How neuronal morphology impacts the synchronisation state of neuronal networks

How neuronal morphology impacts the synchronisation state of neuronal networks Robert P. Gowers Susanne Schreiber https://orcid.org/0000-0003-3913-5650 Lyle J. Graham

The biophysical properties of neurons not only affect how information is processed within cells, they can also impact the dynamical states of the network. Specifically, the cellular dynamics of action-potential generation have shown relevance for setting the (de)synchronisation state of the network. The dynamics of tonically spiking neurons typically fall into one of three qualitatively distinct types that arise from distinct mathematical bifurcations of voltage dynamics at the onset of spiking. Accordingly, changes in ion channel composition or even external factors, like temperature, have been demonstrated to switch network behaviour via changes in the spike onset bifurcation and hence its associated dynamical type. A thus far less addressed modulator of neuronal dynamics is cellular morphology. Based on simplified and anatomically realistic mathematical neuron models, we show here that the extent of dendritic arborisation has an influence on the neuronal dynamical spiking type and therefore on the (de)synchronisation state of the network. Specifically, larger dendritic trees prime neuronal dynamics for in-phase-synchronised or splayed-out activity in weakly coupled networks, in contrast to cells with otherwise identical properties yet smaller dendrites. Our biophysical insights hold for generic multicompartmental classes of spiking neuron models (from ball-and-stick-type to anatomically reconstructed models) and establish a connection between neuronal morphology and the susceptibility of neural tissue to synchronisation in health and disease.
3 4 2024 e1011874 10.1371/journal.pcbi.1011874 1 10.1371/journal.pcbi.corrections_policy www.ploscompbiol.org false 10.1371/journal.pcbi.1011874 H2020 European Research Council http://dx.doi.org/10.13039/100010663 864243 Einstein Stiftung Berlin http://dx.doi.org/10.13039/501100006188 EP-2021-621 http://creativecommons.org/licenses/by/4.0/ 10.1371/journal.pcbi.1011874 202403141055370000 https://dx.plos.org/10.1371/journal.pcbi.1011874 https://dx.plos.org/10.1371/journal.pcbi.1011874 Current biology E Marder 11 23 R986 2001 10.1016/S0960-9822(01)00581-4 Central pattern generators and the control of rhythmic movements Nature S Hürkey 1 2023 Gap junctions desynchronize a neural circuit to stabilize insect flight Movement Disorders H Bergman 17 S3 S28 2002 10.1002/mds.10140 Pathophysiology of Parkinson’s disease: From clinical neurology to basic neuroscience and back Nature Reviews Neuroscience PJ Uhlhaas 11 2 100 2010 10.1038/nrn2774 Abnormal neural oscillations and synchrony in schizophrenia The Journal of physiology P Jiruska 591 4 787 2013 10.1113/jphysiol.2012.239590 Synchronization and desynchronization in epilepsy: controversies and hypotheses The Journal of Mathematical Neuroscience I Al-Darabsah 11 1 1 2021 10.1186/s13408-021-00103-5 M-current induced Bogdanov–Takens bifurcation and switching of neuron excitability class Nature Communications J Hesse 13 1 1 2022 10.1038/s41467-022-31195-6 Temperature elevations can induce switches to homoclinic action potentials that alter neural encoding and synchronization The Journal of physiology AL Hodgkin 107 2 165 1948 10.1113/jphysiol.1948.sp004260 The local electric changes associated with repetitive action in a non-medullated axon 10.7551/mitpress/2526.001.0001 Izhikevich EM. Synchronization. In: Dynamical systems in neuroscience. MIT press; 2007. p. 443–505. Physical Review E J Hesse 95 5 052203 2017 10.1103/PhysRevE.95.052203 Qualitative changes in phase-response curve and synchronization at the saddle-node-loop bifurcation PloS one KM Stiefel 3 12 e3947 2008 10.1371/journal.pone.0003947 Cholinergic neuromodulation changes phase response curve shape and type in cortical pyramidal neurons PLoS computational biology SA Prescott 4 10 e1000198 2008 10.1371/journal.pcbi.1000198 Biophysical basis for three distinct dynamical mechanisms of action potential initiation bioRxiv C Kirst 206581 2017 GABA regulates resonance and spike rate encoding via a universal mechanism that underlies the modulation of action potential generation PLoS Computational Biology SA Contreras 17 5 e1008510 2021 10.1371/journal.pcbi.1008510 Activity-mediated accumulation of potassium induces a switch in firing pattern and neuronal excitability type Nature ZF Mainen 382 6589 363 1996 10.1038/382363a0 Influence of dendritic structure on firing pattern in model neocortical neurons Journal of Neuroscience G Eyal 34 24 8063 2014 10.1523/JNEUROSCI.5431-13.2014 Dendrites impact the encoding capabilities of the axon PLOS Computational Biology L Tiroshi 15 2 e1006782 2019 10.1371/journal.pcbi.1006782 Population dynamics and entrainment of basal ganglia pacemakers are shaped by their dendritic arbors bioRxiv D Beniaguev 2022 Multiple Synaptic Contacts combined with Dendritic Filtering enhance Spatio-Temporal Pattern Recognition capabilities of Single Neurons Neural computation B Ermentrout 8 5 979 1996 10.1162/neco.1996.8.5.979 Type I membranes, phase resetting curves, and synchrony Physical review letters Jn Teramae 93 20 204103 2004 10.1103/PhysRevLett.93.204103 Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators Physical Review E TW Ko 79 1 016211 2009 10.1103/PhysRevE.79.016211 Phase-response curves of coupled oscillators Journal of Neuroscience A Larkman 10 5 1407 1990 10.1523/JNEUROSCI.10-05-01407.1990 Correlations between morphology and electrophysiology of pyramidal neurons in slices of rat visual cortex. I. Establishment of cell classes Cerebral Cortex H Mohan 25 12 4839 2015 10.1093/cercor/bhv188 Dendritic and axonal architecture of individual pyramidal neurons across layers of adult human neocortex Cerebral cortex KI Van Aerde 25 3 788 2015 10.1093/cercor/bht278 Morphological and physiological characterization of pyramidal neuron subtypes in rat medial prefrontal cortex Entropy U Pereira 17 12 7859 2015 10.3390/e17127850 The Bogdanov–Takens normal form: a minimal model for single neuron dynamics Experimental neurology W Rall 2 5 503 1960 10.1016/0014-4886(60)90029-7 Membrane potential transients and membrane time constant of motoneurons Introduction to theoretical neurobiology: linear cable theory and dendritic structure HC Tuckwell 1988 Biophysical journal W Rall 13 7 648 1973 10.1016/S0006-3495(73)86014-X Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model Comprehensive Physiology W Rall 39 2011 Elife G Eyal 5 e16553 2016 10.7554/eLife.16553 Unique membrane properties and enhanced signal processing in human neocortical neurons Cell L Beaulieu-Laroche 175 3 643 2018 10.1016/j.cell.2018.08.045 Enhanced dendritic compartmentalization in human cortical neurons Experimental brain research L Bindman 69 3 489 1988 10.1007/BF00247303 Comparison of the electrical properties of neocortical neurones in slices in vitro and in the anaesthetized rat Journal of neurophysiology D Paré 79 3 1450 1998 10.1152/jn.1998.79.3.1450 Impact of spontaneous synaptic activity on the resting properties of cat neocortical pyramidal neurons in vivo Journal of neurophysiology A Destexhe 81 4 1531 1999 10.1152/jn.1999.81.4.1531 Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo Biophysical journal C Morris 35 1 193 1981 10.1016/S0006-3495(81)84782-0 Voltage oscillations in the barnacle giant muscle fiber Annual review of neuroscience G Major 36 1 2013 10.1146/annurev-neuro-062111-150343 Active properties of neocortical pyramidal neuron dendrites Neuroscience ME Larkum 2022 The guide to dendritic spikes of the mammalian cortex in vitro and in vivo Neurocomputing K Tsumoto 69 4-6 293 2006 10.1016/j.neucom.2005.03.006 Bifurcations in Morris–Lecar neuron model Biological cybernetics C Liu 108 1 75 2014 10.1007/s00422-013-0580-4 Bifurcation analysis of a Morris–Lecar neuron model Journal of neuroscience XJ Wang 16 20 6402 1996 10.1523/JNEUROSCI.16-20-06402.1996 Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model Elements of applied bifurcation theory YA Kuznetsov 293 2013 The Journal of Mathematical Neuroscience (JMN) P De Maesschalck 5 1 1 2015 10.1186/s13408-015-0029-2 Neural excitability and singular bifurcations SIAM journal on mathematical analysis S Schecter 18 4 1142 1987 10.1137/0518083 The saddle-node separatrix-loop bifurcation Bulletin of Mathematical Biology J Guckenheimer 55 5 937 1993 10.1016/S0092-8240(05)80197-1 Bifurcation of the Hodgkin and Huxley equations: a new twist Bifurcations EM Izhikevich 2007 Kirst C. Synchronization, Neuronal Excitability, and Information Flow in Networks of Neuronal Oscillators. Georg-August-Universität Göttingen; 2011. PLoS computational biology E Phoka 6 4 e1000768 2010 10.1371/journal.pcbi.1000768 A new approach for determining phase response curves reveals that Purkinje cells can act as perfect integrators Journal of neurophysiology S Wang 109 11 2757 2013 10.1152/jn.00721.2012 Hippocampal CA1 pyramidal neurons exhibit type 1 phase-response curves and type 1 excitability Neural computation D Hansel 7 2 307 1995 10.1162/neco.1995.7.2.307 Synchrony in excitatory neural networks Neural computation E Brown 16 4 673 2004 10.1162/089976604322860668 On the phase reduction and response dynamics of neural oscillator populations Mathematical Methods in the Applied Sciences JH Schleimer 41 18 8844 2018 10.1002/mma.5232 Phase-response curves of ion channel gating kinetics Journal of neurophysiology P Vetter 85 2 926 2001 10.1152/jn.2001.85.2.926 Propagation of action potentials in dendrites depends on dendritic morphology Journal of Neuroscience GA Ascoli 27 35 9247 2007 10.1523/JNEUROSCI.2055-07.2007 NeuroMorpho. Org: a central resource for neuronal morphologies Nature communications O Amsalem 11 1 1 2020 10.1038/s41467-019-13932-6 An efficient analytical reduction of detailed nonlinear neuron models Chemical oscillations, waves and turbulence Y Kuramoto 1984 10.1007/978-3-642-69689-3 GB Ermentrout 2010 Frontiers in Applied Mathematics and Statistics P Ashwin 2 7 2016 10.3389/fams.2016.00007 Identical phase oscillator networks: Bifurcations, symmetry and reversibility for generalized coupling Journal of computational neuroscience C Van Vreeswijk 1 4 313 1994 10.1007/BF00961879 When inhibition not excitation synchronizes neural firing SIAM Journal on Applied Mathematics GB Ermentrout 52 6 1665 1992 10.1137/0152096 Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators Physical Review E MA Schwemmer 83 3 031906 2011 10.1103/PhysRevE.83.031906 Effects of dendritic load on the firing frequency of oscillating neurons Frontiers in cellular neuroscience M Psarrou 8 287 2014 10.3389/fncel.2014.00287 A simulation study on the effects of dendritic morphology on layer V prefrontal pyramidal cell firing behavior Journal of computational neuroscience SM Crook 5 3 315 1998 10.1023/A:1008839112707 Dendritic and synaptic effects in systems of coupled cortical oscillators Journal of Neurophysiology JA Goldberg 97 1 208 2007 10.1152/jn.00810.2006 Response Properties and Synchronization of Rhythmically Firing Dendritic Neurons PLoS Comput Biol MW Remme 5 9 e1000493 2009 10.1371/journal.pcbi.1000493 The role of ongoing dendritic oscillations in single-neuron dynamics Biophysical journal G Major 65 1 423 1993 10.1016/S0006-3495(93)81037-3 Solutions for transients in arbitrarily branching cables: I. Voltage recording with a somatic shunt Biological cybernetics WA Wybo 107 6 685 2013 10.1007/s00422-013-0568-0 The Green’s function formalism as a bridge between single-and multi-compartmental modeling Elife WA Wybo 10 2021 Data-driven reduction of dendritic morphologies with preserved dendro-somatic responses Journal of Neuroscience Y Wei 34 35 11733 2014 10.1523/JNEUROSCI.0516-14.2014 Unification of neuronal spikes, seizures, and spreading depression Journal of computational neuroscience D Depannemaecker 50 1 33 2022 10.1007/s10827-022-00811-1 A unified physiological framework of transitions between seizures, sustained ictal activity and depolarization block at the single neuron level PLoS computational biology BF Behabadi 8 7 e1002599 2012 10.1371/journal.pcbi.1002599 Location-dependent excitatory synaptic interactions in pyramidal neuron dendrites Nature communications A Tzilivaki 10 1 1 2019 10.1038/s41467-019-11537-7 Challenging the point neuron dogma: FS basket cells as 2-stage nonlinear integrators Science A Gidon 367 6473 83 2020 10.1126/science.aax6239 Dendritic action potentials and computation in human layer 2/3 cortical neurons Neuromorphic Computing and Engineering A Stöckel 2022 Computational properties of multi-compartment LIF neurons with passive dendrites Brain research WR Holmes 505 1 12 1989 10.1016/0006-8993(89)90110-8 Effects of uniform and non-uniform synaptic ‘activation-distributions’ on the cable properties of modeled cortical pyramidal neurons Neuron M Häusser 19 3 665 1997 10.1016/S0896-6273(00)80379-7 Tonic synaptic inhibition modulates neuronal output pattern and spatiotemporal synaptic integration Journal of Neuroscience M Rudolph 23 6 2466 2003 10.1523/JNEUROSCI.23-06-02466.2003 A Fast-Conducting, Stochastic Integrative Mode for Neocortical Neurons InVivo Biological Cybernetics C Koch 50 1 15 1984 10.1007/BF00317936 Cable theory in neurons with active, linearized membranes Biological Cybernetics S Coombes 97 2 137 2007 10.1007/s00422-007-0161-5 Branching dendrites with resonant membrane: a “sum-over-trips” approach Journal of computational neuroscience MW Remme 31 1 13 2011 10.1007/s10827-010-0295-7 Role of active dendritic conductances in subthreshold input integration PLoS One E Zhuchkova 8 11 e78908 2013 10.1371/journal.pone.0078908 Somatic versus dendritic resonance: differential filtering of inputs through non-uniform distributions of active conductances Journal of Neuroscience NW Schultheiss 30 7 2767 2010 10.1523/JNEUROSCI.3959-09.2010 Phase response curve analysis of a full morphological globus pallidus neuron model reveals distinct perisomatic and dendritic modes of synaptic integration Nature ME Larkum 398 6725 338 1999 10.1038/18686 A new cellular mechanism for coupling inputs arriving at different cortical layers The Journal of physiology SR Williams 521 Pt 2 467 1999 10.1111/j.1469-7793.1999.00467.x Mechanisms and consequences of action potential burst firing in rat neocortical pyramidal neurons Neuron C Grienberger 81 6 1274 2014 10.1016/j.neuron.2014.01.014 NMDA receptor-dependent multidendrite Ca2+ spikes required for hippocampal burst firing in vivo Scientific Reports G Yi 7 1 1 2017 Action potential initiation in a two-compartment model of pyramidal neuron mediated by dendritic Ca2+ spike Nature neuroscience MH Kole 11 2 178 2008 10.1038/nn2040 Action potential generation requires a high sodium channel density in the axon initial segment Neuron MHP Kole 73 2 235 2012 10.1016/j.neuron.2012.01.007 Signal Processing in the Axon Initial Segment PNAS MS Hamada 113 51 2016 10.1073/pnas.1607548113 Covariation of axon initial segment location and dendritic tree normalizes the somatic action potential Elife S Goethals 9 e53432 2020 10.7554/eLife.53432 Theoretical relation between axon initial segment geometry and excitability PLoS computational biology C Zhang 18 1 e1009775 2022 10.1371/journal.pcbi.1009775 Ultrafast population coding and axo-somatic compartmentalization Journal of Open Research Software C Rackauckas 5 1 2017 10.5334/jors.151 Differentialequations.jl–a performant and feature-rich ecosystem for solving differential equations in julia SIAM review J Bezanson 59 1 65 2017 10.1137/141000671 Julia: A fresh approach to numerical computing Gowers R. morph-excite-code GitHub repository; 2024. Available from: https://github.com/rpgowers/morph-excite-code. 10.1371/journal.pcbi.1011874.g001 https://dx.plos.org/10.1371/journal.pcbi.1011874.g001 10.1371/journal.pcbi.1011874.g002 https://dx.plos.org/10.1371/journal.pcbi.1011874.g002 10.1371/journal.pcbi.1011874.g003 https://dx.plos.org/10.1371/journal.pcbi.1011874.g003 10.1371/journal.pcbi.1011874.g004 https://dx.plos.org/10.1371/journal.pcbi.1011874.g004 10.1371/journal.pcbi.1011874.g005 https://dx.plos.org/10.1371/journal.pcbi.1011874.g005 10.1371/journal.pcbi.1011874.g006 https://dx.plos.org/10.1371/journal.pcbi.1011874.g006 10.1371/journal.pcbi.1011874.g007 https://dx.plos.org/10.1371/journal.pcbi.1011874.g007 10.1371/journal.pcbi.1011874.g008 https://dx.plos.org/10.1371/journal.pcbi.1011874.g008 10.1371/journal.pcbi.1011874.s001 https://dx.plos.org/10.1371/journal.pcbi.1011874.s001