Cortical network models to understand differential input response properties during active and silent states

Mathematical modelling of neural networks will be used to understand the neuronal computational principles underlying input response properties in neocortex. Methods from dynamical systems theory, including bifurcation analysis, will be applied to analyse the neural field models developed.

The mammalian neocortex is involved in all aspects of brain function, including sensory processing, motor control, decision making and language. Different cortical network states are associated with different types of behaviour. For example, in mice, synchronised large amplitude slow oscillations of cortical activity during quiet wakefulness give way to higher frequency low amplitude fluctuations when the animal is exploring its environment with its whiskers. Spontaneous transitions between synchronous periods of high activity (a so-called Up state) and low activity (Down state) most frequently occur during slow-wave sleep, where they are believed to be important for memory consolidation in mammals. Sensory cortical areas respond to inputs in different ways depending on whether the network is in an Up state or a Down state, and whether inputs arrive via sensory stimulation (primary inputs) or from other cortical regions (higher order inputs). The governing principles behind these important differences remains to be established. It is an opportune time to achieve this with mathematical modelling, which will shed light on the functional role of Up and Down states.

The project will develop a dynamical model in the neural field framework, which gives a spatially averaged description of neural activity across multiple cortical columns (several mm of cortex). This provides the ideal framework in which to probe differences between primary sensory inputs, which may be local due to receptive field properties, and higher-order inputs. It is hypothesised that during Down states cortical areas are generally responsive to inputs. However, during Up states sensory areas are differentially response to primary and secondary inputs. The modelling work will be done in close collaboration with experiments investigating input responses during slow-wave sleep, activating whiskers for primary inputs and using optogenetic stimulation of cortico-cortical afferents for higher-order inputs. Existing models have focused on local networks and have not considered the spatial aspects that are likely to be crucial for developing a general theory about response properties that depend on both network state and type of input.

The successful candidate will receive training in the development and analysis of neuronal population models. The model will be defined by systems of integro-differential equations describing firing rates of different neuron subtypes and will be analysed with dynamical systems methods. This will allow experimentally testable predictions to be generated on cortical response properties. Collaborators can test these in new experiments to confirm, reject or refine modelling hypotheses. This project provides a unique opportunity to receive training in mathematical modelling alongside close collaboration with experimentalists using cutting-edge optogenetic methods. Experience working on such interdisciplinary projects is highly sought after.

Candidates with quantitative backgrounds (mathematics, physics, engineering) and from neuroscience programmes are encouraged to apply to this 3.5 year PhD Scholarship. Programming experience, knowledge of dynamical systems theory and training in biological modelling are a plus.