Mechanism, dynamics, and biological existence of multistability in a large class of bursting neurons

Multistability, the coexistence of multiple attractors in a dynamical system, is explored in bursting nerve cells. A modeling study is performed to show that a large class of bursting systems, as defined by a shared topology when represented as dynamical systems, is inherently suited to support multistability. We derive the bifurcation structure and parametric trends leading to multistability in these systems. Evidence for the existence of multirhythmic behavior in neurons of the aquatic mollusc Aplysia californica that is consistent with our proposed mechanism is presented. Although these experimental results are preliminary, they indicate that single neurons may be capable of dynamically storing information for longer time scales than typically attributed to nonsynaptic mechanisms.Comment: 24 pages, 8 figure

Multimodal transition and stochastic antiresonance in squid giant axons

The experimental data of N. Takahashi, Y. Hanyu, T. Musha, R. Kubo, and G. Matsumoto, Physica D \textbf{43}, 318 (1990), on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the Hodgkin-Huxley model. The minimum of the firing rate as a function of the stimulus amplitude $I_0$ in the high-frequency regime is due to the multimodal transition. Below this singular point only odd multiples of the driving period remain and the system is highly sensitive to noise. The coefficient of variation has a maximum and the firing rate has a minimum as a function of the noise intensity which is an indication of the stochastic coherence antiresonance. The model calculations reproduce the frequency of occurrence of the most common modes in the vicinity of the transition. A linear relation of output frequency vs. $I_0$ for above the transition is also confirmed.Comment: 5 pages, 9 figure

The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability

We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoing Hopf bifurcation, we explore the dynamical properties. Matching the normal form coefficients to a coupled Wilson-Cowan oscillator network gives an understanding of different types of behaviour that arise in a model of perceptual bistability. Notably, we find bistability between in-phase and anti-phase solutions that demonstrates the feasibility for synchronisation to act as the mechanism by which periodic inputs can be segregated (rather than via strong inhibitory coupling, as in existing models). Using numerical continuation we confirm our theoretical analysis for small coupling strength and explore the bifurcation diagrams for large coupling strength, where the normal form approximation breaks down

Auditory streaming and bistability paradigm extended to a dynamic environment

This is the final version. Available on open access from Elsevier via the DOI in this recordData availability: All experimental data and model code are available in the github repository james-rankin/auditory-streaming: https://github.com/james-rankin/auditory-streamingWe explore stream segregation with temporally modulated acoustic features using behavioral experiments and modelling. The auditory streaming paradigm in which alternating high- A and low-frequency tones B appear in a repeating ABA-pattern, has been shown to be perceptually bistable for extended presentations (order of minutes). For a fixed, repeating stimulus, perception spontaneously changes (switches) at random times, every 2–15 s, between an integrated interpretation with a galloping rhythm and segregated streams. Streaming in a natural auditory environment requires segregation of auditory objects with features that evolve over time. With the relatively idealized ABA-triplet paradigm, we explore perceptual switching in a non-static environment by considering slowly and periodically varying stimulus features. Our previously published model captures the dynamics of auditory bistability and predicts here how perceptual switches are entrained, tightly locked to the rising and falling phase of modulation. In psychoacoustic experiments we find that entrainment depends on both the period of modulation and the intrinsic switch characteristics of individual listeners. The extended auditory streaming paradigm with slowly modulated stimulus features presented here will be of significant interest for future imaging and neurophysiology experiments by reducing the need for subjective perceptual reports of ongoing perception.Swartz FoundationEngineering and Physical Sciences Research Council (EPSRC

Methods to assess binocular rivalry with periodic stimuli

This is the final version. Available on open access from SpringerOpen via the DOI in this recordAvailability of data and materials: Source code for the model is available in the GitHub repository farzaneh-darki/Darki2020_methods: https://github.com/farzaneh-darki/Darki2020_methods.Binocular rivalry occurs when the two eyes are presented with incompatible stimuli and perception alternates between these two stimuli. This phenomenon has been investigated in two types of experiments: (1) Traditional experiments where the stimulus is fixed, (2) eye-swap experiments in which the stimulus periodically swaps between eyes many times per second (Logothetis et al. in Nature 380(6575):621–624, 1996). In spite of the rapid swapping between eyes, perception can be stable for many seconds with specific stimulus parameter configurations. Wilson introduced a two-stage, hierarchical model to explain both types of experiments (Wilson in Proc. Natl. Acad. Sci. 100(24):14499–14503, 2003). Wilson’s model and other rivalry models have been only studied with bifurcation analysis for fixed inputs and different types of dynamical behavior that can occur with periodically forcing inputs have not been investigated. Here we report (1) a more complete description of the complex dynamics in the unforced Wilson model, (2) a bifurcation analysis with periodic forcing. Previously, bifurcation analysis of the Wilson model with fixed inputs has revealed three main types of dynamical behaviors: Winner-takes-all (WTA), Rivalry oscillations (RIV), Simultaneous activity (SIM). Our results have revealed richer dynamics including mixed-mode oscillations (MMOs) and a period-doubling cascade, which corresponds to low-amplitude WTA (LAWTA) oscillations. On the other hand, studying rivalry models with numerical continuation shows that periodic forcing with high frequency (e.g. 18 Hz, known as flicker) modulates the three main types of behaviors that occur with fixed inputs with forcing frequency (WTA-Mod, RIV-Mod, SIM-Mod). However, dynamical behavior will be different with low frequency periodic forcing (around 1.5 Hz, so-called swap). In addition to WTA-Mod and SIM-Mod, cycle skipping, multi-cycle skipping and chaotic dynamics are found. This research provides a framework for either assessing binocular rivalry models to check consistency with empirical results, or for better understanding neural dynamics and mechanisms necessary to implement a minimal binocular rivalry model.Engineering and Physical Sciences Research Council (EPSRC

Rhythmic inhibition allows neural networks to search for maximally consistent states

Gamma-band rhythmic inhibition is a ubiquitous phenomenon in neural circuits yet its computational role still remains elusive. We show that a model of Gamma-band rhythmic inhibition allows networks of coupled cortical circuit motifs to search for network configurations that best reconcile external inputs with an internal consistency model encoded in the network connectivity. We show that Hebbian plasticity allows the networks to learn the consistency model by example. The search dynamics driven by rhythmic inhibition enable the described networks to solve difficult constraint satisfaction problems without making assumptions about the form of stochastic fluctuations in the network. We show that the search dynamics are well approximated by a stochastic sampling process. We use the described networks to reproduce perceptual multi-stability phenomena with switching times that are a good match to experimental data and show that they provide a general neural framework which can be used to model other 'perceptual inference' phenomena

Modelling the Emergence and Dynamics of Perceptual Organisation in Auditory Streaming

Many sound sources can only be recognised from the pattern of sounds they emit, and not from the individual sound events that make up their emission sequences. Auditory scene analysis addresses the difficult task of interpreting the sound world in terms of an unknown number of discrete sound sources (causes) with possibly overlapping signals, and therefore of associating each event with the appropriate source. There are potentially many different ways in which incoming events can be assigned to different causes, which means that the auditory system has to choose between them. This problem has been studied for many years using the auditory streaming paradigm, and recently it has become apparent that instead of making one fixed perceptual decision, given sufficient time, auditory perception switches back and forth between the alternatives—a phenomenon known as perceptual bi- or multi-stability. We propose a new model of auditory scene analysis at the core of which is a process that seeks to discover predictable patterns in the ongoing sound sequence. Representations of predictable fragments are created on the fly, and are maintained, strengthened or weakened on the basis of their predictive success, and conflict with other representations. Auditory perceptual organisation emerges spontaneously from the nature of the competition between these representations. We present detailed comparisons between the model simulations and data from an auditory streaming experiment, and show that the model accounts for many important findings, including: the emergence of, and switching between, alternative organisations; the influence of stimulus parameters on perceptual dominance, switching rate and perceptual phase durations; and the build-up of auditory streaming. The principal contribution of the model is to show that a two-stage process of pattern discovery and competition between incompatible patterns can account for both the contents (perceptual organisations) and the dynamics of human perception in auditory streaming