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

神经网络的数学建模将被用来理解新皮层中输入响应特性的神经元计算原理。从动力系统理论的方法，包括分叉分析，将被应用到分析神经场模型的开发。哺乳动物的新皮层参与大脑功能的各个方面，包括感觉处理、运动控制、决策和语言。不同的皮层网络状态与不同类型的行为有关。例如，在小鼠中，当动物用胡须探索其环境时，在安静的清醒状态下皮质活动的同步大幅度缓慢振荡让位于更高频率的低幅度波动。高活动（所谓的上升状态）和低活动（下降状态）的同步周期之间的自发转换最常发生在慢波睡眠期间，在慢波睡眠中，它们被认为对哺乳动物的记忆巩固很重要。感觉皮层区域以不同的方式响应输入，这取决于网络是处于向上状态还是向下状态，以及输入是通过感觉刺激（初级输入）还是来自其他皮层区域（高阶输入）。这些重要差异背后的指导原则仍有待确立。这是一个合适的时机来实现这一目标的数学建模，这将揭示的功能作用的向上和向下状态。该项目将在神经场框架中开发一个动态模型，该模型给出了多个皮层列（几毫米的皮层）上神经活动的空间平均描述。这提供了一个理想的框架，在其中探测初级感觉输入之间的差异，这可能是局部的，由于感受野特性，和高阶输入。据推测，在下状态下，皮质区通常对输入作出反应。然而，在向上状态下，感觉区域对初级和次级输入的反应不同。建模工作将与研究慢波睡眠期间输入反应的实验密切合作，激活主要输入的胡须，并使用皮质-皮质传入的光遗传学刺激进行高阶输入。现有的模型都集中在本地网络，并没有考虑到空间方面，可能是至关重要的发展一个一般的理论，依赖于网络状态和输入类型的响应特性。成功的候选人将接受神经元群体模型开发和分析方面的培训。该模型将由描述不同神经元亚型的放电率的积分微分方程系统定义，并将用动力系统方法进行分析。这将允许实验测试的预测，以产生对皮层的反应特性。合作者可以在新的实验中测试这些假设，以确认、拒绝或改进建模假设。该项目提供了一个独特的机会，接受数学建模培训，同时与使用尖端光遗传学方法的实验人员密切合作。在这样的跨学科项目工作的经验是非常抢手的。鼓励具有定量背景（数学，物理，工程）和神经科学课程的候选人申请这个3.5年的博士奖学金。有编程经验，动力系统理论知识和生物建模培训者优先。

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.