Morphogenesis as Bayesian inference: A variational approach to pattern formation and control in complex biological systems.

Recent advances in molecular biology such as gene editing [1], bioelectric recording and manipulation [2] and live cell microscopy using fluorescent reporters [3], [4] - especially with the advent of light-controlled protein activation through optogenetics [5] - have provided the tools to measure and manipulate molecular signaling pathways with unprecedented spatiotemporal precision. This has produced ever increasing detail about the molecular mechanisms underlying development and regeneration in biological organisms. However, an overarching concept - that can predict the emergence of form and the robust maintenance of complex anatomy - is largely missing in the field. Classic (i.e., dynamic systems and analytical mechanics) approaches such as least action principles are difficult to use when characterizing open, far-from equilibrium systems that predominate in Biology. Similar issues arise in neuroscience when trying to understand neuronal dynamics from first principles. In this (neurobiology) setting, a variational free energy principle has emerged based upon a formulation of self-organization in terms of (active) Bayesian inference. The free energy principle has recently been applied to biological self-organization beyond the neurosciences [6], [7]. For biological processes that underwrite development or regeneration, the Bayesian inference framework treats cells as information processing agents, where the driving force behind morphogenesis is the maximization of a cell's model evidence. This is realized by the appropriate expression of receptors and other signals that correspond to the cell's internal (i.e., generative) model of what type of receptors and other signals it should express. The emerging field of the free energy principle in pattern formation provides an essential quantitative formalism for understanding cellular decision-making in the context of embryogenesis, regeneration, and cancer suppression. In this paper, we derive the mathematics behind Bayesian inference - as understood in this framework - and use simulations to show that the formalism can reproduce experimental, top-down manipulations of complex morphogenesis. First, we illustrate this 'first principle' approach to morphogenesis through simulated alterations of anterior-posterior axial polarity (i.e., the induction of two heads or two tails) as in planarian regeneration. Then, we consider aberrant signaling and functional behavior of a single cell within a cellular ensemble - as a first step in carcinogenesis as false 'beliefs' about what a cell should 'sense' and 'do'. We further show that simple modifications of the inference process can cause - and rescue - mis-patterning of developmental and regenerative events without changing the implicit generative model of a cell as specified, for example, by its DNA. This formalism offers a new road map for understanding developmental change in evolution and for designing new interventions in regenerative medicine settings.