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Intrinsic Plasticity Underlies the Malleability of Neural Network Heterogeneity
PRX Life 4, 013023 – Published 20 February, 2026
DOI: https://doi.org/10.1103/hrp5-sgvr
Abstract
Diversity exists throughout biology, playing an important role in maintaining robustness and stability. The same is true of the brain, as has become increasingly apparent in recent years with the accumulation of datasets of unparalleled resolution. These datasets show widespread neural heterogeneity, spanning cells, circuits, and system dynamics, marking it as an unavoidable component of the brain's composition. Recent experiments found that declines in heterogeneity among neurons may accompany pathological states. While heterogeneity has been linked to stability, robustness, and increased computational potential, the loss of biophysical diversity was found conducive to the onset of seizurelike activity, suggesting an important functional role. Despite this, how changes in heterogeneity arise remains unknown. Oftentimes considered a static metaparameter resulting from solely genetic disposition, heterogeneity is, in fact, a highly dynamic property of biological networks arising from various sources. Here, we consider this through the lens of intrinsic plasticity, the activity-dependent modulation of neuron biophysical properties, which we propose allows the degree of biophysical diversity to fluctuate in time. Using a network of Poisson neurons endowed with intrinsic plasticity, we combine analytical and numerical approaches to measure the effect of input statistics on the excitability of individual cells, and how this translates into changes in network heterogeneity at the population scale. Our results indicate that, through intrinsic plasticity, diversity in synaptic inputs promotes heterogeneity in cell-to-cell excitability due to changes in the statistics of presynaptic firing rates and network topology. In contrast, whenever the statistics of synaptic input between cells were too similar, intrinsic plasticity promoted the decline in heterogeneity. Further, we show that changes in heterogeneity can coexist with degeneracy in the firing rate between neurons. Taken together, understanding how input statistics affect neuronal network heterogeneity may provide key insights into brain function, resilience, and the manipulability of neural diversity through intrinsic plasticity.
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PRX Life Collection on adaptation and learning
PRX Life presents a special collection on ‘Biological systems that learn’, curated by the organizers of the National Institute for Theory and Mathematics in Biology (NITMB) workshop together with early-career researchers. The papers in this collection illustrate how living systems acquire functions, showing it is useful to describe them as tunable matter with many individually adjustable degrees of freedom characterizing microscopic properties. Drawing inspiration from AI and non-biological systems that can acquire desired functions, the featured research highlights the timeliness of the topic and its potential to drive unifying frameworks for emergent collective function in living tunable matter.
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References (110)
- M. R. Gardner and W. R. Ashby, Connectance of large dynamic (cybernetic) systems: Critical values for stability, Nature (London) 228, 784 (1970).
- R. M. May, Will a large complex system be stable? Nature (London) 238, 413 (1972).
- S. Allesina and S. Tang, Stability criteria for complex ecosystems, Nature (London) 483, 205 (2012).
- S. Tang, S. Pawar, and S. Allesina, Correlation between interaction strengths drives stability in large ecological networks, Ecol. Lett. 17, 1094 (2014).
- J. Vanalstine, S. R. Cox, and D. M. Roden, Cultural diversity in the United States and its impact on human development, J. Indiana Acad. Soc. Sci. 18, 10 (2015).
- D. Manheim, The fragile world hypothesis: Complexity, fragility, and systemic existential risk, Futures 122, 102570 (2020).
- H. Kitano, Biological robustness, Nat. Rev. Genet. 5, 826 (2004).
- A. Lesne, Robustness: Confronting lessons from physics and biology, Biol. Rev. 83, 509 (2008).
- B. R. Lee, R. Dalley, J. A. Miller, T. Chartrand, J. Close, R. Mann, A. Mukora, L. Ng, L. Alfiler, K. Baker, et al., Signature morphoelectric properties of diverse gabaergic interneurons in the human neocortex, Science 382, eadf6484 (2023).
- E. Braun, M. Danan-Gotthold, L. E. Borm, K. W. Lee, E. Vinsland, P. Lönnerberg, L. Hu, X. Li, X. He, Ž. Andrusivová, et al., Comprehensive cell atlas of the first-trimester developing human brain, Science 382, eadf1226 (2023).
- S. J. Tripathy, K. Padmanabhan, R. C. Gerkin, and N. N. Urban, Intermediate intrinsic diversity enhances neural population coding, Proc. Natl. Acad. Sci. USA 110, 8248 (2013).
- M. S. Cembrowski and N. Spruston, Heterogeneity within classical cell types is the rule: Lessons from hippocampal pyramidal neurons, Nat. Rev. Neurosci. 20, 193 (2019).
- S. Rich, H. M. Chameh, J. Lefebvre, and T. A. Valiante, Loss of neuronal heterogeneity in epileptogenic human tissue impairs network resilience to sudden changes in synchrony, Cell Rep. 39, 110863 (2022).
- R. Gast, S. A. Solla, and A. Kennedy, Neural heterogeneity controls computations in spiking neural networks, Proc. Natl. Acad. Sci. USA 121, e2311885121 (2024).
- D. Dahmen, A. Hutt, G. Indiveri, A. Kennedy, J. Lefebvre, L. Mazzucato, A. E. Motter, R. Narayanan, M. Payvand, H. Planert, et al., How heterogeneity shapes dynamics and computation in the brain, Neuron 114, 1 (2025).
- H. Moradi Chameh, S. Rich, L. Wang, F.-D. Chen, L. Zhang, P. L. Carlen, S. J. Tripathy, and T. A. Valiante, Diversity amongst human cortical pyramidal neurons revealed via their sag currents and frequency preferences, Nat. Commun. 12, 2497 (2021).
- L. Campagnola, S. C. Seeman, T. Chartrand, L. Kim, A. Hoggarth, C. Gamlin, S. Ito, J. Trinh, P. Davoudian, C. Radaelli, et al., Local connectivity and synaptic dynamics in mouse and human neocortex, Science 375, eabj5861 (2022).
- J. F. Mejias and A. Longtin, Differential effects of excitatory and inhibitory heterogeneity on the gain and asynchronous state of sparse cortical networks, Front. Comput. Neurosci. 8, 107 (2014).
- K. A. Ferguson and J. A. Cardin, Mechanisms underlying gain modulation in the cortex, Nat. Rev. Neurosci. 21, 80 (2020).
- J. Gjorgjieva, R. A. Mease, W. J. Moody, and A. L. Fairhall, Intrinsic neuronal properties switch the mode of information transmission in networks, PLoS Comput. Biol. 10, e1003962 (2014).
- J. H. Reynolds and D. J. Heeger, The normalization model of attention, Neuron 61, 168 (2009).
- T. Ohshiro, D. E. Angelaki, and G. C. DeAngelis, A normalization model of multisensory integration, Nat. Neurosci. 14, 775 (2011).
- P. J. Mineault, E. Tring, J. T. Trachtenberg, and D. L. Ringach, Enhanced spatial resolution during locomotion and heightened attention in mouse primary visual cortex, J. Neurosci. 36, 6382 (2016).
- W. Zhang and D. J. Linden, The other side of the engram: Experience-driven changes in neuronal intrinsic excitability, Nat. Rev. Neurosci. 4, 885 (2003).
- G. Daoudal and D. Debanne, Long-term plasticity of intrinsic excitability: Learning rules and mechanisms, Learn. Memory 10, 456 (2003).
- G. Turrigiano, L. Abbott, and E. Marder, Activity-dependent changes in the intrinsic properties of cultured neurons, Science 264, 974 (1994).
- N. S. Desai, L. C. Rutherford, and G. G. Turrigiano, Plasticity in the intrinsic excitability of cortical pyramidal neurons, Nat. Neurosci. 2, 515 (1999).
- E. Hanse, Associating synaptic and intrinsic plasticity, J. Physiol. 586, 691 (2008).
- D. Debanne, Y. Inglebert, and M. Russier, Plasticity of intrinsic neuronal excitability, Curr. Opin. Neurobiol. 54, 73 (2019).
- C. Gasselin, Y. Inglebert, and D. Debanne, Homeostatic regulation of H-conductance controls intrinsic excitability and stabilizes the threshold for synaptic modification in CA1 neurons, J. Physiol. 593, 4855 (2015).
- P. R. Brotchie, R. A. Andersen, L. H. Snyder, and S. J. Goodman, Head position signals used by parietal neurons to encode locations of visual stimuli, Nature (London) 375, 232 (1995).
- G. Maimon, A. D. Straw, and M. H. Dickinson, Active flight increases the gain of visual motion processing in Drosophila, Nat. Neurosci. 13, 393 (2010).
- S. Treue and J. C. M. Trujillo, Feature-based attention influences motion processing gain in macaque visual cortex, Nature (London) 399, 575 (1999).
- E. Salinas and N. M. Bentley, Gain modulation as a mechanism for switching reference frames, tasks, and targets, in Coherent Behavior in Neuronal Networks (Springer, New York, NY, 2009), pp. 121–142.
- H. Beck and Y. Yaari, Plasticity of intrinsic neuronal properties in CNS disorders, Nat. Rev. Neurosci. 9, 357 (2008).
- S. Li, V. Choi, and T. Tzounopoulos, Pathogenic plasticity of kv7. 2/3 channel activity is essential for the induction of tinnitus, Proc. Natl. Acad. Sci. USA 110, 9980 (2013).
- A. Henton and T. Tzounopoulos, What's the buzz? the neuroscience and the treatment of tinnitus, Physiol. Rev. 101, 1609 (2021).
- L. Chen, X. Li, M. Tjia, and S. Thapliyal, Homeostatic plasticity and excitation-inhibition balance: The good, the bad, and the ugly, Curr. Opin. Neurobiol. 75, 102553 (2022).
- T. M. Marschall, S. G. Brederoo, B. Ćurčić-Blake, and I. E. Sommer, Deafferentation as a cause of hallucinations, Curr. Opin. Psychiatry 33, 206 (2020).
- C. S. Chan, J. N. Guzman, E. Ilijic, J. N. Mercer, C. Rick, T. Tkatch, G. E. Meredith, and D. J. Surmeier, ‘Rejuvenation' protects neurons in mouse models of Parkinson's disease, Nature (London) 447, 1081 (2007).
- M. A. Busche, G. Eichhoff, H. Adelsberger, D. Abramowski, K.-H. Wiederhold, C. Haass, M. Staufenbiel, A. Konnerth, and O. Garaschuk, Clusters of hyperactive neurons near amyloid plaques in a mouse model of Alzheimer's disease, Science 321, 1686 (2008).
- P. Boulenguez, S. Liabeuf, R. Bos, H. Bras, C. Jean-Xavier, C. Brocard, A. Stil, P. Darbon, D. Cattaert, E. Delpire, et al., Down-regulation of the potassium-chloride cotransporter KCC2 contributes to spasticity after spinal cord injury, Nat. Med. 16, 302 (2010).
- J. Lisman, Excitation, inhibition, local oscillations, or large-scale loops: What causes the symptoms of schizophrenia? Curr. Opin. Neurobiol. 22, 537 (2012).
- C. Tsantoulas and S. B. McMahon, Opening paths to novel analgesics: The role of potassium channels in chronic pain, Trends Neurosci. 37, 146 (2014).
- B. J. Wainger, E. Kiskinis, C. Mellin, O. Wiskow, S. S. Han, J. Sandoe, N. P. Perez, L. A. Williams, S. Lee, G. Boulting, et al., Intrinsic membrane hyperexcitability of amyotrophic lateral sclerosis patient-derived motor neurons, Cell Rep. 7, 1 (2014).
- S. B. Nelson and V. Valakh, Excitatory/inhibitory balance and circuit homeostasis in autism spectrum disorders, Neuron 87, 684 (2015).
- M. V. Fogaça and R. S. Duman, Cortical GABAergic dysfunction in stress and depression: New insights for therapeutic interventions, Front. Cell. Neurosci. 13, 87 (2019).
- H. Moradi Chameh, M. Falby, Y. Yang, M. Movahed, K. Arbabi, C. Sarathy, S. J. Tripathy, L. Zhang, J. Lefebvre, and T. A. Valiante, Hyperpolarization activated cation channel mediated intrinsic plasticity changes underlie the malleability of with-in cell-type electrophysiological heterogeneity, biorXiv (2025).
- A. Hutt, S. Rich, T. A. Valiante, and J. Lefebvre, Intrinsic neural diversity quenches the dynamic volatility of neural networks, Proc. Natl. Acad. Sci. USA 120, e2218841120 (2023).
- A. Hutt, D. Trotter, A. Pariz, T. A. Valiante, and J. Lefebvre, Diversity-induced trivialization and resilience of neural dynamics, Chaos 34, 013147 (2024).
- K. Padmanabhan and N. N. Urban, Intrinsic biophysical diversity decorrelates neuronal firing while increasing information content, Nat. Neurosci. 13, 1276 (2010).
- M. S. Cembrowski and V. Menon, Continuous variation within cell types of the nervous system, Trends Neurosci. 41, 337 (2018).
- F. Scala, D. Kobak, M. Bernabucci, Y. Bernaerts, C. R. Cadwell, J. R. Castro, L. Hartmanis, X. Jiang, S. Laturnus, E. Miranda, et al., Phenotypic variation of transcriptomic cell types in mouse motor cortex, Nature (London) 598, 144 (2021).
- T. M. Stöber, D. Batulin, J. Triesch, R. Narayanan, and P. Jedlicka, Degeneracy in epilepsy: Multiple routes to hyperexcitable brain circuits and their repair, Commun. Biol. 6, 479 (2023).
- B. Tasic, Z. Yao, L. T. Graybuck, K. A. Smith, T. N. Nguyen, D. Bertagnolli, J. Goldy, E. Garren, M. N. Economo, S. Viswanathan, et al., Shared and distinct transcriptomic cell types across neocortical areas, Nature (London) 563, 72 (2018).
- R. D. Hodge, T. E. Bakken, J. A. Miller, K. A. Smith, E. R. Barkan, L. T. Graybuck, J. L. Close, B. Long, N. Johansen, O. Penn, et al., Conserved cell types with divergent features in human versus mouse cortex, Nature (London) 573, 61 (2019).
- C. Yang, Z. Liu, Q. Wang, G. Luan, and F. Zhai, Epileptic seizures in a heterogeneous excitatory network with short-term plasticity, Cognit. Neurodynam. 15, 43 (2021).
- J. Lefebvre, A. Hutt, J.-F. Knebel, K. Whittingstall, and M. M. Murray, Stimulus statistics shape oscillations in nonlinear recurrent neural networks, J. Neurosci. 35, 2895 (2015).
- A. Talidou, P. W. Frankland, D. Mabbott, and J. Lefebvre, Homeostatic coordination and up-regulation of neural activity by activity-dependent myelination, Nat. Comput. Sci. 2, 665 (2022).
- J. Lefebvre, A. Clappison, A. Longtin, and A. Hutt, Myelin-induced gain control in nonlinear neural networks, Commun. Phys. 8, 145 (2025).
- H. Kim, C. I. Del Genio, K. E. Bassler, and Z. Toroczkai, Constructing and sampling directed graphs with given degree sequences, New J. Phys. 14, 023012 (2012).
- C. W. Gardiner, Stochastic Methods: A Handbook for the Natural and Social Sciences, 4th ed., Springer Series in Synergetics Vol. 13 (Springer-Verlag, Berlin, 2009), pp. xviii + 447.
- V. V. Uteshev, A. G. Gusev, and E. A. Sametsky, Network control mechanisms—cellular milieu, in Neuronal Networks in Brain Function, CNS Disorders, and Therapeutics (Elsevier, Amsterdam, 2014), pp. 135–144.
- E. W. Ng and M. Geller, A table of integrals of the error functions, J. Res. Nat. Bur. Stand. B 73B, 1 (1969).
- W. Gerstner, W. M. Kistler, R. Naud, and L. Paninski, Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition (Cambridge University Press, Cambridge, 2014).
- J. Benda, A. Longtin, and L. Maler, Spike-frequency adaptation separates transient communication signals from background oscillations, J. Neurosci. 25, 2312 (2005).
- J. Benda, Neural adaptation, Curr. Biol. 31, R110 (2021).
- A. I. Weber, K. Krishnamurthy, and A. L. Fairhall, Coding principles in adaptation, Annu. Rev. Vis. Sci. 5, 427 (2019).
- A. I. Weber and A. L. Fairhall, The role of adaptation in neural coding, Curr. Opin. Neurobiol. 58, 135 (2019).
- P. Kudela, D. Boatman-Reich, D. Beeman, and W. S. Anderson, Modeling neural adaptation in auditory cortex, Front. Neural Circuits 12, 72 (2018).
- T. P. Reber, S. Mackay, M. Bausch, M. S. Kehl, V. Borger, R. Surges, and F. Mormann, Single-neuron mechanisms of neural adaptation in the human temporal lobe, Nat. Commun. 14, 2496 (2023).
- R. K. Rathour and R. Narayanan, Degeneracy in hippocampal physiology and plasticity, Hippocampus 29, 980 (2019).
- L. Albantakis, C. Bernard, N. Brenner, E. Marder, and R. Narayanan, The brain's best kept secret is its degenerate structure, J. Neurosci. 44, e1339242024 (2024).
- D. Klooster, A. J. de Louw, A. Aldenkamp, R. Besseling, R. Mestrom, S. Carrette, S. Zinger, J. W. Bergmans, W. Mess, K. Vonck, et al., Technical aspects of neurostimulation: Focus on equipment, electric field modeling, and stimulation protocols, Neurosci. Biobehav. Rev. 65, 113 (2016).
- D. Sterratt, B. Graham, A. Gillies, G. Einevoll, and D. Willshaw, Principles of Computational Modelling in Neuroscience, 2nd ed. (Cambridge University Press, Cambridge, 2023).
- J. Benda, L. Maler, and A. Longtin, Linear versus nonlinear signal transmission in neuron models with adaptation currents or dynamic thresholds, J. Neurophysiol. 104, 2806 (2010).
- A. A. Prinz, D. Bucher, and E. Marder, Similar network activity from disparate circuit parameters, Nat. Neurosci. 7, 1345 (2004).
- J.-M. Goaillard and E. Marder, Ion channel degeneracy, variability, and covariation in neuron and circuit resilience, Annu. Rev. Neurosci. 44, 335 (2021).
- T. O'Leary, A. H. Williams, A. Franci, and E. Marder, Cell types, network homeostasis, and pathological compensation from a biologically plausible ion channel expression model, Neuron 82, 809 (2014).
- L. M. Alonso and E. Marder, Visualization of currents in neural models with similar behavior and different conductance densities, eLife 8, e42722 (2019).
- Z. Fournier, L. M. Alonso, and E. Marder, Rhythmic circuit function is more robust to changes in synaptic than intrinsic conductances, eLife 13, RP102938 (2025).
- M. Steriade, I. Timofeev, and F. Grenier, Natural waking and sleep states: A view from inside neocortical neurons, J. Neurophysiol. 85, 1969 (2001).
- I. Timofeev, S. Chauvette, and S. Soltani, Neocortical focus: Experimental view, Int. Rev. Neurobiol. 114, 9 (2014).
- N. E. Crone, D. L. Miglioretti, B. Gordon, and R. P. Lesser, Functional mapping of human sensorimotor cortex with electrocorticographic spectral analysis. II. Event-related synchronization in the gamma band, Brain: J. Neurol. 121, 2301 (1998).
- B. Gähwiler, Organotypic monolayer cultures of nervous tissue, J. Neurosci. Methods 4, 329 (1981).
- S. Avramescu and I. Timofeev, Synaptic strength modulation after cortical trauma: A role in epileptogenesis, J. Neurosci. 28, 6760 (2008).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/hrp5-sgvr for three additional figures demonstrating (1) the stability of the network dynamics under the stimulation regimes; (2) the non-plastic network dynamics under additional stimuli types; and (3) the benefits of heterogeneous excitability to encoding.
- M. I. Chelaru and V. Dragoi, Efficient coding in heterogeneous neuronal populations, Proc. Natl. Acad. Sci. USA 105, 16344 (2008).
- J. F. Mejias and A. Longtin, Optimal heterogeneity for coding in spiking neural networks, Phys. Rev. Lett. 108, 228102 (2012).
- Z. Ma, G. G. Turrigiano, R. Wessel, and K. B. Hengen, Cortical circuit dynamics are homeostatically tuned to criticality in vivo, Neuron 104, 655 (2019).
- M. Di Volo and A. Destexhe, Optimal responsiveness and information flow in networks of heterogeneous neurons, Sci. Rep. 11, 17611 (2021).
- F. Zeldenrust, B. Gutkin, and S. Denéve, Efficient and robust coding in heterogeneous recurrent networks, PLoS Comput. Biol. 17, e1008673 (2021).
- J. Park, A. Brureau, K. Kernan, A. Starks, S. Gulati, B. Ogunnaike, J. Schwaber, and R. Vadigepalli, Inputs drive cell phenotype variability, Genome Res. 24, 930 (2014).
- J. Eberwine and J. Kim, Cellular deconstruction: Finding meaning in individual cell variation, Trends Cell Biol. 25, 569 (2015).
- Z. J. Huang and A. Paul, The diversity of GABAergic neurons and neural communication elements, Nat. Rev. Neurosci. 20, 563 (2019).
- K. Siletti, R. Hodge, A. Mossi Albiach, K. W. Lee, S.-L. Ding, L. Hu, P. Lönnerberg, T. Bakken, T. Casper, M. Clark, et al., Transcriptomic diversity of cell types across the adult human brain, Science 382, eadd7046 (2023).
- S. Marom and E. Marder, A biophysical perspective on the resilience of neuronal excitability across timescales, Nat. Rev. Neurosci. 24, 640 (2023).
- J. Yang, H. Shakil, S. Ratté, and S. A. Prescott, Minimal requirements for a neuron to coregulate many properties and the implications for ion channel correlations and robustness, eLife 11, e72875 (2022).
- A. Roxin, N. Brunel, D. Hanel, G. Mongillo, and C. van Vreeswijk, On the distribution of firing rates in networks of cortical neurons, J. Neurosci. 31, 16217 (2011).
- C. Y. Chou, H. H. Wong, C. Guo, K. E. Boukoulou, C. Huang, J. Jannat, T. Klimenko, V. Y. Li, T. A. Liang, V. C. Wu, et al., Principles of visual cortex excitatory microcircuit organization, The Innovation 6, 100735 (2025).
- G. Buzsáki and K. Mizuseki, The log-dynamic brain: How skewed distributions affect network operations, Nat. Rev. Neurosci. 15, 264 (2014).
- E.-L. Yap and M. E. Greenberg, Activity-regulated transcription: Bridging the gap between neural activity and behavior, Neuron 100, 330 (2018).
- B. E. Lonze and D. D. Ginty, Function and regulation of CREB family transcription factors in the nervous system, Neuron 35, 605 (2002).
- R. Butler, P.-M. Bernier, J. Lefebvre, G. Gilbert, and K. Whittingstall, Decorrelated input dissociates narrow band power and BOLD in human visual cortex, J. Neurosci. 37, 5408 (2017).
- https://github.com/djtrotter/intrinsic_plast.
- A. Mierau, W. Klimesch, and J. Lefebvre, State-dependent alpha peak frequency shifts: Experimental evidence, potential mechanisms and functional implications, Neuroscience 360, 146 (2017).
- R. Unnikrishnan and M. Hebert, Measures of similarity, in 2005 Seventh IEEE Workshops on Applications of Computer Vision (WACV/MOTION'05) (IEEE, 2005), Vol. 1, pp. 394–394.
- S. Kullback and R. A. Leibler, On information and sufficiency, Ann. Math. Stat. 22, 79 (1951).
- A. Bhattacharyya, On a measure of divergence between two multinomial populations, Sankhyā : The Indian Journal of Statistics 7, 401 (1946).
- H. Cramér, Mathematical Methods of Statistics (Princeton University Press, Princeton, NJ, 1999), Vol. 26.