1952), who developed amechanisticmodel for action-potential generation and propagation in squid giant axons, biophysics-basedmodeling of neurons is nowwell estab- lished (Koch, 1999; Dayan and Abbott, 2001; Sterratt et al., 2011).”
BackgroundSingle-layer graphene modulates neuronal communication and augments membrane ion currents
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“In fact, the Nernst equilibrium 247 potential depends on the K concentrations outside and inside the membranes 248 [35].”
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Pursuing Impactful Entrepreneurship Research Using Artificial Intelligence
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“Moreover, AI plays an important role in neuroscience by enabling more powerful theory testing, such as through func - tional magnetic resonance imaging (e.g., Cortese et al., 2012) and computational modeling ( Sterratt et al., 2011 ).”
MethodModelling Nature: An Opinionated Introduction to Scientific Representation
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“Computational modeling has become a useful tool for examining various phenomena in biology in general (Brodland, 2015) and neuroscience in particular (Koch and Segev, 1998; Dayan and Abbott, 2001; Sterratt et al., 2011).”
BackgroundMethodInfluentialCalibration of ionic and cellular cardiac electrophysiology models
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MethodHow Cells Can Control Their Size by Pumping Ions
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“Here I show how one can set up a system of equations, derived from physical laws (Sterrat et al., 2011; Nelson, 2014), which model the interaction between ion and water fluxes, allowing one to calculate both the membrane potential (V) and cell volume (w).”
BackgroundPotassium and sodium microdomains in thin astroglial processes: A computational model study
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“The alternative brain-inspired hardware approach must address three key issues simultaneously: mimic the complex biological network of neurons, replicate synaptic structures, and allow implementation of standard computational algorithms [16].”
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Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive FlowsPreprint
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“…such as particle collisions in high energy physics [1, 71], universe evolution in cosmology [2, 67], stochastic dynamical systems in ecology and evolutionary biology [64, 65, 84, 85], macroeconomic models in econometrics [3, 26], and biological neural networks in neuroscience [48, 62, 73].”
BackgroundSelf-citationThe turn of the valve: representing with material models
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“…that the classification of organisms as models has recently been opposed by Levy and Currie (2014)), molecules (Toon 2011), brain functions (Sterratt et al. 2011), insects (Webb 2001), camera obscura (Wade and Finger 2001), volcanoes (Spieler et al. 2004), San Francisco Bay (Weisberg…”
BackgroundTveito, A., Jæger, K. H., Lines, G. T., Paszkowski, Ł., Sundnes, J., Edwards, A. G., Mäki‐Marttunen, T., Halnes, G., & Einevoll, G. T. (2017) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2017.00027 · Cited by 61 · see citing works
“…a major assumption is introduced; it is assumed that the extracellular potential varies so little that it can be taken to be a constant (see e.g., Sterratt et al., 2011) 1 ; Building on this assumption we arrive at the classical Cable equation Note that the term we ignored in the derivation of…”
InfluentialSpike-based local synaptic plasticity: a survey of computational models and neuromorphic circuits
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“, 2007; Wilkinson, 2011), neuroscience (Pospischil et al., 2008; Sterratt et al., 2011) and cognitive science (van Opheusden et al.”
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“More information about the LIF neuron can be found in [12]–[16], [30, Ch. 4], and [31, Sec.”
BackgroundComputational modeling of neurostimulation in brain diseases
Wang, Y., Hutchings, F., & Kaiser, M. (2015) · Progress in brain research · doi:10.1016/bs.pbr.2015.06.012 · Cited by 39 · see citing works
Systematic variational method for statistical nonlinear state and parameter estimation
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Robust forecasting using predictive generalized synchronization in reservoir computing
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“Figure 6: Top Panel Three dimensional display of the PGS and nonPGS regions in the case of an NaKL Hodgkin-Huxley neuron [80, 46, 47], driven by an external current with a waveform derived from the components associated with the Lorenz63 [40] model, and presented to a tanh RC.”
BackgroundMethodInfluentialHow does the presence of neural probes affect extracellular potentials?
Buccino, A. P., Kuchta, M., Jæger, K. H., Ness, T. V., Berthet, P., Mardal, K., Cauwenberghs, G., & Tveito, A. (2019) · Journal of Neural Engineering · doi:10.1088/1741-2552/ab03a1 · Cited by 35 · see citing works
“This equation is used to compute the membrane potential of a neuron and the solution is commonly obtained by dividing the neuron into compartments and replacing the continuous model (12) by a discrete model [43].”
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A Computational Framework for Realistic Retina Modeling
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“…that the simulation step ∆ t is sufficiently small, numerical integration of the single-compartment model is approximated by the Euler method 34; 36 : and Most of the interesting electrical properties of neurons arise from nonlinearities associated with changes of membrane conductances over…”
MethodKolaric, K. V., Thomson, G., Edgar, J. M., & Brown, A. M. (2013) · Physiological Reports · doi:10.1002/phy2.59 · Cited by 34 · see citing works
“(B) Action potentials are recorded at sequential nodes (6 – 20). practice in such simulations (Carnevale and Hones 2006; Sterratt et al. 2011).”
BackgroundMethodLiang, J., Kulasiri, D., & Samarasinghe, S. (2015) · Biosystems · doi:10.1016/j.biosystems.2015.05.003 · Cited by 33 · see citing works
“Also, the complexity of the models can be increased by including diffusion of Ca ions in the intracellular spaces, the buffering effects of endogenous Ca buffers, IP3 diffusion and metabolism and interactions of ER with mitochondria (Berridge et al., 2003; Sterratt et al., 2011).”
InfluentialConstructing Neuronal Network Models in Massively Parallel Environments
Ippen, T., Eppler, J. M., Pleßer, H. E., & Diesmann, M. (2017) · Frontiers in Neuroinformatics · doi:10.3389/fninf.2017.00030 · Cited by 31 · see citing works
“Typically on the order of ten to one hundred PSPs need to arrive within a few milliseconds in order to elicit an action potential in the postsynaptic neuron (see Abeles, 1991; Sterratt et al., 2011, for textbooks).”
BackgroundActivity-dependent switches between dynamic regimes of extracellular matrix expression
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“5 models individual PSCs with instantaneous rise time and exponential decay [64].”
BackgroundA biophysically detailed computational model of urinary bladder small DRG neuron soma
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Review of brain–computer interface based on steady‐state visual evoked potential
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“These signals are transmitted to the center through complex processing in the sensory pathway and finally result in perception [29].”
BackgroundDerivation of a Cell-Based Mathematical Model of Excitable Cells
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“For example, in the derivation of the cable equation, the extracellular potential is often assumed to be constant (30; 15).”
BackgroundDiversity of neuronal activity is provided by hybrid synapses
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Computational translation of drug effects from animal experiments to human ventricular myocytes
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Exploring the significance of morphological diversity for cerebellar granule cell excitability
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An Event-driven Neuromorphic System with Biologically Plausible Temporal Dynamics
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“They are defined as the following: [26]: Exponential kernel:K(t) = e− t τs (3)”
BackgroundMethodA stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics
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A color-coded graphical guide to the Hodgkin and Huxley papers
Hopper, A. J., Beswick‐Jones, H., & Brown, A. M. (2022) · AJP Advances in Physiology Education · doi:10.1152/advan.00178.2022 · Cited by 23 · see citing works
Bond graph modelling of chemoelectrical energy transduction
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“[36] can be rewritten in a similar form to (33) as”
BackgroundThe scope and limits of a mechanistic view of computational explanation
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Estimation of neural network model parameters from local field potentials (LFPs)
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“Starting with Hodgkin and Huxley’s development of a mechanistic model for action-potential generation and propagation in squid giant axons [3], mechanistic modeling of neurons is now well established [1, 4, 5].”
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“A practical way to estimate the optimal set of model parameter values is to fix certain known model parameters and manipulate others within a physiologically reasonable range until the model is able to mimic experimentally observed pattern(s) (Maex et al., 2009; Sterratt et al., 2011).”
Kadakia, N., Armstrong, E., Breen, D., Morone, U. I., Daou, A., Margoliash, D., & Abarbanel, H. D. I. (2016) · Biological Cybernetics · doi:10.1007/s00422-016-0697-3 · Cited by 21 · see citing works
Etiology of the membrane potential of rat white fat adipocytes
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“3- m-thick submembrane sheet, due to internal resistance considerations, Rin and G may be considered to be under- and overestimated, respectively (45).”
BackgroundA Cell-Based Model for Ionic Electrodiffusion in Excitable Tissue
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“33 · 10−9 m2/s (23) K diffusion coefficient DK r 1.”
BackgroundInfluentialCalcium Microdomain Formation at the Perisynaptic Cradle Due to NCX Reversal: A Computational Study
Wade, J. J., Breslin, K., Wong‐Lin, K., Harkin, J., Flanagan, B., van Zalinge, H., Hall, S., Dallas, M. L., Bithell, A., Verkhratsky, A., et al. (2019) · Frontiers in Cellular Neuroscience · doi:10.3389/fncel.2019.00185 · Cited by 19 · see citing works
“They were modeled as a simple passive electrochemical gradient dependent channel given by Sterratt et al. (2011): where i is the ion under consideration, g iBNeu is the channel conductance.”
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“Biophysical or conductance-based neuron models with voltage-gated currents have been shown to successfully reproduce membrane potential fluctuations in single neurons (Koch and Segev, 1998; Gerstner and Kistler, 2002; Dayan and Abbott, 2005; Sterratt et al., 2011).”
BackgroundLangthaler, S., Šajić, J. L., Rienmüller, T. M., Weinberg, S. H., & Baumgärtner, C. (2022) · Cells · doi:10.3390/cells11020239 · Cited by 19 · see citing works
“Such simplified models are phenomenological rather than representing the actual conformational states and are generally used in a way, similar to HH models, to simulate the measured macroscopic currents from whole-cell measurements deterministically [1,11].”
BackgroundMethodInfluentialA computational model of a human single sinoatrial node cell
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Spiking Autoencoders With Temporal Coding
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Biopotential Measurements and Electrodes
Akinin, A., Paul, A., Wang, J., Buccino, A. P., & Cauwenberghs, G. (2020) · Springer eBooks · doi:10.1007/978-3-030-43395-6_2 · Cited by 19 · see citing works
An intra-body linear channel model based on neuronal subthreshold stimulation
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“length constant, defined as follows [23]: λ = √ {Zm}da 4Ra , where {.”
BackgroundResultInfluentialCellular Spacing: Analysis and Modelling of Retinal Mosaics
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“• Principles of computational modelling in neuroscience (Sterratt et al, 2011).”
BackgroundNeuronify: An Educational Simulator for Neural Circuits
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“The integrate-and-fire model (see, e.g., Sterratt et al., 2011) is the most commonly used spiking neuron model and is a standard part of the curriculum in neuroscience courses with a computational component.”
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“Levels of organization in the brain (redrawn from [28,29]).”
BackgroundNetwork Thermodynamical Modeling of Bioelectrical Systems: A Bond Graph Approach
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“32 Away from equilibrium, the flow f depends on the channel characteristics and is typically modeled by the Goldman/ Hodgkin/Katz equation 32 and can be implemented by suitably modifying the basic Re flow equation (8).”
Langthaler, S., Rienmüller, T. M., Scheruebel, S., et al. (2021) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1009091 · Cited by 15 · see citing works
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Q10: The Effect of Temperature on Ion Channel Kinetics
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Computing Extracellular Electric Potentials from Neuronal Simulations
Ness, T. V., Halnes, G., Næss, S., Pettersen, K. H., & Einevoll, G. T. (2021) · Advances in experimental medicine and biology · doi:10.1007/978-3-030-89439-9_8 · Cited by 13 · see citing works
“In neuroscience this approach has been used to model activity in individual neurons using, for example, biophysically detailed neuron models based on the cable equation formalism (see, e.g., Koch [1999]; Sterratt et al. [2011]).”
MethodStable chaos in fluctuation driven neural circuits
Angulo‐García, D., & Torcini, A. (2014) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2014.10.009 · Cited by 12 · see citing works
Lin, Z., Tropper, C., Patoary, M. N. I., et al. (2015) · ACM SIGSIM Conference on Principles of Advanced Discrete Simulation (SIGSIM-PADS) · doi:10.1145/2769458.2769459 · Cited by 12 · see citing works
“Stochastic model is a far more realistic and accurate representation [23, 20] for this sort of situation.”
BackgroundShort-term plasticity as a mechanism to regulate and retain multistability
Zhou, X., Tian, C., Zhang, X., Zheng, M., & Xu, K. (2022) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2022.112891 · Cited by 12 · see citing works
Varvak, M. S. (2014) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2014.09.017 · Cited by 12 · see citing works
Sudhakar, S., Choi, T. J., & Ahmed, O. J. (2018) · Journal of Neurotrauma · doi:10.1089/neu.2018.6065 · Cited by 12 · see citing works
Computational modeling of the effects of auditory nerve dysmyelination
Brown, A. M., & Hamann, M. (2014) · Frontiers in Neuroanatomy · doi:10.3389/fnana.2014.00073 · Cited by 12 · see citing works
“Each INR was divided into compartments such that the length of each compartment was less than 0.1 λ (length constant), to ensure each compartment was isopotential, the generally accepted practice in such simulations (Carnevale and Hones, 2006; Sterratt et al., 2011).”
MethodInfluentialThe effects of temperature on the dynamics of the biological neural network
Jabbari, M. B., & Rezaei, M. (2022) · Journal of Biological Physics · doi:10.1007/s10867-021-09598-1 · Cited by 11 · see citing works
Aminzare, Z., & Kay, A. R. (2024) · The Journal of General Physiology · doi:10.1085/jgp.202413554 · Cited by 11 · see citing works
Accurate numerical simulation of electrodiffusion and water movement in brain tissue
Ellingsrud, A. J., Boullé, N., Farrell, P. E., et al. (2021) · Mathematical Medicine and Biology A Journal of the IMA · doi:10.1093/imammb/dqab016 · Cited by 11 · see citing works
Reduced-Dimension, Biophysical Neuron Models Constructed From Observed Data
Clark, R., Fuller, L., Platt, J. A., et al. (2022) · Neural Computation · doi:10.1162/neco_a_01515 · Cited by 11 · see citing works
“Our first step is to work with numerically generated data from the HH NaKL model neuron [18, 34].”
MethodInfluentialAnalytical CPG model driven by limb velocity input generates accurate temporal locomotor dynamics
Yakovenko, S., Sobinov, A. R., & Gritsenko, V. (2018) · PeerJ · doi:10.7717/peerj.5849 · Cited by 11 · see citing works
Multithreaded Stochastic PDES for Reactions and Diffusions in Neurons
Lin, Z., Tropper, C., McDougal, R. A., et al. (2016) · ACM Transactions on Modeling and Computer Simulation · doi:10.1145/2987373 · Cited by 11 · see citing works
“It is well known that a system consisting of a collection of chemical reactions can be represented by a chemical master equation, the solution of which is a probability distribution of the chemical reactants in the system [Sterratt et al. 2011].”
BackgroundHistory Dependent Neuronal Activity Modeled with Fractional Order Dynamics
Weinberg, S. H., & Santamarı́a, F. (2017) · doi:10.1002/9781119159193.ch39 · Cited by 11 · see citing works
Of Barrels and Pipes: Representation-as in Art and Science
Frigg, R., & Nguyen, J. (2019) · The frontiers collection · doi:10.1007/978-3-030-27577-8_12 · Cited by 10 · see citing works
Xolotl: An Intuitive and Approachable Neuron and Network Simulator for Research and Teaching
Gorur-Shandilya, S., Hoyland, A., & Marder, E. E. (2018) · Frontiers in Neuroinformatics · doi:10.3389/fninf.2018.00087 · Cited by 10 · see citing works
Artificial Neural Network Model with Astrocyte-Driven Short-Term Memory
Zimin, I. A., Kazantsev, V., & Викторович, С. С. (2023) · Biomimetics · doi:10.3390/biomimetics8050422 · Cited by 10 · see citing works
Sisyphus effect in pulse-coupled excitatory neural networks with spike-timing-dependent plasticity
Mikkelsen, K. B., Imparato, A., & Torcini, A. (2014) · Physical Review E · doi:10.1103/physreve.89.062701 · Cited by 10 · see citing works
“where Vr = −60 mV, Vth = −50 mV [61,62].”
Amsalem, O., King, J. G., Reimann, M., Ramaswamy, S., Muller, E. B., Markram, H., Nelken, I., & Segev, I. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.05.31.126466 · Cited by 10 · see citing works
“…and explain” approach differs from the typical computational route taken to study circuit dynamics, whereby simplified circuit models are constructed to study the dependence of an observed phenomenon, e.g., SSA, on unobserved biophysical parameters 38,39 , for example, synaptic depression.”
BackgroundA model for studying the energetics of sustained high frequency firing
Joós, B., Markham, M. R., Lewis, J. E., & Morris, C. E. (2018) · PLoS ONE · doi:10.1371/journal.pone.0196508 · Cited by 8 · see citing works
- Authors
- Sterratt, D., Graham, B., Gillies, A., & Willshaw, D.
- Affiliations
- University of Edinburgh (GB)
- University of Stirling (GB)
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2011-06-30
- OpenAlex
- W1481371813
- Cited by
- 320
- References
- 0
- Citations by year
- 2026: 3 · 2025: 5 · 2024: 16 · 2023: 16 · 2022: 23 · 2021: 21 · 2020: 33 · 2019: 50 · 2018: 30 · 2017: 32 · 2016: 20 · 2015: 28 · 2014: 25 · 2013: 11 · 2012: 4
- FWCI
- 5.05
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Life Sciences › Neuroscience › Cognitive Neuroscience › Undergraduate Neuroscience Education and Research
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- computational neuroscience, neuron models, neural circuits, ion channels, neuronal morphology, synapses, intracellular signaling, neuronal networks, model abstraction, brain development, circuit modeling
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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