Molkov's Theoretical Neuroscience Group

About Our Research

We use the methods of the qualitative theory of differential equations and statistical approaches to model and analyze a wide range of physical and biological systems. Our main research interests are the reconstruction of dynamical systems from data of different origins. Our current research projects are concerned with modeling the interactions between respiratory and cardio-vascular neural circuits in the brainstem, as well as spinal circuits that control quadrupedal and bipedal locomotion.

Neural Control of Breathing

Mechanisms of respiratory rhythm generation, pattern formation, and control by interacting pontine and pulmonary feedback loops.

Locomotion & Motor Control

Neural control of quadrupedal locomotion, motor adaptation, and left-right coordination mechanisms in mammalian circuits.

Alzheimer's Disease

Integrative theory linking molecular mechanisms of neurotoxicity, beta-amyloid biomarkers, and clinical diagnosis.

Publications

Locomotion & Motor Control

2026
Speed-Dependent Turning Strategies in Quadrupedal Locomotion: Insights from Computational Modeling. Y.I. Molkov, M.A.Y. Mohammed, T. Stell, A. Harralson, R. Jeter, I.A. Rybak. bioRxiv
2025
Ionic Mechanisms Underlying Bistability in Spinal Motoneurons: Insights from a Computational Model. Y.I. Molkov, F. Krust, R. Jeter, M. Mohammed, F. Brocard, I.A. Rybak. Front. Cell. Neurosci. 19:1710893
2024
Sensory feedback and central neuronal interactions in mouse locomotion. Molkov YI, Yu G, Ausborn J, Bouvier J, Danner SM, Rybak IA. R. Soc. Open Sci. 11:240207
2020
On the organization of the locomotor CPG: insights from split-belt locomotion and mathematical modeling. E.M. Latash, C.G. Lecomte, S.M. Danner, A. Frigon, I.A. Rybak, Y.I. Molkov. Front. Neurosci. 14:598888
2020
Frontal plane dynamics of the centre of mass during quadrupedal locomotion on a split-belt treadmill. E.M. Latash, W.H. Barnett, H. Park, J.M. Rider, A.N. Klishko, B.I. Prilutsky, Y.I. Molkov. J R Soc Interface 17(170)
2019
The interplay between cerebellum and basal ganglia in motor adaptation: A modeling study. D.I. Todorov, R.A. Capps, W.H. Barnett, E.M. Latash, T. Kim, K.C. Hamade, S.N. Markin, I.A. Rybak, Y.I. Molkov. PLOS ONE 14(4):e0214926
2019
Cutaneous sensory feedback from paw pads affects lateral balance control during split-belt locomotion in the cat. H. Park, E.M. Latash, Y.I. Molkov, A.N. Klishko, A. Frigon, S.P. DeWeerth, B.I. Prilutsky. Journal of Experimental Biology 222
2019
The functional role of striatal cholinergic interneurons in reinforcement learning from computational perspective. T. Kim, R.A. Capps, K.C. Hamade, W.H. Barnett, D.I. Todorov, E.M. Latash, S.N. Markin, I.A. Rybak, Y.I. Molkov. Front. Neural Circuits 13:10
2017
Reward based motor adaptation mediated by basal ganglia. T. Kim, K. Hamade, D. Todorov, W. Barnett, R. Capps, E. Latash, S. Markin, I. Rybak, Y. Molkov. Frontiers in Computational Neuroscience 11(19)
2017
From motor cortex to the movement and back again. W.W. Teka, K. Hamade, W.H. Barnett, T. Kim, S.N. Markin, I.A. Rybak, Y.I. Molkov. PLOS One 12(6): e0179288
2015
Mechanisms of Left-Right Coordination in Mammalian Locomotor Pattern Generation Circuits: A Mathematical Modeling View. Y.I. Molkov, B.J. Bacak, A.E. Talpalar, I.A. Rybak. PLoS Comput Biol 11(5): e1004270
1999
Dynamical model of locomotor-like movements of human evoked by muscle vibration. Y.I. Molkov, M.M. Sushchik, A.S. Kuznetsov, A.K. Kozlov, D.G. Zakharov. Applied Nonlinear Dynamics
1998
A dynamical model of locomotor-like movements evoked by muscle vibration in humans. Y.I. Molkov, M.M. Sushchik, A.S. Kuznetsov, A.K. Kozlov, D.G. Zakharov. Bulletin of UNN

Respiratory Neuroscience

2025
Inference technique for the synaptic conductances in rhythmically active networks and application to respiratory central pattern generation circuits. Molkov, Y. I., A. Borgmann, H. Koizumi, N. Hama, R. Zhang, J. C. Smith. eLife 13:RP101959
2024
Exploring the role of the Kölliker-Fuse nucleus in breathing variability by mathematical modelling. John SR, Barnett WH, Abdala APL, Zoccal DB, Rubin JE, Molkov YI. J Physiol. 602(1):93-112
2022
Predictions and experimental tests of a new biophysical model of the mammalian respiratory oscillator. Ryan S. Phillips, Hidehiko Koizumi, Yaroslav I. Molkov, Jonathan E. Rubin, Jeffrey C. Smith. eLife 11:e74762
2021
Heartbeats entrain breathing via baroreceptor-mediated modulation of expiratory activity. W.H. Barnett, D.M. Baekey, J.F.R. Paton, T.E. Dick, E.A. Wehrwein, Y.I. Molkov. Exp. Physiol. 106:1181-1195
2020
Traube-Hering Waves Are Formed by Interaction of Respiratory Sinus Arrhythmia and Pulse Pressure Modulation in Healthy Males. Barnett WH, Latash EM, Capps RE, Dick TE, Wehrwein EA, Molkov YI. J Appl Physiol 129(5)
2020
Inhibitory control of active expiration by the Botzinger complex in rats. K.C. Flor, W.H. Barnett, M. Karlen-Amarante, Y.I. Molkov, D.B. Zoccal. J Physiol.
2019
Pre- and Post-inspiratory neurons changed their firing properties in female rats exposed to chronic intermittent hypoxia. G.M.P.R. Souza, W.H. Barnett, M.R. Amorim, L. Lima-Silveira, D.J.A. Moraes, Y.I. Molkov, B.H. Machado. Neuroscience 406
2019
Biophysical mechanisms in the mammalian respiratory oscillator re-examined with a new data-driven computational model. R.S. Phillips, T.T. John, H. Koizumi, Y.I. Molkov, J.C. Smith. eLife 8:e41555
2018
Interaction between the retrotrapezoid nucleus and the parafacial respiratory group to regulate active expiration. D.B. Zoccal, J.N. Silva, W.H. Barnett, E.V. Lemes, B. Falquetto, E. Colombari, Y.I. Molkov, T.S. Moreira, A.C. Takakura. Am J Physiol Lung Cell Mol Physiol.
2018
Organization of the core respiratory network: Insights from optogenetic and modeling studies. J. Ausborn, H. Koizumi, W.H. Barnett, T. John, R. Zhang, Y.I. Molkov, J.C. Smith, I.A. Rybak. PLoS Comput Biol. 14(4):e1006148
2018
Kölliker-Fuse orchestrates the timing of expiratory abdominal nerve bursting. W.H. Barnett, S. Jenkin, W. Milsom, J.F.R. Paton, A.P.L. Abdala, Y.I. Molkov, D.B. Zoccal. J. Neurophysiol. 119(2)
2017
Chemoreception and neuroplasticity in respiratory circuits. W.H. Barnett, A.P. Abdala, J.F.R. Paton, I.A. Rybak, D.B. Zoccal, Y.I. Molkov. Experimental Neurology 287
2016
Computational Models of the Neural Control of Breathing. Y.I. Molkov, J.E. Rubin, I.A. Rybak, J.C. Smith. WIREs Systems Biology and Medicine
2016
Perturbations of Respiratory Rhythm and Pattern by Disrupting Synaptic Inhibition within Pre-Botzinger and Botzinger Complexes. V. Marchenko, H. Koizumi, B. Mosher, M. Tariq, N. Koshiya, T. Bezdudnaya, R. Zhang, Y. Molkov, I. Rybak, J. Smith. eNeuro
2016
Modeling the effects of extracellular potassium on bursting properties in pre-Botzinger complex neurons. B.J. Bacak, J. Segaran, Y.I. Molkov. J Comput Neurosci. 40(2)
2014
A Closed-Loop Model of the Respiratory System: Focus on Hypercapnia and Active Expiration. Y.I. Molkov, N.A. Shevtsova, C. Park, A. Ben-Tal, J.C. Smith, J.E. Rubin, I.A. Rybak. PLoS ONE 9(10): e109894
2014
Coupled Oscillations in Neural Control of Breathing. Y.I. Molkov. Encyclopedia of Computational Neuroscience
2014
Baroreflex models. Y.I. Molkov. Encyclopedia of Computational Neuroscience
2014
Physiological and pathophysiological interactions between the respiratory central pattern generator and the sympathetic nervous system. Y.I. Molkov, D.B. Zoccal, D.M. Baekey, A.P.L. Abdala, B.H. Machado, T.E. Dick, J.F.R. Paton, I.A. Rybak. Prog Brain Res. 212
2014
Rhythmic bursting in the pre-botzinger complex: mechanisms and models. I.A. Rybak, Y.I. Molkov, P.E. Jasinski, N.A. Shevtsova, J.C. Smith. Prog Brain Res. 209
2014
Effects of Glycinergic Inhibition Failure on Respiratory Rhythm and Pattern Generation. N.A. Shevtsova, D. Busselberg, Y.I. Molkov, A.M. Bischoff, J.C. Smith, D.W. Richter, I.A. Rybak. Prog Brain Res. 209
2013
Control of breathing by interacting pontine and pulmonary feedback loops. Y.Y. Molkov, B.J. Bacak, T.E. Dick, I.A. Rybak. Front. Neural Circuits 7:16
2012
Sodium and calcium mechanisms of rhythmic bursting in the excitatory neural networks of the pre-Botzinger complex: a computational modeling study. P.E. Jasinski, Y.I. Molkov, N.A. Shevtsova, J.C. Smith, I.A. Rybak. Eur J Neurosci. 37(2)
2012
Modeling the Autonomic Nervous System. I.A. Rybak, Y.I. Molkov, J.F.R. Paton, A.P.L. Abdala, D.B. Zoccal. Primer on the Autonomic Nervous System, 3rd edition
2011
Intermittent Hypoxia-Induced Sensitization of Central Chemoreceptors Contributes to Sympathetic Nerve Activity during Late Expiration in Rats. Y.I. Molkov, D.B. Zoccal, D.J.A. Moraes, J.F.R. Paton, B.H. Machado, I.A. Rybak. J Neurophysiol. 105(6)
2011
Computational modelling of 5-HT receptor-mediated reorganization of the brain stem respiratory network. N.A. Shevtsova, T. Manzke, Y.I. Molkov, A. Bischoff, J.C. Smith, I.A. Rybak, D.W. Richter. Eur J Neurosci. 34(8)
2011
Interacting oscillations in neural control of breathing: modeling and qualitative analysis. J.E. Rubin, B.J. Bacak, Y.I. Molkov, N.A. Shevtsova, J.C. Smith, I.A. Rybak. J Comput Neurosci. 30(3)
2010
Late-Expiratory Activity: Emergence and Interactions with the Respiratory CPG. Y.I. Molkov, A.P.L. Abdala, B.J. Bacak, J.C. Smith, J.F.R. Paton, I.A. Rybak. J. Neurophysiology 104
2010
Effect of baroreceptor stimulation on the respiratory pattern: Insights into respiratory-sympathetic interactions. D.M. Baekey, Y.I. Molkov, J.F.R. Paton, I.A. Rybak, T.E. Dick. Respir Physiol Neurobiol. 174

Alzheimer's Disease & Pathophysiology

2023
Towards the integrative theory of Alzheimer’s disease: linking molecular mechanisms of neurotoxicity, beta-amyloid biomarkers, and the diagnosis. Molkov YI, Zaretskaia MV, Zaretsky DV. Current Alzheimer Research 20(9)
2022
Patients with Alzheimer’s disease have an increased removal rate of soluble beta-amyloid-42. Zaretsky DV, Zaretskaia MV, Molkov YI. PLoS ONE 17(10): e0276933
2021
Membrane channel hypothesis of lysosomal permeabilization by beta-amyloid. Zaretsky DV, Zaretskaia MV, Molkov YI. Neurosci Lett. 136338
2018
Tissue oxidative metabolism can increase the difference between local temperature and arterial blood temperature. D.V. Zaretsky, A.A. Romanovsky, M.V. Zaretskaia, Y.I. Molkov. Temperature 5(1)
2018
Circadian variability of body temperature responses to methamphetamine. A. Behrouzvaziri, Y. Yoo, M.V. Zaretskaia, D.E. Rusyniak, D.V. Zaretsky, Y.I. Molkov. Am J Physiol Regul Integr Comp Physiol 314
2016
Amphetamine enhances endurance by increasing heat dissipation. E. Morozova, Y. Yoo, A. Behrouzvaziri, M. Zaretskaia, D. Rusyniak, D. Zaretsky, Y.I. Molkov. Physiological Reports 1(17)
2016
Why is it easier to run in the cold? Y.I. Molkov, D.V. Zaretsky. Temperature 3(4)
2015
Exercise Activates Compensatory Thermoregulatory Reaction in Rats: A Modeling Study. Y. Yoo, M. LaPradd, H. Kline, M.V. Zaretskaia, A. Behrouzvaziri, D.E. Rusyniak, Y.I. Molkov, D.V. Zaretsky. J Appl Physiol 119(12)
2015
Orexinergic Neurotransmission in Temperature Responses to Methamphetamine and Stress: Mathematical Modeling as a Data Assimilation Approach. A. Behrouzvaziri, D. Fu, P. Tan, Y. Yoo, M.V. Zaretskaia, D.E. Rusyniak, Y.I. Molkov, D.V. Zaretsky. PLoS ONE 10(5):e0126719
2014
Balanced Excitation and Inhibition in Temperature Responses to Meth. Y.I. Molkov, D.V. Zaretsky. Temperature 1(3)
2014
Meth Math: Modeling Temperature Responses to Methamphetamine. Y.I. Molkov, M.V. Zaretskaia, D.V. Zaretsky. Am J Physiol Regul Integr Comp Physiol. 306(8)
2012
Linking Inflammation and Cardiorespiratory Variability in Sepsis via Computational Modeling. T.E. Dick, Y.I. Molkov, I.A. Rybak et al. Frontiers in Physiology 3:222

Applied Mathematics & Dynamical Systems

2014
Chaos and Robustness in a Single Family of Genetic Oscillatory Networks. Fu D, Tan P, Kuznetsov A, Molkov YI. PLoS ONE 9(3): e90666
2012
Random dynamical models from time series. Y.I. Molkov, E.M. Loskutov, D.N. Mukhin, A.M. Feigin. Phys. Rev. E 85, 036216
2011
Prognosis of qualitative system behavior by noisy, nonstationary, chaotic time series. Y.I. Molkov, D.N. Mukhin, E.M. Loskutov, R.I. Timushev, A.M. Feigin. Phys. Rev. E 84, 036215
2011
Reconstruction of an evolution operator as a technique of analysis of epileptiform electric brain activity. Y.V. Yakhno, Y.I. Molkov, D.N. Mukhin, E.M. Loskutov, A.M. Feigin. Applied Nonlinear Dynamics 19(6)
2009
Using the minimum description length principle for global reconstruction of dynamic systems from noisy time series. Y.I. Molkov, Mukhin D.N., Feigin A.M., Loskutov E.M., G.A. Fidelin. Physical Review E 80, 046207
2008
Markov chain Monte Carlo method in Bayesian reconstruction of dynamical systems from noisy chaotic time series. E.M. Loskutov, A.M. Feigin, Y.I. Molkov, D.N. Mukhin. Physical Review E 77, 066214
2006
Bayesian approach to retrieval of vertical ozone profile from radiometry data. D.N. Mukhin, A.M. Feigin, Y.I. Molkov, E.V. Suvorov. Adv. Space Res. 37(12)
2003
Bayesian Approach to Retrieving a Vertical Ozone Profile from Radiometric Measurement Data. Y.I. Molkov, D.N. Mukhin, E.V. Suvorov, A.M. Feigin. Radiophysics and Quantum Electronics 46(8-9)
2002
Investigation of Nonlinear Dynamical Properties by the Observed Complex Behaviour as a Basis for Construction of the Dynamical Models of Atmospheric Photochemical Systems. A.M. Feigin, Y.I. Molkov, D.N. Mukhin, E.M. Loskutov. Faraday Discussions 120
1999
On the influence of diffusion upon the nonlinear behaviour of the photochemistry of the mesopause region. G.R. Sonnemann, A.M. Feigin, Y.I. Molkov. J. Geophys. Res. 104(D23)
1999
Bistable phase synchronization and chaos in a system of coupled Van-der-Pol - Duffing oscillators. A.K. Kozlov, M.M. Sushchik, Y.I. Molkov, A.S. Kuznetsov. Int. J. Bifurcation and Chaos 9(12)
1998
Toward understanding nonlinear nature of atmospheric photochemistry. A.M. Feigin, I.B. Konovalov, Y.I. Molkov. J. Geophys. Res. 103(D19)
1996
On kink dynamics of the perturbed sine-Gordon equation. A.G. Maksimov, N.F. Pedersen, P.L. Christiansen, Y.I.Molkov, V.I. Nekorkin. Wave Motion 23