Neurons are a specialised part of the extremely complex structure of the nervous system. They generate electrical signals in response to chemical and other inputs and transmit them to other cells. Over the past hundred years experimental research has accumulated an enormous amount of knowledge about the structure and function of an individual nerve cell as well as neural networks. However, there are still fundamental questions that remain unanswered. Theoretical analysis and computational modelling of neural systems are important tools that help to characterise what neurons do and determine the ways in which they function. It has recently become increasingly clear that calcium plays an important role in controlling a great variety of neuronal processes. Calcium channels activated by voltage (voltage-gated channels) in different neuronal cell types are believed, for example, to regulate components of learning and memory and to be involved in coincidence detection mechanisms. The overall aim of the project is to develop a biophysically realistic and computationally inexpensive model of a nerve cell for better understanding the interaction between electrical and chemical signalling (membrane voltage and calcium concentration). This interaction plays important functional roles in neuronal excitability and synaptic integration and plasticity. Experimental studies demonstrate that calcium channels open in response to membrane depolarisation and in turn cause further depolarisation by generating calcium-dependent action potentials. At the same time the propagation of action potential produces an increase in calcium concentration and generates rich patterns in both space and time, from widespread calcium influx in dendrites to heterogeneous calcium transients in axons. Moreover, the properties of the same voltage-gated calcium channels can be different in somatic and dendritic membranes with substantial variability in channel density. The major objectives of the research are i) to explore the implications of the heterogeneous distribution of calcium channels on amplification or boosting of distal synaptic inputs, ii) to investigate the role of calcium in the induction and maintenance of synaptic plasticity, and iii) to study how calcium waves can generate recently-discovered graded persistent activity in single neurons that may underly working memory. The proposed methodology draws from a number of established principles in different scientific disciplines, predominantly those of nonlinear dynamics, numerical analysis of deterministic and stochastic systems, biophysics, computational neuroscience and molecular signalling. A combination of theoretical analysis, numerical simulations and experimental verification will be used to address important issues of calcium signals underlying vital brain functions. Showing that the persistence of activity in a single neuron can be observed in the presence of calcium may reveal that as a computational system, the single neuron is a far more powerful unit that was previously assumed. Calcium dynamics could thus be the physiological basis for a single-neuron mechanism sub-serving working memory. Also, an understanding of the mechanism of calcium regulation in neurons during brain damage is crucially important, and this might provide the ground for a specific future application of the proposed work. As experiments show, ischemia increases calcium concentration in nerve cells, particularly in their dendrites and synaptic terminals. Due to this large calcium increase, dendritic tissue is very susceptible to damage. This is an area where further research can potentially generate explosive rates of development.

Technical Abstract:
In recent years it has become increasingly clear that calcium plays a vital role in controlling a great variety of neuronal processes. For example, calcium ions are believed to regulate components of learning and memory and to be involved in coincidence detection mechanisms. Neurons have an elaborate endoplasmic reticulum (a calcium source) that extends throughout the cell and can be considered as a neuron-within-a neuron, in that together with the plasma membrane it creates a binary membrane system and plays integrative roles between different parts of neurons. Elevation in calcium can be highly localised within compartments such as spines or the terminals, or it can spread throughout neurons as global calcium waves. Many of the current mathematical approaches used in systems neuroscience are built upon a core set of assumptions that exclude the notion of the neuron as a spatially extended object with nonlinear processing capability. Here we propose to integrate calcium and electrical signalling into a new theoretical framework that will address the important issues of potential-evoked calcium signals underlying neuronal functions. The proposed methodology is based on a mixture of well established techniques from different disciplines, predominantly those of biophysics, computational neuroscience, cell signalling, nonlinear dynamics, and numerical analysis of deterministic and stochastic systems. The major objectives of the proposed research are i) to explore the significance and implications of the heterogeneous distribution of calcium channels on amplification or boosting of distal synaptic inputs, ii) to investigate the role of calcium in synaptic plasticity, and iii) to study how calcium dynamics can generate graded persistent activity that is believed to underly working memory.

Potential Impact:
An important step toward gaining insight into the workings of the human brain involves understanding the role of an individual neuron and the computations it performs within the network. Our work will help to establish a theoretical underpinning for a new theory of information processing in single cells with branched dendritic structures. By considering the combined role of space, heterogeneity and noise in generating the variety of observed calcium signals we will be able to explore the mechanisms which allow simple ions such as calcium to play an important role in cell excitation. This study will encourage a transfer of ideas between the research areas of dynamical systems, computer science, cell neurophysiology and molecular biology. The involvement of experimental collaborators (M. Bootman and N. Emptage) in this project will initiate a link between UK-based theoretical neuroscientists and two of the leading experimental laboratories for cellular signalling. We intend to raise the international awareness of the benefits of this project at conferences covering both theoretical and experimental biology including the Annual Society for Mathematical Biology meeting, the Federation of European Neuroscience Societies conference, British Neuroscience Association events and Society for Industrial and Applied Mathematics conference on Life Sciences and Dynamical Systems. Workshops and training activities will also be planned to advertise and promote this research. Papers will be submitted to multi-disciplinary journals such as the PLoS J. of Computational Biology, the J. of Computational Neuroscience, Neural Computation, J. of Neuroscience, J. of Mathematical Biology, Physica D and Biophysical Journal. A professional website will be established for the free dissemination of code (including a graphical user interface) and results. This website will also include sections providing lay summaries of the work for the general public. During the project, the 'Warwick iCast' team which specialises in developing internet video for the promotion of the University's research will be engaged to communicate our scientific activities. In addition, we intend to increase awareness of our project through active participation in the University's regular Open Days. We will examine the possibilities of presenting elements of our research to a school level audience. The interdisciplinary nature of our work can generate a broad interest given the great variety of perspectives and aspirations of young minds that will form the future students of UK academic establishments.