Exploring temporal computation in neuronal systems

This thesis presents two approaches to identifying computational properties of networks of neurons. The first of these involves a bottom-up approach through detailed modelling of neuronal properties, while the second is a top-down approach using principal component analysis that quantifies the behaviour of neurons in complex networks from measurements. An object-oriented modelling tool has been developed that is fast, flexible, and easy to use. A graphical user interface allows the user to manipulate neurons, synapses, and currents visually on the screen during prototyping. Subsequently, a systematic study of the model can be processed in batch mode, for example to tune it to a particular behaviour. Small invertebrate neuronal circuits have been considered where the neuronal outputs can be related to the behaviour of the animal. The fundamental problem faced by experimental neurobiologists is that only one state variable per neuron is readily accessible, i.e. the membrane potential at the cell body. A neuron contains a vast number of state variables, but these are generally all hidden. The modelling tool enables one to "record" from hidden state variables and to manipulate inaccessible parameters of the real neurons. The tool has been evaluated through an investigation involving a leech heart model. Significant findings include non-spiking oscillations, and the modelling has suggested further experimental work involving the real system. The modelling tool provided close to real-time performance in this application which indicates its potential for its interactive use in an experimental environment, including dynamic voltage-clamp. The top-down approach uses principal component analysis to quantify a trace of neuronal activity during a time interval. During this interval, the feedback loops within the neuron and through the neuronal network will affect the output of the neuron. Thus, the resulting measure of the neuronal output will indirectly include the states of "hidden" compartments away from the cell soma and other inaccessible state variables, like channel states. Although the technique offer no promise for tracing these hidden state variables, it will enable us to include them in quantifying the outputs of a neuron. Further, the technique serves as an "objective critic" that display the largest sources of variance over the data set. Therefore, one avoids testing successively and explicitly through a large set of possible features. This also makes the measure low-dimensional and easy to analyse further. Application of the Karhunen-Loeve transform to the crayfish swimmeret showed that the principal components represented features like spike count, burst width, burst concentration, and burst latency. The burst latency proved to be significantly modulated. Principal component analysis was also performed on the membrane potential after having removed the action potentials with a low pass filter. The membrane potential deviations did not correlate with those of the spikes from the same neuron. This demonstrates the point that the membrane potential at the cell body does not solely determine the spiking pattern, but other (unobservable) state variables influence the spiking dynamics. Recently developed imaging techniques show possibilities in terms of measuring the spatial distribution of the membrane potential and ion concentrations throughout a cell, as well as the temporal interaction between these state variables. These imaging techniques are of potential value for validating theoretical models of a more complex kind for the study of which the object-oriented modelling tool could be readily applied. This work has shown that the Karhunen-Loeve transform can be used to quantify the relative coupling strength between two outputs. The coupling strength is estimated at the level of behaviour and relative to normal background activity in the system. This compares to the absolute estimate that at the level of individual synapses measures the coupling strength between two cells. The techniques above enables the effective coupling between two cells to be measured, where the coupling may occur through several pathways and through several cells. These results suggest that the long range intersegmental coupling is not much weaker than short range intrasegmental coupling and that the coupling performs phase locking only.