The potential landscape of genetic circuits imposes the arrow of time in stem cell differentiation.
ABSTRACT: Differentiation from a multipotent stem or progenitor state to a mature cell is an essentially irreversible process. The associated changes in gene expression patterns exhibit time-directionality. This "arrow of time" in the collective change of gene expression across multiple stable gene expression patterns (attractors) is not explained by the regulated activation, the suppression of individual genes which are bidirectional molecular processes, or by the standard dynamical models of the underlying gene circuit which only account for local stability of attractors. To capture the global dynamics of this nonequilibrium system and gain insight in the time-asymmetry of state transitions, we computed the quasipotential landscape of the stochastic dynamics of a canonical gene circuit that governs branching cell fate commitment. The potential landscape reveals the global dynamics and permits the calculation of potential barriers between cell phenotypes imposed by the circuit architecture. The generic asymmetry of barrier heights indicates that the transition from the uncommitted multipotent state to differentiated states is inherently unidirectional. The model agrees with observations and predicts the extreme conditions for reprogramming cells back to the undifferentiated state.
Project description:Stem cell differentiation has been viewed as coming from transitions between attractors on an epigenetic landscape that governs the dynamics of a regulatory network involving many genes. Rigorous definition of such a landscape is made possible by the realization that gene regulation is stochastic, owing to the small copy number of the transcription factors that regulate gene expression and because of the single-molecule nature of the gene itself. We develop an approximation that allows the quantitative construction of the epigenetic landscape for large realistic model networks. Applying this approach to the network for embryonic stem cell development explains many experimental observations, including the heterogeneous distribution of the transcription factor Nanog and its role in safeguarding the stem cell pluripotency, which can be understood by finding stable steady-state attractors and the most probable transition paths between those attractors. We also demonstrate that the switching rate between attractors can be significantly influenced by the gene expression noise arising from the fluctuations of DNA occupancy when binding to a specific DNA site is slow.
Project description:BACKGROUND: The gene regulatory circuit motif in which two opposing fate-determining transcription factors inhibit each other but activate themselves has been used in mathematical models of binary cell fate decisions in multipotent stem or progenitor cells. This simple circuit can generate multistability and explains the symmetric "poised" precursor state in which both factors are present in the cell at equal amounts as well as the resolution of this indeterminate state as the cell commits to either cell fate characterized by an asymmetric expression pattern of the two factors. This establishes the two alternative stable attractors that represent the two fate options. It has been debated whether cooperativity of molecular interactions is necessary to produce such multistability. PRINCIPAL FINDINGS: Here we take a general modeling approach and argue that this question is not relevant. We show that non-linearity can arise in two distinct models in which no explicit interaction between the two factors is assumed and that distinct chemical reaction kinetic formalisms can lead to the same (generic) dynamical system form. Moreover, we describe a novel type of bifurcation that produces a degenerate steady state that can explain the metastable state of indeterminacy prior to cell fate decision-making and is consistent with biological observations. CONCLUSION: The general model presented here thus offers a novel principle for linking regulatory circuits with the state of indeterminacy characteristic of multipotent (stem) cells.
Project description:Cancer metabolism is critical for understanding the mechanism of tumorigenesis, yet the understanding is still challenging. We studied gene-metabolism regulatory interactions and quantified the global driving forces for cancer-metabolism dynamics as the underlying landscape and probability flux. We uncovered four steady-state attractors: a normal state attractor, a cancer OXPHOS state attractor, a cancer glycolysis state attractor, and an intermediate cancer state attractor. We identified the key regulatory interactions through global sensitivity analysis based on the landscape topography. Different landscape topographies of glycolysis switch between normal cells and cancer cells were identified. We uncovered that the normal state to cancer state transformation is associated with the peaks of the probability flux and the thermodynamic dissipation, giving dynamical and thermodynamic origin of cancer formation. We found that cancer metabolism oscillations consume more energy to support cancer malignancy. This study provides a quantitative understanding of cancer metabolism and suggests a metabolic therapeutic strategy.
Project description:Cancer is a disease regulated by the underlying gene networks. The emergence of normal and cancer states as well as the transformation between them can be thought of as a result of the gene network interactions and associated changes. We developed a global potential landscape and path framework to quantify cancer and associated processes. We constructed a cancer gene regulatory network based on the experimental evidences and uncovered the underlying landscape. The resulting tristable landscape characterizes important biological states: normal, cancer and apoptosis. The landscape topography in terms of barrier heights between stable state attractors quantifies the global stability of the cancer network system. We propose two mechanisms of cancerization: one is by the changes of landscape topography through the changes in regulation strengths of the gene networks. The other is by the fluctuations that help the system to go over the critical barrier at fixed landscape topography. The kinetic paths from least action principle quantify the transition processes among normal state, cancer state and apoptosis state. The kinetic rates provide the quantification of transition speeds among normal, cancer and apoptosis attractors. By the global sensitivity analysis of the gene network parameters on the landscape topography, we uncovered some key gene regulations determining the transitions between cancer and normal states. This can be used to guide the design of new anti-cancer tactics, through cocktail strategy of targeting multiple key regulation links simultaneously, for preventing cancer occurrence or transforming the early cancer state back to normal state.
Project description:Epithelial-mesenchymal transition (EMT), as a crucial process in embryonic development and cancer metastasis, has been investigated extensively. However, how to quantify the global stability and transition dynamics for EMT under fluctuations remains to be elucidated. Starting from a core EMT genetic circuit composed of three key proteins or microRNAs (microRNA-200, ZEB and SNAIL), we uncovered the potential landscape for the EMT process. Three attractors emerge from the landscape, which correspond to epithelial, mesenchymal and partial EMT states respectively. Based on the landscape, we analyzed two important quantities of the EMT system: the barrier heights between different basins of attraction that describe the degree of difficulty for EMT or backward transition, and the mean first passage time (MFPT) that characterizes the kinetic transition rate. These quantities can be harnessed as measurements for the stability of cell types and the degree of difficulty of transitions between different cell types. We also calculated the minimum action paths (MAPs) by path integral approaches. The MAP delineates the transition processes between different cell types quantitatively. We propose two different EMT processes: a direct EMT from E to P, and a step-wise EMT going through an intermediate state, depending on different extracellular environments. The landscape and kinetic paths we acquired offer a new physical and quantitative way for understanding the mechanisms of EMT processes, and indicate the possible roles for the intermediate states.
Project description:Ageing is a natural phenomenon that is inherently complex and remains a mystery. Conceptual model of cellular ageing landscape was proposed for computational studies of ageing. However, there is a lack of quantitative model of cellular ageing landscape. This study aims to investigate the mechanism of cellular ageing in a theoretical model using the framework of Waddington's epigenetic landscape. We construct an ageing gene regulatory network (GRN) consisting of the core cell cycle regulatory genes (including p53). A model parameter (activation rate) is used as a measure of the accumulation of DNA damage. Using the bifurcation diagrams to estimate the parameter values that lead to multi-stability, we obtained a conceptual model for capturing three distinct stable steady states (or attractors) corresponding to homeostasis, cell cycle arrest, and senescence or apoptosis. In addition, we applied a Monte Carlo computational method to quantify the potential landscape, which displays: I) one homeostasis attractor for low accumulation of DNA damage; II) two attractors for cell cycle arrest and senescence (or apoptosis) in response to high accumulation of DNA damage. Using the Waddington's epigenetic landscape framework, the process of ageing can be characterized by state transitions from landscape I to II. By in silico perturbations, we identified the potential landscape of a perturbed network (inactivation of p53), and thereby demonstrated the emergence of a cancer attractor. The simulated dynamics of the perturbed network displays a landscape with four basins of attraction: homeostasis, cell cycle arrest, senescence (or apoptosis) and cancer. Our analysis also showed that for the same perturbed network with low DNA damage, the landscape displays only the homeostasis attractor. The mechanistic model offers theoretical insights that can facilitate discovery of potential strategies for network medicine of ageing-related diseases such as cancer.
Project description:Aging attracts the attention throughout the history of humankind. However, it is still challenging to understand how the internal driving forces, for example, the fundamental building blocks of life, such as genes and proteins, as well as the environments work together to determine longevity in mammals. In this study, we built a gene regulatory network for mammalian cellular aging based on the experimental literature and quantify its underlying driving force for the dynamics as potential and flux landscape. We found three steady-state attractors: a fast-aging state attractor, slow-aging state attractor, and intermediate state attractor. The system can switch from one state attractor to another driven by the intrinsic or external forces through the genetics and the environment. We identified the dominant path from the slow-aging state directly to the fast-aging state. We also identified the dominant path from slow-aging to fast-aging through an intermediate state. We quantified the evolving landscape for revealing the dynamic characteristics of aging through certain regulation changes in time. We also predicted the key genes and regulations for fast-aging and slow-aging through the analysis of the stability for landscape basins. We also found the oscillation dynamics between fast-aging and slow-aging and showed that more energy is required to sustain such oscillations. We found that the flux is the dynamic cause and the entropy production rate the thermodynamic origin of the phase transitions or the bifurcations between the three-state phase and oscillation phase. The landscape quantification provides a global and physical approach to explore the underlying mechanisms of cellular aging in mammals.
Project description:Cutaneous leishmaniasis is the most common form of leishmaniasis, caused by Leishmania major and is spread by the bite of a sandfly .This species infects the macrophages and dendritic cells Due to multi-drug resistance, there is a need for a new therapeutic technique. Recently, a novel molecular motor of Leishmania, Myosin XXI, was classified and characterized. In addition, the drug resistance in this organism has been linked with the overexpression of ABC transporters. Systems biology aims to study the simulation and modeling of natural biological systems whereas synthetic biology deals with building novel and artificial biological parts and devices Together they have contributed enormously to drug discovery, vaccine design and development, infectious disease detection and diagnostics. Synthetic genetic regulatory networks with desired properties, like toggling and oscillation have been proposed to be useful for gene therapy. In this work, a nanocircuit with coupled bistable switch - repressilator has been designed, simulated in the presence and absence of inducer, in silico, using Tinker Cell. When inducer is added, the circuit has been shown to produce reporter at high levels, which will impair the activity of Myosin XXI and ABC transporters. Validation of the circuit was also performed using GRENITS and BoolNet. The influence of inducer on the working of the circuit, i.e., the type of gene expression, response time delay, the steady states formed by the circuit and the quasipotential landscape of the circuit were performed. It was found that the addition of inducer reduced the response time delay in the graded type of gene expression and removed the multiple intermediate attractors of the circuit. Thus, the inducer increased the probability of the circuit to be present in the dominant stable state with high reporter concentration and hence the designed nanocircuit may be used for the treatment of leishmaniasis .
Project description:The epithelial-mesenchymal transition (EMT) is a basic developmental process that converts epithelial cells to mesenchymal cells. Although EMT might promote cancer metastasis, the molecular mechanisms for it remain to be fully clarified. To address this issue, we constructed an EMT-metastasis gene regulatory network model and quantified the potential landscape of cancer metastasis-promoting system computationally. We identified four steady-state attractors on the landscape, which separately characterize anti-metastatic (A), metastatic (M), and two other intermediate (I1 and I2) cell states. The tetrastable landscape and the existence of intermediate states are consistent with recent single-cell measurements. We identified one of the two intermediate states I1 as the EMT state. From a MAP approach, we found that for metastatic progression cells need to first undergo EMT (enter the I1 state), and then become metastatic (switch from the I1 state to the M state). Specifically, for metastatic progression, EMT genes (such as ZEB) should be activated before metastasis genes (such as BACH1). This suggests that temporal order is important for the activation of cellular programs in biological systems, and provides a possible mechanism of EMT-promoting cancer metastasis. To identify possible therapeutic targets from this landscape view, we performed sensitivity analysis for individual molecular factors, and identified optimal interventions for landscape control. We found that minimizing transition actions more effectively identifies optimal combinations of targets that induce transitions between attractors than single-factor sensitivity analysis. Overall, the landscape view not only suggests that intermediate states increase plasticity during cell fate decisions, providing a possible source for tumor heterogeneity that is critically important in metastatic progress, but also provides a way to identify therapeutic targets for preventing cancer progression.
Project description:The species in ecosystems are mutually interacting and self sustainable stable for a certain period. Stability and dynamics are crucial for understanding the structure and the function of ecosystems. We developed a potential and flux landscape theory of ecosystems to address these issues. We show that the driving force of the ecological dynamics can be decomposed to the gradient of the potential landscape and the curl probability flux measuring the degree of the breaking down of the detailed balance (due to in or out flow of the energy to the ecosystems). We found that the underlying intrinsic potential landscape is a global Lyapunov function monotonically going down in time and the topology of the landscape provides a quantitative measure for the global stability of the ecosystems. We also quantified the intrinsic energy, the entropy, the free energy and constructed the non-equilibrium thermodynamics for the ecosystems. We studied several typical and important ecological systems: the predation, competition, mutualism and a realistic lynx-snowshoe hare model. Single attractor, multiple attractors and limit cycle attractors emerge from these studies. We studied the stability and robustness of the ecosystems against the perturbations in parameters and the environmental fluctuations. We also found that the kinetic paths between the multiple attractors do not follow the gradient paths of the underlying landscape and are irreversible because of the non-zero flux. This theory provides a novel way for exploring the global stability, function and the robustness of ecosystems.