Oscillators and relaxation phenomena in Pleistocene climate theory

Ice sheets appeared in the northern hemisphere around 3 million years ago and glacial-interglacial cycles have paced Earth's climate since then. Superimposed on these long glacial cycles comes an intricate pattern of millennial and sub-millennial variability, including Dansgaard-Oeschger and Heinrich events. There are numerous theories about theses oscillations. Here, we review a number of them in order to draw a parallel between climatic concepts and dynamical system concepts, including, in particular, the relaxation oscillator, excitability, slow-fast dynamics and homoclinic orbits. Namely, almost all theories of ice ages reviewed here feature a phenomenon of synchronisation between internal climate dynamics and the astronomical forcing. However, these theories differ in their bifurcation structure and this has an effect on the way the ice age phenomenon could grow 3 million years ago. All theories on rapid events reviewed here rely on the concept of a limit cycle in the ocean circulation, which may be excited by changes in the surface freshwater surface balance. The article also reviews basic effects of stochastic fluctuations on these models, including the phenomenon of phase dispersion, shortening of the limit cycle and stochastic resonance. It concludes with a more personal statement about the potential for inference with simple stochastic dynamical systems in palaeoclimate science. Keywords: palaeoclimates, dynamical systems, limit cycle, ice ages, Dansgaard-Oeschger eventsComment: Published in the Transactions of the Philosophical Transactions of the Royal Society (Series A, Physical Mathematical and Engineering Sciences), as a contribution to the Proceedings of the workshop on Stochastic Methods in Climate Modelling, Newton Institute (23-27 August). Philosophical Transactions of the Royal Society (Series A, Physical Mathematical and Engineering Sciences), vol. 370, pp. xx-xx (2012); Source codes available on request to author and on http://www.uclouvain.be/ito

Neurosystems: brain rhythms and cognitive processing

Neuronal rhythms are ubiquitous features of brain dynamics, and are highly correlated with cognitive processing. However, the relationship between the physiological mechanisms producing these rhythms and the functions associated with the rhythms remains mysterious. This article investigates the contributions of rhythms to basic cognitive computations (such as filtering signals by coherence and/or frequency) and to major cognitive functions (such as attention and multi-modal coordination). We offer support to the premise that the physiology underlying brain rhythms plays an essential role in how these rhythms facilitate some cognitive operations.098352 - Wellcome Trust; 5R01NS067199 - NINDS NIH HH

A multiscale model for collagen alignment in wound healing

It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this process. We consider fibroblasts as discrete units moving within an extracellular matrix of collagen and fibrin modelled as continua. Our model includes flux induced alignment of collagen by fibroblasts, and contact guidance of fibroblasts by collagen fibres. We can use the model to predict the effects of certain manipulations, such as varying fibroblast speed, or placing an aligned piece of tissue in the wound. We also simulate experiments which alter the TGF-β concentrations in a healing dermal wound and use the model to offer an explanation of the observed influence of this growth factor on scarring

Cancer modelling: Getting to the heart of the problem

Paradoxically, improvements in healthcare that have enhanced the life expectancy of humans in the Western world have, indirectly, increased the prevalence of certain types of cancer such as prostate and breast. It remains unclear whether this phenomenon should be attributed to the ageing process itself or the cumulative effect of prolonged exposure to harmful environmental stimuli such as ultraviolet light, radiation and carcinogens (Franks and Teich, 1988). Equally, there is also compelling evidence that certain genetic abnormalities can predispose individuals to specific cancers (Ilyas et al., 1999). The variety of factors that have been implicated in the development of solid tumours stems, to a large extent, from the fact that ‘cancer’ is a generic term, often used to characterize a series of disorders that share common features. At this generic level of description, cancer may be viewed as a cellular disease in which controls that usually regulate growth and maintain homeostasis are disrupted. Cancer is typically initiated by genetic mutations that lead to enhanced mitosis of a cell lineage and the formation of an avascular tumour. Since it receives nutrients by diffusion from the surrounding tissue, the size of an avascular tumour is limited to several millimeters in diameter. Further growth relies on the tumour acquiring the ability to stimulate the ingrowth of a new, circulating blood supply from the host vasculature via a process termed angiogenesis (Folkman, 1974). Once vascularised, the tumour has access to a vast nutrient source and rapid growth ensues. Further, tumour fragments that break away from the primary tumour, on entering the vasculature, may be transported to other organs in which they may establish secondary tumours or metastases that further compromise the host. Invasion is another key feature of solid tumours whereby contact with the tissue stimulates the production of enzymes that digest the tissue, liberating space into which the tumour cells migrate. Thus, cancer is a complex, multiscale process. The spatial scales of interest range from the subcellular level, to the cellular and macroscopic (or tissue) levels while the timescales may vary from seconds (or less) for signal transduction pathways to months for tumour doubling times The variety of phenomena involved, the range of spatial and temporal scales over which they act and the complex way in which they are inter-related mean that the development of realistic theoretical models of solid tumour growth is extremely challenging. While there is now a large literature focused on modelling solid tumour growth (for a review, see, for example, Preziosi, 2003), existing models typically focus on a single spatial scale and, as a result, are unable to address the fundamental problem of how phenomena at different scales are coupled or to combine, in a systematic manner, data from the various scales. In this article, a theoretical framework will be presented that is capable of integrating a hierarchy of processes occurring at different scales into a detailed model of solid tumour growth (Alarcon et al., 2004). The model is formulated as a hybrid cellular automaton and contains interlinked elements that describe processes at each spatial scale: progress through the cell cycle and the production of proteins that stimulate angiogenesis are accounted for at the subcellular level; cell-cell interactions are treated at the cellular level; and, at the tissue scale, attention focuses on the vascular network whose structure adapts in response to blood flow and angiogenic factors produced at the subcellular level. Further coupling between the different spatial scales arises from the transport of blood-borne oxygen into the tissue and its uptake at the cellular level. Model simulations will be presented to illustrate the effect that spatial heterogeneity induced by blood flow through the vascular network has on the tumour’s growth dynamics and explain how the model may be used to compare the efficacy of different anti-cancer treatment protocols

Flexible resonance in prefrontal networks with strong feedback inhibition

[EN] Oscillations are ubiquitous features of brain dynamics that undergo task-related changes in synchrony, power, and frequency. The impact of those changes on target networks is poorly understood. In this work, we used a biophysically detailed model of prefrontal cortex (PFC) to explore the effects of varying the spike rate, synchrony, and waveform of strong oscillatory inputs on the behavior of cortical networks driven by them. Interacting populations of excitatory and inhibitory neurons with strong feedback inhibition are inhibition-based network oscillators that exhibit resonance (i.e., larger responses to preferred input frequencies). We quantified network responses in terms of mean firing rates and the population frequency of network oscillation; and characterized their behavior in terms of the natural response to asynchronous input and the resonant response to oscillatory inputs. We show that strong feedback inhibition causes the PFC to generate internal (natural) oscillations in the beta/gamma frequency range (>15 Hz) and to maximize principal cell spiking in response to external oscillations at slightly higher frequencies. Importantly, we found that the fastest oscillation frequency that can be relayed by the network maximizes local inhibition and is equal to a frequency even higher than that which maximizes the firing rate of excitatory cells; we call this phenomenon population frequency resonance. This form of resonance is shown to determine the optimal driving frequency for suppressing responses to asynchronous activity. Lastly, we demonstrate that the natural and resonant frequencies can be tuned by changes in neuronal excitability, the duration of feedback inhibition, and dynamic properties of the input. Our results predict that PFC networks are tuned for generating and selectively responding to beta- and gamma-rhythmic signals due to the natural and resonant properties of inhibition-based oscillators. They also suggest strategies for optimizing transcranial stimulation and using oscillatory networks in neuromorphic engineering.This material is based upon research supported by the U. S. Army Research Office under award number ARO W911NF-12-R-0012-02 to N. K., the U. S. Office of Naval Research under award number ONR MURI N00014-16-1-2832 to M. H., and the National Science Foundation under award number NSF DMS-1042134 (Cognitive Rhythms Collaborative: A Discovery Network) to N. K. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Sherfey, JS.; Ardid-Ramírez, JS.; Hass, J.; Hasselmo, ME.; Kopell, NJ. (2018). Flexible resonance in prefrontal networks with strong feedback inhibition. 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Pleistocene glacial variability as a chaotic response to obliquity forcing

The mid-Pleistocene Transition from 40 ky to ~100 ky glacial cycles is generally characterized as a singular transition attributable to scouring of continental regolith or a long-term decrease in atmospheric CO<sub>2</sub> concentrations. Here an alternative hypothesis is suggested, that Pleistocene glacial variability is chaotic and that transitions from 40 ky to ~100 ky modes of variability occur spontaneously. This alternate view is consistent with the presence of ~80 ky glacial cycles during the early Pleistocene and the lack of evidence for a change in climate forcing during the mid-Pleistocene. A simple model illustrates this chaotic scenario. When forced at a 40 ky period the model chaotically transitions between small 40 ky glacial cycles and larger 80 and 120 ky cycles which, on average, give the ~100 ky variability

The Role of Plasma Membrane ATPase Pumps in the Regulation of Rhythmic Activity in Electrically Excitable Cells

Membrane bound ion pumps have long been studied in a housekeeping role, and it is well known that they play a major part in creating the ionic gradients which determine the electrical excitability in a cell. Recent work has begun to highlight other, more direct roles for ion pumps in rhythm generation and information processing. As many pumps obtain energy for active ion transport from adenosine triphosphate (ATP) hydrolysis, they can exchange ions in an electrically asymmetric manner, generating an outward current, which along with ion channel currents, drives the membrane potential of the cell. Membrane potential is a major determining characteristic for how information is transferred between neurons, and so in persistently active excitable cells, pumps can provide a considerable contribution to neuron dynamics. Specialized networks of neurons and non-neural cells which drive rhythmic behaviors such as breathing and locomotion, must robustly produce useful patterns for the animal under dynamic behavioral goals in a highly variable environment. Here we will focus on two well-studied classes of ATPase pumps (the plasma membrane calcium ATPase pump (PMCA) and the sodium-potassium ATPase pump (Na+/K+ pump)) and investigate the role of these pumps in two rhythm generating biological subsystems with a combination of modeling and experimental approaches. In a model of a leech heartbeat central pattern generator, we demonstrate how the neuromodulator myomodulin can regulate the temporal properties of rhythm generation through effects on the hyperpolarization-activated current and the Na+/K+ pump current, and discuss the benefits of modulators which target multiple currents. With this model, we also show how synaptic inhibition can support a functional pattern when pump current is downregulated. Then, in a model of interstitial cells of Cajal (ICC) in the muscular syncytium of the intestinal walls, we demonstrate that due to the importance of complex intracellular calcium oscillations in the generation of ICC rhythms, the PMCA pump can play a major role in regulating the temporal properties of rhythm generation. We discuss rhythm generation mechanisms in both systems and predict parameter domains of multistability which correspond to both functional and pathological states of rhythm generation

Computational reconstruction of pacemaking and intrinsic electroresponsiveness in cerebellar Golgi cells.

The Golgi cells have been recently shown to beat regularly in vitro (Forti et al., 2006. J. Physiol. 574, 711-729). Four main currents were shown to be involved, namely a persistent sodium current (I(Na-p)), an h current (I(h)), an SK-type calcium-dependent potassium current (I(K-AHP)), and a slow M-like potassium current (I(K-slow)). These ionic currents could take part, together with others, also to different aspects of neuronal excitability like responses to depolarizing and hyperpolarizing current injection. However, the ionic mechanisms and their interactions remained largely hypothetical. In this work, we have investigated the mechanisms of Golgi cell excitability by developing a computational model. The model predicts that pacemaking is sustained by subthreshold oscillations tightly coupled to spikes. I(Na-p) and I(K-slow) emerged as the critical determinants of oscillations. I(h) also played a role by setting the oscillatory mechanism into the appropriate membrane potential range. I(K-AHP), though taking part to the oscillation, appeared primarily involved in regulating the ISI following spikes. The combination with other currents, in particular a resurgent sodium current (I(Na-r)) and an A-current (I(K-A)), allowed a precise regulation of response frequency and delay. These results provide a coherent reconstruction of the ionic mechanisms determining Golgi cell intrinsic electroresponsiveness and suggests important implications for cerebellar signal processing, which will be fully developed in a companion paper (Solinas et al., 2008. Front. Neurosci. 2:4)