Highlights d Modeling time-resolved scRNA-seq data avoids pitfalls of splicing RNA velocities d Dynamo reconstructs analytical vector fields from discrete velocity vectors d Vector fields reveal the timing and mechanisms of human hematopoiesis d Dynamo allows cell-state transition path and in silico perturbation predictions

Recently, a novel framework to handle stochastic processes emerges from a series of studies in biology, showing situations beyond "Itô vs. Stratonovich". Its internal consistency can be demonstrated via the zero mass limit of a generalized Klein-Kramers equation. Moreover, the connection to other integrations becomes evident: The obtained Fokker-Planck equation defines a new type of stochastic calculus that in general differs from the α-type interpretation. A unique advantage of this new approach is a natural correspondence between stochastic and deterministic dynamics, which is useful or may even be essential in practice. The core of the framework is a transformation from a usual Langevin equation to a form that contains a potential function with two additional dynamical matrices, which reveals an underlying symplectic structure. The framework has a direct physical meaning and a straightforward experimental realization. A recent experiment offers a first empirical validation of such new stochastic integration. [This article has been published in J. Stat. Mech. (2012) P07010. Note that a typo in Sect. III B has been corrected (See also [39]). ]

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Cancer is a complex disease: its pathology cannot be properly understood in terms of independent players-genes, proteins, molecular pathways, or their simple combinations. This is similar to many-body physics of a condensed phase that many important properties are not determined by a single atom or molecule. The rapidly accumulating large 'omics' data also require a new mechanistic and global underpinning to organize for rationalizing cancer complexity. A unifying and quantitative theory was proposed by some of the present authors that cancer is a robust state formed by the endogenous molecular-cellular network, which is evolutionarily built for the developmental processes and physiological functions. Cancer state is not optimized for the whole organism. The discovery of crucial players in cancer, together with their developmental and physiological roles, in turn, suggests the existence of a hierarchical structure within molecular biology systems. Such a structure enables a decision network to be constructed from experimental knowledge. By examining the nonlinear stochastic dynamics of the network, robust states corresponding to normal physiological and abnormal pathological phenotypes, including cancer, emerge naturally. The nonlinear dynamical model of the network leads to a more encompassing understanding than the prevailing linear-additive thinking in cancer research. So far, this theory has been applied to prostate, hepatocellular, gastric cancers and acute promyelocytic leukemia with initial success. It may offer an example of carrying physics inquiring spirit beyond its traditional domain: while quantitative approaches can address individual cases, however there must be general rules/laws to be discovered in biology and medicine.