Macroscopic Models and Phase Resetting of Coupled Biological Oscillators

This thesis concerns the derivation and analysis of macroscopic mathematical models for coupled biological oscillators. Circadian rhythms, heart beats, and brain waves are all examples of biological rhythms formed through the aggregation of the rhythmic contributions of thousands of cellular oscillations. These systems evolve in an extremely high-dimensional phase space having at least as many degrees of freedom as the number of oscillators. This high-dimensionality often contrasts with the low-dimensional behavior observed on the collective or macroscopic scale. Moreover, the macroscopic dynamics are often of greater interest in biological applications. Therefore, it is imperative that mathematical techniques are developed to extract low-dimensional models for the macroscopic behavior of these systems. One such mathematical technique is the Ott-Antonsen ansatz. The Ott-Antonsen ansatz may be applied to high-dimensional systems of heterogeneous coupled oscillators to derive an exact low-dimensional description of the system in terms of macroscopic variables. We apply the Ott-Antonsen technique to determine the sensitivity of collective oscillations to perturbations with applications to neuroscience. The power of the Ott-Antonsen technique comes at the expense of several limitations which could limit its applicability to biological systems. To address this we compare the Ott-Antonsen ansatz with experimental measurements of circadian rhythms and numerical simulations of several other biological systems. This analysis reveals that a key assumption of the Ott-Antonsen approach is violated in these systems. However, we discover a low-dimensional structure in these data sets and characterize its emergence through a simple argument depending only on general phase-locking behavior in coupled oscillator systems. We further demonstrate the structure's emergence in networks of noisy heterogeneous oscillators with complex network connectivity. We show how this structure may be applied as an ansatz to derive low-dimensional macroscopic models for oscillator population activity. This approach allows for the incorporation of cellular-level experimental data into the macroscopic model whose parameters and variables can then be directly associated with tissue- or organism-level properties, thereby elucidating the core properties driving the collective behavior of the system. We first apply our ansatz to study the impact of light on the mammalian circadian system. To begin we derive a low-dimensional macroscopic model for the core circadian clock in mammals. Significantly, the variables and parameters in our model have physiological interpretations and may be compared with experimental results. We focus on the effect of four key factors which help shape the mammalian phase response to light: heterogeneity in the population of oscillators, the structure of the typical light phase response curve, the fraction of oscillators which receive direct light input and changes in the coupling strengths associated with seasonal day-lengths. We find these factors can explain several experimental results and provide insight into the processing of light information in the mammalian circadian system. In a second application of our ansatz we derive a pair of low-dimensional models for human circadian rhythms. We fit the model parameters to measurements of light sensitivity in human subjects, and validate these parameter fits with three additional data sets. We compare our model predictions with those made by previous phenomenological models for human circadian rhythms. We find our models make new predictions concerning the amplitude dynamics of the human circadian clock and the light entrainment properties of the clock. These results could have applications to the development of light-based therapies for circadian disorders.PHDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138766/1/khannay_1.pd

Role of water in physics of blood and cerebrospinal fluid

Known physical mechanisms of temperature dependence anomalies of water properties were used to explain the regularities in temperature dependence (TDs) of dynamic, electrical and optical characteristics of biological systems. The dynamics of hydrogen bonds in bulk and hydrated water affected the activation energies TDs of ion currents of voltage-dependent channels that regulate signaling and trophic bonds in the neuropil of the cortical parenchyma. The physics of minimizing the TD of the isobaric heat capacity of water made it possible to explain the stabilization and functional optimization of the thermodynamics of eyeball fluids at 34.5 C and the human brain during sleep at 36.5 C. At these temperatures, the thermoreceptors of the cornea and the cells of the ganglionic layer of the retina, through connections with the suprachiasmatic nucleus and the pineal gland, switch the circadian rhythm from daytime to nighttime. The phylogenesis of the circadian rhythm was reflected in the dependence of the duration of the nighttime sleep of mammals on the diameter of the eyeball and the mass of the pineal gland. The activity of all the nerves of the eyeball led to the division of the nocturnal brain metabolism into NREM and REM phases. These phases correspond to two modes of the glymphatic system - electrochemical and dynamic. The first is responsible for the relaxation processes of synaptic plasticity and chemical neutralization of toxins with the participation of water and melatonin. Rapid eye movement and an increase in cerebral blood flow in the second mode increase water exchange in the parenchyma and flush out toxins into the venous system. Electrophysics of clearance and conductivity of ionic and water channels of membranes of blood vessels and astrocytes modulate oscillations of polarization potentials of water dipole domains in parietal plasma layers of arterioles and capillaries

Dynamics and precursor signs for phase transitions in neural systems

This thesis investigates neural state transitions associated with sleep, seizure and anaesthesia. The aim is to address the question: How does a brain traverse the critical threshold between distinct cortical states, both healthy and pathological? Specifically we are interested in sub-threshold neural behaviour immediately prior to state transition. We use theoretical neural modelling (single spiking neurons, a network of these, and a mean-field continuum limit) and in vitro experiments to address this question. Dynamically realistic equations of motion for thalamic relay neuron, reticular nuclei, cortical pyramidal and cortical interneuron in different vigilance states are developed, based on the Izhikevich spiking neuron model. A network of cortical neurons is assembled to examine the behaviour of the gamma-producing cortical network and its transition to lower frequencies due to effect of anaesthesia. Then a three-neuron model for the thalamocortical loop for sleep spindles is presented. Numerical simulations of these networks confirms spiking consistent with reported in vivo measurement results, and provides supporting evidence for precursor indicators of imminent phase transition due to occurrence of individual spindles. To complement the spiking neuron networks, we study the Wilson–Cowan neural mass equations describing homogeneous cortical columns and a 1D spatial cluster of such columns. The abstract representation of cortical tissue by a pair of coupled integro-differential equations permits thorough linear stability, phase plane and bifurcation analyses. This model shows a rich set of spatial and temporal bifurcations marking the boundary to state transitions: saddle-node, Hopf, Turing, and mixed Hopf–Turing. Close to state transition, white-noise-induced subthreshold fluctuations show clear signs of critical slowing down with prolongation and strengthening of autocorrelations, both in time and space, irrespective of bifurcation type. Attempts at in vitro capture of these predicted leading indicators form the last part of the thesis. We recorded local field potentials (LFPs) from cortical and hippocampal slices of mouse brain. State transition is marked by the emergence and cessation of spontaneous seizure-like events (SLEs) induced by bathing the slices in an artificial cerebral spinal fluid containing no magnesium ions. Phase-plane analysis of the LFP time-series suggests that distinct bifurcation classes can be responsible for state change to seizure. Increased variance and growth of spectral power at low frequencies (f < 15 Hz) was observed in LFP recordings prior to initiation of some SLEs. In addition we demonstrated prolongation of electrically evoked potentials in cortical tissue, while forwarding the slice to a seizing regime. The results offer the possibility of capturing leading temporal indicators prior to seizure generation, with potential consequences for understanding epileptogenesis. Guided by dynamical systems theory this thesis captures evidence for precursor signs of phase transitions in neural systems using mathematical and computer-based modelling as well as in vitro experiments

Mechanistic insights into neuronal oscillatory activity in the dopamine-intact and dopamine-depleted primary motor cortex

In Parkinson’s disease (PD) the loss of the neurotransmitter dopamine (DA) results in abnormal oscillations of the cortico-basal ganglia network, the emergence of which correlate with symptoms. Increased oscillatory power in the primary motor cortex (M1) is reduced by dopamine replacement therapy and by targeted stimulation, suggesting that M1 plays an important role in the pathology of PD. In this study we have investigated, using pharmacology, the mechanisms by which oscillatory activity in rat M1 is generated and determined the power changes associated with DA depletion and DA receptor modulation. Extracellular local field potential recordings were made in brain slices of M1 which were prepared using a modified protocol to improve viability. Co-application of carbachol (5 μM) and kainic acid (100 nM) elicited simultaneous theta (4-8 Hz) and gamma (30-40 Hz) oscillations in layer V of M1. These oscillations displayed phase-amplitude coupling; the first report of such findings in vitro. These oscillations were found to be pharmacologically distinct with theta oscillations generated by intrinsic non-synaptic mechanisms while gamma oscillations required contributing excitatory and inhibitory networks. Following successful unilateral lesions using 6-hydroxydopamine (6-OHDA), as determined by the adjusting step test, DA-depleted (ipsilateral) and DA-intact (contralateral) slices were obtained. Although no difference in the oscillatory profile of M1 ipsilateral, contralateral or age-matched control (AMC) slices was found, bath application of DA reduced gamma power only in the ipsilateral slices and amphetamine only decreased gamma power in contralateral slices. Furthermore, D2-like receptor activation consistently increased both theta and gamma power in contralateral and AMC slices, while only theta power was increased in ipsilateral slices. Overall, these data suggest that DA, through action at multiple sites, differentially modulates the power of both theta and gamma oscillations in M1. Using the 6-OHDA model, the oscillatory activity of M1 in vivo was investigated. Successful lesions were determined by using the rotometer, the locomotor activity and the adjusting stepping tests at 2-4 weeks post-surgery. Further testing at 22 weeks post-surgery indicated the long-term stability of the lesions. Using depth electrode and EEG recordings, oscillatory activity in the 2-10 Hz range was found in the ipsilateral and contralateral hemispheres of both lesioned and sham animals. However, only in the ipsilateral hemisphere of DA-depleted animals did we detect a 30-40 Hz oscillatory peak, which was localised to layer V of M1. In EEG recordings this led to a significant increase in the interhemispheric ratio. Using depth electrode recordings, the ipsilateral 30-40 Hz oscillation (but not 2-10 Hz oscillation) was reduced by the administration of L-DOPA (6 mg/kg) with a reduction in interhemispheric ratio. However, administration of zolpidem (0.3 mg/kg), which previously reduced abnormal beta oscillatory activity in vivo and in vitro resulting in the rebalancing of interhemispheric beta power (Hall et al., 2014; Prokic et al., 2015), was without effect. Overall, these studies demonstrate that M1 alone can generate multiple, pharmacologically distinct, but interacting oscillations, which contribute to pathological activity in the DA-depleted state

Theoretical and experimental investigation of anaesthetic effects in the brain

The main motivation of this study is to develop a better understanding of anaesthetic drug effects on brain dynamics including the paradoxical enhancement of seizure activity by some anaesthetic drugs. This thesis investigates two mean-field descriptions for the effect of general anaesthetic agents on brain activity: the extended Waikato cortical model (WM) and the Hindriks and van Putten (HvP) thalamocortical model. In the standard Waikato model, the population-average neuron voltage is determined by incoming activity at both electrical (gap-junction) and chemical synapses, the latter mediated by AMPA (excitatory) and GABAA (inhibitory) receptors. Here we extend the standard WM by including NMDA (excitatory) and GABAB (inhibitory) synapses. GABAergic anaesthetics, such as propofol, boost cortical inhibition by prolonging the tail of the unitary IPSP (inhibitory postsynaptic potential) at GABAA receptors, while increasing the synaptic gain at the slower-acting GABAB receptors. Dissociative anaesthetics act on NMDA receptors to give a voltage-dependent alteration of excitatory synaptic gain. We find that increasing GABAB or NMDA effect can alter the spatiotemporal dynamics of the standard WM, tending to suppress spatial (Turing) patterns in favour of temporal (Hopf) oscillations. The extended WM predicts increased susceptibility to seizure when GABAB effect is increased, particularly if the GABAergic agent reduces gap-junction diffusion. We tested these WM predictions with two biological experiments. We found that potentiation of GABAB receptors in slices of mouse cortical tissue tended to enhance seizure-like activity. However, our in vivo investigation of the effect of closure of gap junctions did not reveal any seizure patterns in mouse EEG signals. In the second part of this thesis, we present a detailed analysis of the HvP thalamocortical mean-field model for propofol anaesthesia. While we were able to confirm the Hindriks and van Putten predictions of increases in delta and alpha power at low levels of anaesthetic sedation, we find that for deeper anaesthetic effect, the model jumps from the low-firing state to an extremely high-firing stable state (~250 spikes/s), and remains stuck there even at GABAA prolongations as high as 300% which would be expected to induce full comatose suppression of all firing activity. To overcome this pathological behaviour, we tested two possible modifications: first, eliminating the population-dependent anaesthetic sensitivity (efficacy) of the HvP model; second, incorporating reversal potentials and tuning the excitatory sigmoid parameters defining the mapping from voltage to firing rate. The first modification removes the pathological state, but predicts de-creasing alpha and delta power as drug concentration increases. The second modification predicts induction-emergence hysteresis (drug concentration is higher at induction than at emergence), but the alpha rhythm is lost, being replaced by a dominant delta-band oscillation

29th Annual Computational Neuroscience Meeting: CNS*2020

Meeting abstracts This publication was funded by OCNS. The Supplement Editors declare that they have no competing interests. Virtual | 18-22 July 202

An organic memristor as the building block for bio-inspired adaptive networks

This thesis reports the research path I followed during my PhD course, which i followed from January 2008 to December 2010 working at the University of Parma, in the Laboratory of Molecular Nanotechnologies, under the supervision of Prof. Marco P. Fontana and Dr. Victor Erokhin, within the framework of an interdisciplinary, international research project called BION – Biologically inspired Organized Networks. The keystone of my research is an organic memristor, a two terminal polymeric electronic device recently developed in our research group at the university of Parma. A memristor is a passive electronic device in which the electrical resistance depends on the electrical charge that has passed through it, and hence is adjustable by applying the appropriate electric potential or sequence of potentials. As of the beginning of my PhD, the device was in its early characterization stages, but it was already clear that it could be used to mimic the kind of plasticity found in synapses within neuronal circuits. In the thesis I show some further characterization work, used for engineering the device to maximize its more useful characteristics and to deepen our understanding of the functioning of the device, as well as the work done on. The knowledge of computational neuroscience acquired during this side project has proved very useful to better coordinate research in the material science side of the project, whose ultimate goal is the realization of a new, highly innovative technology for the production of functional molecular assemblies that can perform advanced tasks of information processing, involving learning and decision making, and that can be tailored down to the nanoscale.Questa tesi riporta il percorso di ricerca seguito durante il mio dottorato di ricerca, che ho svolto da gennaio 2008 a dicembre 2010 lavorando nel Laboratorio di Nanotecnologie Molecolari, presso l'Università di Parma, , sotto la supervisione del Prof. Marco P. Fontana e del Dott. Victor Erokhin, nel quadro di un approccio interdisciplinare, progetto di ricerca internazionale denominato BION - Biologically ispired Organized Networks . La chiave di svolta della mia ricerca è un memristor organico, un dispositivo a due terminali elettronici polimerici recentemente messo a punto nel nostro gruppo di ricerca presso l'università di Parma. Un memristor è un dispositivo elettronico passivo in cui la resistenza elettrica dipende dalla carica elettrica che è passata attraverso di essa, e quindi è regolabile applicando il potenziale elettrico appropriato o una sequenza di potenziali. A partire dall'inizio del mio dottorato di ricerca, il dispositivo è stato nelle sue fasi di caratterizzazione iniziale, ma era già chiaro che poteva essere usata per simulare il tipo di plasticità trovato in sinapsi all'interno di circuiti neuronali. Nella tesi ho mostrato un ulteriore lavoro di caratterizzazione, utilizzato per l'ingegneria del dispositivo al fine di massimizzare le sue caratteristiche più utili e di approfondire la nostra comprensione del funzionamento del dispositivo, così come il lavoro svolto. La conoscenza delle neuroscienze computazionali acquisite nel corso di questo progetto parallelo si è rivelato molto utile per meglio coordinare la ricerca per quanto riguarda il materiale scientifico del progetto, il cui scopo ultimo è la realizzazione di una nuova tecnologia altamente innovativa per la produzione di composti molecolari funzionali in grado di eseguire attività avanzate di elaborazione delle informazioni, che coinvolgano l'apprendimento e il processo decisionale, e che può essere adattata fino alla scala nanometrica