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Topographic maps are ubiquitous brain structures that are fundamental to sensory and higher order systems and are composed of connections between two regions obeying the relationship: physically neighbouring cells in a pre-synaptic region connect to physically neighbouring cells in the post-synaptic region. The developmental principles driving topographic map formation are usually studied within the context of genetic perturbations coupled to high resolution measurements and for these the mouse retinotopic map from retina to superior colliculus has emerged as a useful experimental context. Modelling coupled with genetic perturbation experiments has revealed three key developmental mechanisms: neural activity, chemotaxis, and competition. Some principal challenges in modelling this development include explaining the role of the spatio-temporal structure of patterned neural activity, determining the relative interaction between developmental components, and developing models that are sufficiently computationally efficient that statistical methodologies can be applied to them. Neural activity is a well measured component of retinotopic development and several independent measurement techniques have recorded the existence of spatiotemporally patterned waves at key critical points during development. Existing modelling methodologies reduce this rich spatiotemporal context into a distance dependent correlation function and have subsequently had challenges making quantitative predictions about the effect of manipulating these activity patterns. A neural field theory approach is used to develop mathematical theory which can incorporate these spatiotemporal structures. Bayesian MCMC regression analysis is performed on biological measurements to assess the accuracy of the model and make predictions about the time-scale on which activity operates. This time scale is tuned to the length of an average wave pattern suggesting the system is integrating all information in these waves. The interaction between chemotaxis and neural activity has historically been thought of as linearly independent. A recent study which perturbs both developmental mechanisms simultaneously has suggested that these two are highly stochastic and regular development depends on a critical fine- tuned balance between the two: the heterozygous phenotype was observed to present as both a wild-type and homozygote for different specimens. This hypothesis is tested against the data-set used to generate it. Recreating the entire experimental pipeline in silico with the most parsimonious existing model is able to account for the data without the need to appeal to stochasticity in the mechanisms. A statistical analysis demonstrates that the heterozygous state does not significantly overlap with the heterozygotes and that the stochasticity is likely due to the measurement technique. The existing models are computationally demanding; at least O(n3 ) in the number of retinal cells instantiated by the model. This computational demand renders these classes of models incapable of performing statistical regression and means that their parameters spaces are largely unexplored. A modelling framework which integrates the core operating mechanisms of the model is developed and when implemented on modern GPU computational architectures is able to achieve a near- linear time complexity scaling. This model is demonstrated to capture the explanatory power of existing modelling methodologies. Finally, the role of competition is explored in a dimensional reduction framework: the Elastic Net. The Elastic Net has been used both as a heuristic optimiser (validated on the NP-complete Travel- ling Salesman Problem) and to explain the development of cortical feature maps. The addition of competition is demonstrated to act as a counter-measure to the retinotopic distorting components of the Elastic Net as a cortical map generator. Further analysis demonstrates that competition substantially improves heuristic performance on the Travelling Salesman Problem making it competitive against state of the art solvers when performance is normalised by solution times. The heuristic converges on a length scaling law that is discussed in the context of wire-minimisation problem.

In order to successfully interact with the environment, animals need to produce accurate movements towards specific positions in space. A crucial region of the brain that guides such goal-oriented movements is the superior colliculus (SC), an evolutionary conserved structure of the midbrain. While several lines of research in different model organisms have confirmed that the SC contributes to the initiation of orienting movements, how functionally distinct neuronal groups within the SC are organized to support the production of such motor outputs is poorly understood. One of the reasons why the intrinsic circuit organization of the SC remains elusive is the lack of genetic characterization of the neuronal populations of the motor SC. Here, we performed RNAseq to screen for genetic markers for neuronal subpopulations in the motor SC. We identified a transcription factor, Pitx2, which is exclusively expressed in a subpopulation of glutamatergic neurons in the motor domain of the SC. Strikingly, this population of neurons displays a non-homogenous distribution within the motor layer of the SC, being organised in clusters along the mediolateral and anteroposterior axis. We mapped the pre-synaptic network and the post-synaptic targets of Pitx2ON neurons, unveiling that this modular population receives direct inputs from motor and sensory cortical regions, as well as several midbrain nuclei involved in movement control, and sends projection along the cephalomotor pathway. We then asked whether these modules may act as functional units, each integrating multimodal sensory information and encoding a specific feature of head movement, the main ethologically relevant orienting behaviour in rodents. Optogenetic activation of this modular population in freely moving animals produced a stereotyped, robust head motion characterised by a pronounced quantal nature; furthermore, the amplitude of the elicited head movement varied based on the modular unit activated. Our results suggest that distinct clusters of genetically defined neurons produce head displacement along a characteristic vector. In conclusion, we found that a population of premotor neurons in the SC is organised in a modular conformation and we suggest that such modularity may represent a physical implementation of a discontinuous motor map for orienting movements encoded in the mouse SC. Our work complements previous observations of periodicity in SC circuitry, as well as its afferent and efferent systems. Exploiting the genetic toolkit available in the mouse, our work begins to address the functional relevance of this modularity and paves the way for future experiments to investigate principles of sensorimotor integration in SC circuits.

Spontaneous travelling waves of neuronal activity are a prominent feature throughout the developing brain and have been shown to be essential for achieving normal function, but the mechanism of their action on post-synaptic connections remains unknown. A well-known and widespread mechanism for altering synaptic strengths is spike-timing dependent plasticity (STDP), whereby the temporal relationship between the pre- and post-synaptic spikes determines whether a synapse is strengthened or weakened. Here, I answer the theoretical question of how these two phenomenon interact: what types of connectivity patterns can emerge when travelling waves drive a downstream area that implements STDP, and what are the critical features of the waves and the plasticity rules that shape these patterns? I then demonstrate how the theory can be applied to the development of the visual system, where retinal waves are hypothesised to play a role in the refinement of downstream connections. My major findings are as follows. (1) Mathematically, STDP translates the correlated activity of travelling waves into coherent patterns of synaptic connectivity; it maps the spatiotemporal structure in waves into a spatial pattern of synaptic strengths, building periodic structures into feedforward circuits. This is analogous to pattern formation in reaction diffusion systems. The theory reveals a role for the wave speed and time scale of the STDP rule in determining the spatial frequency of the connectivity pattern. (2) Simulations verify the theory and extend it from one-dimensional to two-dimensional cases, and from simplified linear wavefronts to more complex realistic and noisy wave patterns. (3) With appropriate constraints, these pattern formation abilities can be harnessed to explain a wide range of developmental phenomena, including how receptive fields (RFs) in the visual system are refined in size and topography and how simple-cell and direction selective RFs can develop. The theory is applied to the visual system here but generalises across different brain areas and STDP rules. The theory makes several predictions that are testable using existing experimental paradigms.

Adaptation is one of the basic phenomena of biology, while adaptability is an important feature for neural network. Young barn owl can well adapt its visual and auditory integration to the environmental change, such as prism wearing. At first, a mathematical model is introduced by the related study in biological experiment. The model well explained the mechanism of the sensory map realignment through axongenesis and synaptogenesis. Simulation results of this model are consistent with the biological data. Thereafter, to test the model’s application in hardware, the model is implemented into a robot. Visual and auditory signals are acquired by the sensors of the robot and transferred back to PC through bluetooth. Results of the robot experiment are presented, which shows the SC model allowing the robot to adjust visual and auditory integration to counteract the effects of a prism. Finally, based on the model, a silicon Superior Colliculus is designed in VLSI circuit and fabricated. Performance of the fabricated chip has shown the synaptogenesis and axogenesis can be emulated in VLSI circuit. The circuit of neural model provides a new method to update signals and reconfigure the switch network (the chip has an automatic reconfigurable network which is used to correct the disparity between signals). The chip is also the first Superior Colliculus VLSI circuit to emulate the sensory map realignment.