Computational neuroscience and nonlinear dynamics are two distinct but directly related fields. We combine them to study rhythmicity and synchronization in neurological systems, with specific interests in better understanding neuronal information processing and memory in networked neurons. Information and memory play major roles in neuronal functions of both vertebrates and invertebrates including locomotion, digestion, saccadic eye movement, cardiac and respiratory activities, as well as in pathologies such as epilepsy, Parkinson’s and Alzheimer’s disease. We are also interested in machine learning as well as in temperature effects on neuronal activity.
Computational and Experimental Modulation of a Noisy Chaotic Neuronal System
Josselyn Gonzalez, Rosangela Follmann, Epaminondas Rosa Jr, and Wolfgang Stein
Chaos 33, 033109 (2023); https://doi.org/10.1063/5.0130874
In this work we study the interplay between chaos and noise in neuronal state transitions involving period doubling cascades. Our approach involves the implementation of a neuronal mathematical model under the action of neuromod- ulatory input, with and without noise, as well as equivalent experimental work on a biological neuron in the stomato- gastric ganglion of the crab C. borealis. Our simulations show typical transitions between tonic and bursting regimes that are mediated by chaos and period doubling cascades. While this transition is less evident when intrinsic noise is present in the model, the noisy computational output displays features akin to our experimental results. The differences and similarities observed in the computational and experimental approaches are discussed.
Quantitative Description of Neuronal Calcium Dynamics in C. elegans’ Thermoreception
Zachary Mobille, Rosangela Follmann, Andrés Vidal-Gadea, Epaminondas Rosa Jr.
The dynamical mechanisms underlying thermoreception in the nematode C. elegans are studied with a mathematical model for the amphid finger-like ciliated (AFD) neurons. The equations, equipped with Arrhenius temperature factors, account for the worm’s thermotaxis when seeking environments at its cultivation temperature, and for the AFD’s calcium dynamics when exposed to both linearly ramping and oscillatory temperature stimuli. Calculations of the peak time for calcium responses during simulations of pulse-like temperature inputs are consistent with known behavioral time scales of C. elegans.
Artificial Intelligence for Biology
Integrative and Comparative Biology, Volume 61, Issue 6, December 2021, Pages 2267–2275 https://doi.org/10.1093/icb/icab188
Synopsis: Despite efforts to integrate research across different subdisciplines of biology, the scale of integration remains limited. We hypothesize that future generations of Artificial Intelligence (AI) technologies specifically adapted for biological sciences will help enable the reintegration of biology. AI technologies will allow us not only to collect, connect, and analyze data at unprecedented scales, but also to build comprehensive predictive models that span various subdisciplines. They will make possible both targeted (testing specific hypotheses) and untargeted discoveries. AI for biology will be the cross-cutting technology that will enhance our ability to do biological research at every scale. We expect AI to revolutionize biology in the 21st century much like statistics transformed biology in the 20th century. The difficulties, however, are many, including data curation and assembly, development of new science in the form of theories that connect the subdisciplines, and new predictive and interpretable AI models that are more suited to biology than existing machine learning and AI techniques. Development efforts will require strong collaborations between biological and computational scientists. This white paper provides a vision for AI for Biology and highlights some challenges.
Weak-Winner Phase Synchronization: A Curious Case of Weak Interactions
Choudhary, Saha, Krueger, Finke, Rosa, Freund and Feudel
A novel type of chaotic phase synchronization of coupled systems is described in which networked oscillators weakly coupled synchronize while oscillators strongly coupled do not. This phenomenon can be explained by the interplay between nonisochronicity and the natural frequency of the oscillators. Employing a model system from ecology as well as a paradigmatic model from physics, we demonstrate that this phenomenon is a generic feature for a large class of coupled oscillator systems. The realization of this peculiar, yet quite generic, weak-winner synchronization dynamics can have far-reaching consequences on a wide range of scientific disciplines intrinsically exhibiting the phenomenon of phase synchronization, including synchronization of networks.
Analog Hodgkin-Huxley Model Neuron
We construct an electronic circuit for mimicking a single neuron’s behavior in connection with the dynamics of the Hodgkin-Huxley mathematical model. Our results show that the electronic neuron, even though it contains binary-state circuitry components, displays a timing interplay between the ion channels that is consistent with the corresponding timing encountered in the model equations. This is at the core of the mechanism determining not only the creation of action potentials, but also the neuronal firing rate output. The work is suitable for educational purposes in physics, mathematical modeling, electronics, and neurophysiology, and can be extended for implementation in networked neurons for more advanced studies of neuronal behaviors.
Rutherford, Mobille, Brandt-Trainer, Follmann, Rosa
Analog Implementation of a Hodgkin-Huxley Model Neuron
American Journal of Physics 88, 918 (2020)
Fast and Slow Dynamics in Machine Learning
Reservoir computing in machine learning is promoting better and faster predictability at lower computational cost. It consists, basically, of building a random recurrent topology where only a linear readout network layer is trained. Our results show that reservoir computing can be used to predict future states of neuronal activity in both periodic and chaotic states. Bifurcation diagrams of a chaotic time series display remarkable resemblance with the corresponding diagrams of the prediction. This suggests that during the learning phase, reservoir computers may retain information about the intrinsic dynamics of the system.
Follmann & Rosa
Predicting Slow and Fast Neuronal Dynamics with Machine Learning
Chaos 29, 113119 (2019)
Temperature Effects on Neuronal Activity
Temperature fluctuations can affect neurological processes at a variety of levels, with the overall output that higher temperatures in general increase neuronal activity. While variations in firing rates can happen with the neuronal system maintaining its homeostatic firing pattern of tonic firing, or bursting, changes in firing rates can changes in firing rates canalso be associated with transitions between the two patterns of firing. Our results suggest a possible mechanism related to the shortening of the duration of the action potential for higher firing rates with temperature increase.
Burek, Follmann, Rosa
Temperature Effects on Neuronal Firing Rates and Tonic-to-Bursting Transitions
Biosystems 180, 1 (2019)
Neuronal Tonic-to-Bursting Transitions
Tonic-to-bursting transitions in neurons, mediated by a period-doubling cascade and chaos, have been observed in single neurons as well as in networked neurons. A characteristic firing rate found in the single neuron passes on to networked neurons in synchronous states. This suggests that the behavior of distinct networked neurons is deeply rooted in a common feature shared by the coupled neurons when in synchrony.
Shaffer, Follmann, Harris, Postnova, Braun, Rosa
A critical firing rate associated with tonic-to-bursting transitions in synchronized gap-junction coupled neurons
Eur Phys J ST 226, 1939 (2017)
Shaffer, Harris, Follmann, Rosa
Bifurcation Transitions in Gap-Junction-Coupled Neurons
Phys. Rev. E 94, 042301 (2016)
Axonal Action Potential Propagation
Long-range communication in the nervous system is usually carried out with the propagation of action potentials along the axon of nerve cells. It is not uncommon for action potentials to travel in both directions, and eventually colliding. We investigate action potential propagation and collision and characterize propagation speed, refractory period, excitability, and action potential collision. Our numerical and experimental results unequivocally indicate that colliding action potentials do not pass each other, instead they are reciprocally annihilated.
Follmann, Rosa, Stein
Dynamics of Signal Propagation and Collision in Axons
Phys Rev E 93, 032707 (2015)