Abstract
Depicting developmental processes as movements in free energy genetic landscapes is an illustrative tool. However, exploring such landscapes to obtain quantitative or even qualitative predictions is hampered by the lack of free energy functions corresponding to the biochemical Michaelis–Menten or Hill rate equations for the dynamics. Being armed with energy landscapes defined by a network and its interactions would open up the possibility of swiftly identifying cell states and computing optimal paths, including those of cell reprogramming, thereby avoiding exhaustive trial-and-error simulations with rate equations for different parameter sets. It turns out that sigmoidal rate equations do have approximate free energy associations. With this replacement of rate equations, we develop a deterministic method for estimating the free energy surfaces of systems of interacting genes at different noise levels or temperatures. Once such free energy landscape estimates have been established, we adapt a shortest path algorithm to determine optimal routes in the landscapes. We explore the method on three circuits for haematopoiesis and embryonic stem cell development for commitment and reprogramming scenarios and illustrate how the method can be used to determine sequential steps for onsets of external factors, essential for efficient reprogramming.
Highlights
Enforced guiding of developmental processes including those of cellular reprogramming could benefit from in silico dynamical modelling by tuning parameters for protein concentrations and other factors involved in the rate equations describing the systems
While this relationship is often true in physics models, a quantitative relationship between the biochemical dynamics and the free energy landscape has not been widely exploited in developmental processes
In Bhattacharya et al [3] and Zhou et al [4] quasi-potential methods based upon Lyapunov theory are developed where the energy or potential is decomposed into two terms: one related to the dynamical equations and the other chosen to minimize its effect on state transitions
Summary
Enforced guiding of developmental processes including those of cellular reprogramming could benefit from in silico dynamical modelling by tuning parameters for protein concentrations and other factors involved in the rate equations describing the systems. The underlying idea is that the dynamics of biochemical equations, governing a specific developmental process, can be represented as movements in a free energy landscape such that lineage choices are paths between stable cell states This notion is based upon a potential correspondence between solving the equations of motion and minimizing the corresponding free energy. While this relationship is often true in physics models, a quantitative relationship between the biochemical dynamics and the free energy landscape has not been widely exploited in developmental processes This is due to the fact that the frequently used Michaelis–Menten or Hill kinetics do not have a corresponding free energy from which the rate equations are given by a gradient. In Bhattacharya et al [3] and Zhou et al [4] quasi-potential methods based upon Lyapunov theory are developed where the energy or potential is decomposed into two terms: one related to the dynamical equations and the other chosen to minimize its effect on state transitions
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