Computational and experimental modulation of a noisy chaotic neuronal system.

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 neuromodulatory input, with and without noise, as well as equivalent experimental work on a biological neuron in the stomatogastric ganglion of the crab Cancer 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.

Predicting slow and fast neuronal dynamics with machine learning.

In this work, we employ reservoir computing, a recently developed machine learning technique, to predict the time evolution of neuronal activity produced by the Hindmarsh-Rose neuronal model. Our results show accurate short- and long-term predictions for periodic (tonic and bursting) neuronal behaviors, but only short-term accurate predictions for chaotic neuronal states. However, after the accuracy of the short-term predictability deteriorates in the chaotic regime, the predicted output continues to display similarities with the actual neuronal behavior. This is reinforced by a striking resemblance between the bifurcation diagrams of the actual and of the predicted outputs. Error analyses of the reservoir's performance are consistent with standard results previously obtained.

Synchronous tonic-to-bursting transitions in a neuronal hub motif.

We study a heterogeneous neuronal network motif where a central node (hub neuron) is connected via electrical synapses to other nodes (peripheral neurons). Our numerical simulations show that the networked neurons synchronize in three different states: (i) robust tonic, (ii) robust bursting, and (iii) tonic initially evolving to bursting through a period-doubling cascade and chaos transition. This third case displays interesting features, including the carrying on of a characteristic firing rate found in the single neuron tonic-to-bursting transition.

Quantitative description of neuronal calcium dynamics in C. elegans' thermoreception.

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.

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.

Resolving the Rules of Robustness and Resilience in Biology Across Scales.

Why do some biological systems and communities persist while others fail? Robustness, a system's stability, and resilience, the ability to return to a stable state, are key concepts that span multiple disciplines within and outside the biological sciences. Discovering and applying common rules that govern the robustness and resilience of biological systems is a critical step toward creating solutions for species survival in the face of climate change, as well as the for the ever-increasing need for food, health, and energy for human populations. We propose that network theory provides a framework for universal scalable mathematical models to describe robustness and resilience and the relationship between them, and hypothesize that resilience at lower organization levels contribute to robust systems. Insightful models of biological systems can be generated by quantifying the mechanisms of redundancy, diversity, and connectivity of networks, from biochemical processes to ecosystems. These models provide pathways towards understanding how evolvability can both contribute to and result from robustness and resilience under dynamic conditions. We now have an abundance of data from model and non-model systems and the technological and computational advances for studying complex systems. Several conceptual and policy advances will allow the research community to elucidate the rules of robustness and resilience. Conceptually, a common language and data structure that can be applied across levels of biological organization needs to be developed. Policy advances such as cross-disciplinary funding mechanisms, access to affordable computational capacity, and the integration of network theory and computer science within the standard biological science curriculum will provide the needed research environments. This new understanding of biological systems will allow us to derive ever more useful forecasts of biological behaviors and revolutionize the engineering of biological systems that can survive changing environments or disease, navigate the deepest oceans, or sustain life throughout the solar system.

Temperature-dependent stochastic dynamics of the Huber-Braun neuron model.

The response of a four-dimensional mammalian cold receptor model to different implementations of noise is studied across a wide temperature range. It is observed that for noisy activation kinetics, the parameter range decomposes into two regions in which the system reacts qualitatively completely different to small perturbations through noise, and these regions are separated by a homoclinic bifurcation. Noise implemented as an additional current yields a substantially different system response at low temperature values, while the response at high temperatures is comparable to activation-kinetic noise. We elucidate how this phenomenon can be understood in terms of state space dynamics and gives quantitative results on the statistics of interspike interval distributions across the relevant parameter range.

On the role of subthreshold currents in the Huber-Braun cold receptor model.

We study the role of the strength of subthreshold currents in a four-dimensional Hodgkin-Huxley-type model of mammalian cold receptors. Since a total diminution of subthreshold activity corresponds to a decomposition of the model into a slow, subthreshold, and a fast, spiking subsystem, we first elucidate their respective dynamics separately and draw conclusions about their role for the generation of different spiking patterns. These results motivate a numerical bifurcation analysis of the effect of varying the strength of subthreshold currents, which is done by varying a suitable control parameter. We work out the key mechanisms which can be attributed to subthreshold activity and furthermore elucidate the dynamical backbone of different activity patterns generated by this model.

Temperature effects on neuronal firing rates and tonic-to-bursting transitions.

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 also be associated with transitions between the two patterns of firing. Our computer simulations suggest a possible mechanism directly related to the shortening of the duration of the action potential for higher firing rates with temperature increase. Increased temperatures also shorten the period doubling cascade and chaos transition between tonic and burting regimes.

Experimental observation of synchronous competition in the Chua system.

We present experimental results for two different sinusoidal functions competing to phase synchronize a Chua oscillator. Our approach involves real-time observation of the synchronization process. It shows that depending on the amplitude and frequency values of the two sinusoidal functions, the Chua oscillator can stay phase synchronized to one or the other of the inputs all the time or can alternate synchronous states between them. Numerical simulations show good agreement with the experimental observations.

Bifurcation transitions in gap-junction-coupled neurons.

Here we investigate transitions occurring in the dynamical states of pairs of distinct neurons electrically coupled, with one neuron tonic and the other bursting. Depending on the dynamics of the individual neurons, and for strong enough coupling, they synchronize either in a tonic or a bursting regime, or initially tonic transitioning to bursting via a period doubling cascade. Certain intrinsic properties of the individual neurons such as minimum firing rates are carried over into the dynamics of the coupled neurons affecting their ultimate synchronous state.

Dynamics of signal propagation and collision in axons.

Long-range communication in the nervous system is usually carried out with the propagation of action potentials along the axon of nerve cells. While typically thought of as being unidirectional, it is not uncommon for axonal propagation of action potentials to happen in both directions. This is the case because action potentials can be initiated at multiple "ectopic" positions along the axon. Two ectopic action potentials generated at distinct sites, and traveling toward each other, will collide. As neuronal information is encoded in the frequency of action potentials, action potential collision and annihilation may affect the way in which neuronal information is received, processed, and transmitted. We investigate action potential propagation and collision using an axonal multicompartment model based on the Hodgkin-Huxley equations. We characterize propagation speed, refractory period, excitability, and action potential collision for slow (type I) and fast (type II) axons. In addition, our studies include experimental measurements of action potential propagation in axons of two biological systems. Both computational and experimental results unequivocally indicate that colliding action potentials do not pass each other; they are reciprocally annihilated.

Effects of reciprocal inhibitory coupling in model neurons.

Central pattern generators are neuron networks that produce vital rhythmic motor outputs such as those observed in mastication, walking and breathing. Their activity patterns depend on the tuning of their intrinsic ionic conductances, their synaptic interconnectivity and entrainment by extrinsic neurons. The influence of two commonly found synaptic connectivities--reciprocal inhibition and electrical coupling--are investigated here using a neuron model with subthreshold oscillation capability, in different firing and entrainment regimes. We study the dynamics displayed by a network of a pair of neurons with various firing regimes, coupled by either (i) only reciprocal inhibition or by (ii) electrical coupling first and then reciprocal inhibition. In both scenarios a range of coupling strengths for the reciprocal inhibition is tested, and in general the neuron with the lower firing rate stops spiking for strong enough inhibitory coupling, while the faster neuron remains active. However, in scenario (ii) the originally slower neuron stops spiking at weaker inhibitory coupling strength, suggesting that the electrical coupling introduces an element of instability to the two-neuron network.

Phase Oscillatory Network and Visual Pattern Recognition.

We explore a properly interconnected set of Kuramoto type oscillators that results in a new associative-memory network configuration, which includes second- and third-order additional terms in the Fourier expansion of the network's coupling. Investigation of the response of the network to different external stimuli indicates an increase in the network capability for coding and information retrieval. Comparison of the network output with that of an equivalent experiment with subjects, for recognizing perturbed binary patterns, shows comparable results between the two approaches. We also discuss the enhanced storage capacity of the network.

Experimental Chua-plasma phase synchronization of chaos.

Experimental phase synchronization of chaos is demonstrated for two different chaotic oscillators: a plasma discharge and the Chua circuit. Our technique includes real-time capability for observing synchronization-desynchronization transitions. This capability results from a strong combination of synchronization and control, and allows tuning adjustments for search and stabilization of synchronous states. A power law is observed for the mean time between 2pi phase slips for different coupling strenghts. The experimental results are consistent with the numerical simulations.

Phase synchronization in the perturbed Chua circuit.

We show experimental and numerical results of phase synchronization between the chaotic Chua circuit and a small sinusoidal perturbation. Experimental real-time phase synchronized states can be detected with oscilloscope visualization of the attractor, using specific sampling rates. Arnold tongues demonstrate robust phase synchronized states for perturbation frequencies close to the characteristic frequency of the unperturbed Chua.

Phase detection of chaos.

A technique, first introduced in the context of pseudoperiodic sound waves, is here applied to the problem of detecting the phase of phase coherent and also phase noncoherent chaotic oscillators. The approach is based on finding sinusoidal fits to segments of the signal, therefore obtaining, for each segment, an appropriate frequency from which a phase can be derived. Central to the method is a judicious choice for the size of a sliding window and for the frequency range, as well as for the window advancing step. The approach is robust against moderate noise levels and three cases are presented for demonstrating the applicability of the method.

Learning phase synchronization from nonsynchronized chaotic regimes.

We present a novel modeling approach for reconstruction of the global behavior of coupled chaotic systems from bivariate time series. We analyze two coupled chaotic oscillators, which are able to phase synchronize due to coupling. It is shown that our technique enables the recovery of the synchronization diagram from only three data sets. In particular, this allows the estimate of the relative strength of the coupling and the parameter mismatch of both subsystems. The method is most efficient if only data from the nonsynchronized regime are used for the model learning. We also apply this approach to experimental data of a paced plasma tube.