The physics of brain network structure, function and control

The brain is the quintessential complex system, boasting incredible feats of cognition and supporting a wide range of behaviours. Physics has much to offer in the quest to distil the brain's complexity to a number of cogent organizing principles. The brain is characterized by heterogeneous patterns of structural connections supporting unparalleled feats of cognition and a wide range of behaviours. New non-invasive imaging techniques now allow comprehensive mapping of these patterns. However, a fundamental challenge remains to understand how the brain's structural wiring supports cognitive processes, with major implications for personalized mental health treatments. Here, we review recent efforts to meet this challenge, drawing on physics intuitions, models and theories, spanning the domains of statistical mechanics, information theory, dynamical systems and control. We first describe the organizing principles of brain network architecture instantiated in structural wiring under constraints of spatial embedding and energy minimization. We then survey models of brain network function that stipulate how neural activity propagates along structural connections. Finally, we discuss perturbative experiments and models for brain network control; these use the physics of signal transmission along structural connections to infer intrinsic control processes that support goal-directed behaviour and to inform stimulation-based therapies for neurological and psychiatric disease. Throughout, we highlight open questions that invite the creative efforts of pioneering physicists.