Badal Joshi

On Immunotherapies and Cancer Vaccination Protocols: A Mathematical Modelling Approach

In this paper we develop a new mathematical model of immunotherapy and cancer vaccination, focusing on the role of antigen presentation and co-stimulatory signaling pathways in cancer immunology. We investigate the effect of different cancer vaccination protocols on the well-documented phenomena of cancer dormancy and recurrence, and we provide a possible explanation of why adoptive (i.e. passive) immunotherapy protocols can sometimes actually promote tumour growth instead of inhibiting it (a phenomenon called immunostimulation), as opposed to active vaccination protocols based on tumour-antigen pulsed dendritic cells. Significantly, the results of our computational simulations suggest that elevated numbers of professional antigen presenting cells correlate well with prolonged time periods of cancer dormancy.

Simplifying the Jacobian Criterion for Precluding Multistationarity in Chemical Reaction Networks

Chemical reaction networks taken with mass-action kinetics are dynamical systems that arise in chemical engineering and systems biology. In general, determining whether a chemical reaction network admits multiple steady states is difficult, as this requires determining existence of multiple positive solutions to a large system of polynomials with unknown coefficients. However, in certain cases, various easy criteria can be applied. One such test is the Jacobian criterion, due to Craciun and Feinberg, which gives sufficient conditions for ruling out the possibility of multiple steady states. A chemical reaction network is said to pass the Jacobian criterion if all terms in the determinant expansion of its parametrized Jacobian matrix have the same sign. In this article, we present a procedure which simplifies the application of the Jacobian criterion, and as a result, we identify a new class of networks for which multiple steady states is precluded: those in which all chemical species have total moleculari...

Decoding synchronized oscillations within the brain: Phase-delayed inhibition provides a robust mechanism for creating a sharp synchrony filter

The widespread presence of synchronized neuronal oscillations within the brain suggests that a mechanism must exist that is capable of decoding such activity. Two realistic designs for such a decoder include: (1) a read-out neuron with a high spike threshold, or (2) a phase-delayed inhibition network motif. Despite requiring a more elaborate network architecture, phase-delayed inhibition has been observed in multiple systems, suggesting that it may provide inherent advantages over simply imposing a high spike threshold. In this work, we use a computational and mathematical approach to investigate the efficacy of the phase-delayed inhibition motif in detecting synchronized oscillations. We show that phase-delayed inhibition is capable of creating a synchrony detector with sharp synchrony filtering properties that depend critically on the time course of inputs. Additionally, we show that phase-delayed inhibition creates a synchrony filter that is far more robust than that created by a high spike threshold.

Switching mechanisms and bout times in a pair of reciprocally inhibitory neurons

Within the appropriate parameter regime, a deterministic model of a pair of mutually inhibitory neurons receiving excitatory driving currents exhibits bistability—each of the two stable states corresponds to one neuron being active and the other being quiescent. The presence of noise in the driving currents results in a system that randomly switches back and forth between these two states, causing alternating bouts of spiking activity. In this work, we examine the random bout durations of the two neurons and dependence on system parameters. We find that bout durations of each neuron are exponentially distributed, with changes in system parameters altering only the mean of the distribution. Synaptic inhibition independently controls the bout durations of the two neurons—the mean bout time of a neuron is a function of efferent (or outgoing) inhibition, and is independent of afferent (or incoming) inhibition. Furthermore, we find that the mean bout time of a neuron exhibits a critical dependence on the time course (rather than amplitude) of efferent inhibition—mean bout time of a neuron grows exponentially with the time course of efferent inhibition, and the growth rate of this exponential function depends only on the excitatory driving current to that neuron (and not on any other system parameters). We discuss the relevance of our results to the regulation of sleep-wake cycling by medullary and pontine structures within the brain.

Encoding with synchrony: Phase-delayed inhibition allows for reliable and specific stimulus detection

Synchronized oscillations are observed in a diverse array of neuronal systems, suggesting that synchrony represents a common mechanism used by the brain to encode and relay information. Coherent population activity can be deciphered by a decoder neuron with a high spike threshold or by a decoder using phase-delayed inhibition. These two mechanisms are fundamentally different - a high spike threshold detects a minimum number of synchronous input spikes (absolute synchrony), while phase-delayed inhibition requires a fixed fraction of incoming spikes to be synchronous (relative synchrony). We show that, in a system with noisy encoders where stimuli are encoded through synchrony, phase-delayed inhibition enables the creation of a decoder that can respond both reliably and specifically to a stimulus, while a high spike threshold does not.

Modeling the evolving oscillatory dynamics of the rat locus coeruleus through early infancy

The mammalian locus coeruleus (LC) is a brainstem structure that displays extensive interconnections with numerous brain regions, and in particular plays a prominent role in the regulation of sleep and arousal. Postnatal LC development is known to drastically alter sleep-wake switching behavior through early infancy, and, in rats, exerts its most significant influence from about postnatal day 8 to postnatal day 21 (P8-P21). Physiologically, several dramatic changes are seen in LC functionality through this time period. Prior to P8, LC neurons are extensively coupled via electrical gap junctions and chemical synapses, and the entire LC network exhibits synchronized ~0.3 Hz subthreshold oscillations and spiking. From P8 to P21, the network oscillation frequency rises up to ~3 Hz (at P21) while the amplitude of the network oscillation decreases. Beyond P21, synchronized network oscillations vanish and gap junction coupling is sparse or nonexistent. In this work, we develop a large-scale, biophysically realistic model of the rat LC and we use this model to examine the changing physiology of the LC through the pivotal P8-P21 developmental period. We find that progressive gap junction pruning is sufficient to account for all of the physiological changes observed from P8 to P21.

Encoding whisker deflection velocity within the rodent barrel cortex using phase-delayed inhibition

The primary sensory feature represented within the rodent barrel cortex is the velocity with which a whisker has been deflected. Whisker deflection velocity is encoded within the thalamus via population synchrony (higher deflection velocities entail greater synchrony among the corresponding thalamic population). Thalamic (TC) cells project to regular spiking (RS) cells within the barrel cortex, as well as to inhibitory cortical fast-spiking (FS) neurons, which in turn project to RS cells. Thus, TC spikes result in EPSPs followed, with a small time lag, by IPSPs within an RS cell, and hence the RS cell decodes TC population synchrony by employing a phase-delayed inhibition synchrony detection scheme. As whisker deflection velocity is increased, the probability that an RS cell spikes rises, while jitter in the timing of RS cell spikes remains constant. Furthermore, repeated whisker deflections with fixed velocity lead to system adaptation – TC →RS, TC →FS, and FS →RS synapses all weaken substantially, leading to a smaller probability of spiking of the RS cell and increased jitter in the timing of RS cell spikes. Interestingly, RS cell activity is better able to distinguish among different whisker deflection velocities after adaptation. In this work, we construct a biophysical model of a basic ‘building block’ of barrel cortex – the feedforward circuit consisting of TC cells, FS cells, and a single RS cell – and we examine the ability of the purely feedforward circuit to explain the experimental data on RS cell spiking probability, jitter, adaptation, and deflection velocity discrimination. Moreover, we study the contribution of the phase-delayed inhibition network structure to the ability of an RS cell to decode whisker deflection velocity encoded via TC population synchrony.

Deterministic stability regimes and noise-induced quasistable behavior in a pair of reciprocally inhibitory neurons

Reciprocal inhibition is a common motif exploited by neuronal networks; an intuitive and tractable way to examine the behaviors produced by reciprocal inhibition is to consider a pair of neurons that synaptically inhibit each other and receive constant or noisy excitatory driving currents. In this work, we examine reciprocal inhibition using two models (a voltage-based and a current-based integrate-and-fire model with instantaneous or temporally structured input), and we use analytic and computational tools to examine the bifurcations that occur and study the various possible monostable, bistable, and tristable regimes that can exist; we find that, depending on system parameters (and on choice of neuron model), there can exist up to 3 distinct monostable regimes (denoted M0, M1, M2), 3 distinct bistable regimes (denoted B, B1, B2), and a single tristable regime (denoted T). We also find that synaptic inhibition exerts independent control over the two neurons - inhibition from neuron 1 to neuron 2 governs the spiking behavior of neuron 2 but has no impact on the spiking behavior of neuron 1 (and vice versa). The excitatory driving current, however, does not exhibit this property - the excitatory current to neuron 1 affects the spiking behavior of both neurons 1 and 2 (as does the excitatory current to neuron 2). Furthermore, we develop a methodology to examine the behavior of the system when the excitatory driving currents are allowed to be noisy, and we investigate the relationship between the behavior of the noisy system with the stability regime of the corresponding deterministic system.