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.

分子生物学的最新进展，例如基因编辑 [1]、生物电记录和操作 [2] 以及使用荧光报告基因的活细胞显微术 [3]、[4] – 特别是随着光遗传学通过光控蛋白质激活的出现 [5] – 提供了以前所未有的时空精度测量和操纵分子信号通路的工具。这已经产生了关于生物有机体发育和再生的分子机制的越来越详细的信息。然而，一个总体概念——可以预测形态的出现和复杂解剖结构的稳健维护——在该领域中很大程度上缺失。经典（即动态系统和分析力学）方法（例如最小作用原理）在表征开式时很难使用，远离生物学中占主导地位的平衡系统。当试图从第一原理理解神经元动力学时，神经科学中也会出现类似的问题。在这种（神经生物学）环境中，基于（主动）贝叶斯推理的自组织公式，出现了变分自由能原理。自由能原理最近被应用于神经科学之外的生物自组织[6]、[7]。对于支持发育或再生的生物过程，贝叶斯推理框架将细胞视为信息处理代理，其中形态发生背后的驱动力是细胞模型证据的最大化。这是通过受体的适当表达和与细胞内部（即，生成）模型，它应该表达什么类型的受体和其他信号。模式形成中的自由能原理的新兴领域为理解胚胎发生、再生和癌症抑制背景下的细胞决策提供了基本的定量形式。在本文中，我们推导出贝叶斯推理背后的数学——正如在这个框架中所理解的那样——并使用模拟来证明形式主义可以重现复杂形态发生的实验性、自上而下的操作。首先，我们通过模拟改变前后轴极性（即诱导两个头或两个尾）来说明这种形态发生的“第一原则”方法，如在涡虫再生中。然后，我们认为细胞群内单个细胞的异常信号传导和功能行为——作为致癌作用的第一步，是关于细胞应该“感知”和“做什么”的错误“信念”。我们进一步表明，推理过程的简单修改可以导致 - 并挽救 - 发育和再生事件的错误模式，而不改变细胞的隐含生成模型，例如通过其 DNA 指定。这种形式主义为理解进化中的发展变化和设计再生医学环境中的新干预措施提供了新的路线图。我们进一步表明，推理过程的简单修改可以导致 - 并挽救 - 发育和再生事件的错误模式，而不改变细胞的隐含生成模型，例如通过其 DNA 指定。这种形式主义为理解进化中的发展变化和设计再生医学环境中的新干预措施提供了新的路线图。我们进一步表明，推理过程的简单修改可以导致 - 并挽救 - 发育和再生事件的错误模式，而不改变细胞的隐含生成模型，例如通过其 DNA 指定。这种形式主义为理解进化中的发展变化和设计再生医学环境中的新干预措施提供了新的路线图。