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Register a new userReconstructing an epigenetic landscape using a genetic `pulling approach
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Cells use genetic switches to shift between alternate stable gene expression states, e.g., to adapt to new environments or to follow a developmental pathway. Conceptually, these stable phenotypes can be considered as attractive states on an epigenetic landscape with phenotypic changes being transitions between states. Measuring these transitions is challenging because they are both very rare in the absence of appropriate signals and very fast. As such, it has proven difficult to experimentally map the epigenetic landscapes that are widely believed to underly developmental networks. Here, we introduce a new nonequilibrium perturbation method to help reconstruct a regulatory networks epigenetic landscape. We derive the mathematical theory needed and then use the method on simulated data to reconstruct the landscapes. Our results show that with a relatively small number of perturbation experiments it is possible to recover an accurate representation of the true epigenetic landscape. We propose that our theory provides a general method by which epigenetic landscapes can be studied. Finally, our theory suggests that the total perturbation impulse required to induce a switch between metastable states is a fundamental quantity in developmental dynamics.
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Motivated by the famous Waddingtons epigenetic landscape metaphor in developmental biology, biophysicists and applied mathematicians made different proposals to realize this metaphor in a rationalized way. We adopt comprehensive perspectives to systematically investigate three different but closely related realizations in recent literature: namely the potential landscape theory from the steady state distribution of stochastic differential equations (SDEs), the quasi-potential from the large deviation theory, and the construction through SDE decomposition and A-type integral.The connections among these theories are established in this paper. We demonstrate that the quasi-potential is the zero noise limit of the potential landscape. We also show that the potential function in the third proposal coincides with the quasi-potential. The most probable transition path by minimizing the Onsager-Machlup or Freidlin-Wentzell action functional is discussed as well. Furthermore, we compare the difference between local and global quasi-potential through the exchange of limit order for time and noise amplitude. As a consequence of such explorations, we arrive at the existence result for the SDE decomposition while deny its uniqueness in general cases. It is also clarified that the A-type integral is more appropriate to be applied to the decomposed SDEs rather than the original one. Our results contribute to a better understanding of existing landscape theories for biological systems.
Many proteins carry out their biological functions by forming the characteristic tertiary structures. Therefore, the search of the stable states of proteins by molecular simulations is important to understand their functions and stabilities. However, getting the stable state by conformational search is difficult, because the energy landscape of the system is characterized by many local minima separated by high energy barriers. In order to overcome this difficulty, various sampling and optimization methods for conformations of proteins have been proposed. In this study, we propose a new conformational search method for proteins by using genetic crossover and Metropolis criterion. We applied this method to an $alpha$-helical protein. The conformations obtained from the simulations are in good agreement with the experimental results.
Cells are known to utilize biochemical noise to probabilistically switch between distinct gene expression states. We demonstrate that such noise-driven switching is dominated by tails of probability distributions and is therefore exponentially sensitive to changes in physiological parameters such as transcription and translation rates. However, provided mRNA lifetimes are short, switching can still be accurately simulated using protein-only models of gene expression. Exponential sensitivity limits the robustness of noise-driven switching, suggesting cells may use other mechanisms in order to switch reliably.
One of the fundamental cellular processes governed by genetic regulatory networks in cells is the transition among different states under the intrinsic and extrinsic noise. Based on a two-state genetic switching model with positive feedback, we develop a framework to understand the metastability in gene expressions. This framework is comprised of identifying the transition path, reconstructing the global quasi-potential energy landscape, analyzing the uphill and downhill transition paths, etc. It is successfully utilized to investigate the stability of genetic switching models and fluctuation properties in different regimes of gene expression with positive feedback. The quasi-potential energy landscape, which is the rationalized version of Waddington potential, provides a quantitative tool to understand the metastability in more general biological processes with intrinsic noise.
Zero-order ultrasensitivity (ZOU) is a long known and interesting phenomenon in enzyme networks. Here, a substrate is reversibly modified by two antagonistic enzymes (a push-pull system) and the fraction in modified state undergoes a sharp switching from near-zero to near-unity at a critical value of the ratio of the enzyme concentrations, under saturation conditions. ZOU and its extensions have been studied for several decades now, ever since the seminal paper of Goldbeter and Koshland (1981); however, a complete probabilistic treatment, important for the study of fluctuations in finite populations, is still lacking. In this paper, we study ZOU using a modular approach, akin to the total quasi-steady state approximation (tQSSA). This approach leads to a set of Fokker-Planck (drift-diffusion) equations for the probability distributions of the intermediate enzyme-bound complexes, as well as the modified/unmodified fractions of substrate molecules. We obtain explicit expressions for various average fractions and their fluctuations in the linear noise approximation (LNA). The emergence of a critical point for the switching transition is rigorously established. New analytical results are derived for the average and variance of the fractional substrate concentration in various chemical states in the near-critical regime. For the total fraction in the modified state, the variance is shown to be a maximum near the critical point and decays algebraically away from it, similar to a second-order phase transition. The new analytical results are compared with existing ones as well as detailed numerical simulations using a Gillespie algorithm.
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