Potential Landscapes, Bifurcations, and Robustness of Tristable Networks

Interlinked bi-stable switches govern the cell fate commitment of embryonic stem cells

The development of embryonic stem (ES) cells to extraembryonic trophectoderm and primitive endoderm lineages manifests distinct steady-state expression patterns of two key transcription factors-Oct4 and Nanog. How dynamically such kind of steady-state expressions are maintained remains elusive. Herein, we demonstrate that steady-state dynamics involving two bistable switches which are interlinked via a stepwise (Oct4) and a mushroom-like (Nanog) manner orchestrate the fate specification of ES cells. Our hypothesis qualitatively reconciles various experimental observations and elucidates how different feedback and feedforward motifs orchestrate the extraembryonic development and stemness maintenance of ES cells. Importantly, the model predicts strategies to optimize the dynamics of self-renewal and differentiation of embryonic stem cells that may have therapeutic relevance in the future.

State-transition modeling of blood transcriptome predicts disease evolution and treatment response in chronic myeloid leukemia

Chronic myeloid leukemia (CML) is initiated and maintained by BCR::ABL which is clinically targeted using tyrosine kinase inhibitors (TKIs). TKIs can induce long-term remission but are also not curative. Thus, CML is an ideal system to test our hypothesis that transcriptome-based state-transition models accurately predict cancer evolution and treatment response. We collected time-sequential blood samples from tetracycline-off (Tet-Off) BCR::ABL-inducible transgenic mice and wild-type controls. From the transcriptome, we constructed a CML state-space and a three-well leukemogenic potential landscape. The potential's stable critical points defined observable disease states. Early states were characterized by anti-CML genes opposing leukemia; late states were characterized by pro-CML genes. Genes with expression patterns shaped similarly to the potential landscape were identified as drivers of disease transition. Re-introduction of tetracycline to silence the BCR::ABL gene returned diseased mice transcriptomes to a near healthy state, without reaching it, suggesting parts of the transition are irreversible. TKI only reverted the transcriptome to an intermediate disease state, without approaching a state of health; disease relapse occurred soon after treatment. Using only the earliest time-point as initial conditions, our state-transition models accurately predicted both disease progression and treatment response, supporting this as a potentially valuable approach to time clinical intervention, before phenotypic changes become detectable.

Protocol for potential energy-based bifurcation analysis, parameter searching, and phase diagram analysis of noncanonical bistable switches

We have explored the design principles of noncanonical bistable switches using high-throughput bifurcation analysis of positive feedback loops under dual signaling. Here, we present a protocol to carry out bifurcation analysis using pseudo-potential energy of the dynamical system. We also describe steps to perform automated parameter searching for canonical and noncanonical switches and multi-parameter phase diagram analysis of these switches. For complete details on the use and execution of this protocol, please refer to Das et al.1.

State-transition Modeling of Blood Transcriptome Predicts Disease Evolution and Treatment Response in Chronic Myeloid Leukemia

Chronic myeloid leukemia (CML) is initiated and maintained by BCR::ABL which is clinically targeted using tyrosine kinase inhibitors (TKIs). TKIs can induce long-term remission but are also not curative. Thus, CML is an ideal system to test our hypothesis that transcriptome-based state-transition models accurately predict cancer evolution and treatment response. We collected time-sequential blood samples from tetracycline-off (Tet-Off) BCR::ABL-inducible transgenic mice and wild-type controls. From the transcriptome, we constructed a CML state-space and a three-well leukemogenic potential landscape. The potential's stable critical points defined observable disease states. Early states were characterized by anti-CML genes opposing leukemia; late states were characterized by pro-CML genes. Genes with expression patterns shaped similarly to the potential landscape were identified as drivers of disease transition. Re-introduction of tetracycline to silence the BCR::ABL gene returned diseased mice transcriptomes to a near healthy state, without reaching it, suggesting parts of the transition are irreversible. TKI only reverted the transcriptome to an intermediate disease state, without approaching a state of health; disease relapse occurred soon after treatment. Using only the earliest time-point as initial conditions, our state-transition models accurately predicted both disease progression and treatment response, supporting this as a potentially valuable approach to time clinical intervention even before phenotypic changes become detectable.

Coupled Mutual Inhibition and Mutual Activation Motifs as Tools for Cell-Fate Control

Multistability is central to biological systems. It plays a crucial role in adaptation, evolvability, and differentiation. The presence of positive feedback loops can enable multistability. The simplest of such feedback loops are (a) a mutual inhibition (MI) loop, (b) a mutual activation (MA) loop, and (c) self-activation. While it is established that all three motifs can give rise to bistability, the characteristic differences in the bistability exhibited by each of these motifs is relatively less understood. Here, we use dynamical simulations across a large ensemble of parameter sets and initial conditions to study the bistability characteristics of these motifs. Furthermore, we investigate the utility of these motifs for achieving coordinated expression through cyclic and parallel coupling amongst them. Our analysis revealed that MI-based architectures offer discrete and robust control over gene expression, multistability, and coordinated expression among multiple genes, as compared to MA-based architectures. We then devised a combination of MI and MA architectures to improve coordination and multistability. Such designs help enhance our understanding of the control structures involved in robust cell-fate decisions and provide a way to achieve controlled decision-making in synthetic systems.

Incoherent modulation of bi-stable dynamics orchestrates the Mushroom and Isola bifurcations

In biological networks, steady state dynamics of cell-fate regulatory genes often exhibit Mushroom and Isola kind of bifurcations. How these complex bifurcations emerge for these complex networks, and what are the minimal network structures that can generate these bifurcations, remain elusive. Herein, by employing Waddington's landscape theory and bifurcation analysis, we demonstrate that Mushroom and Isola bifurcations can be realized with four minimal network motifs that are constituted by combining a positive feedback motif with various incoherent feed-forward loops. Our study reveals that the intrinsic bi-stable dynamics originating from the positive feedback motif can be fine-tuned by altering the extent of the incoherence of these minimal networks to produce these complex bifurcations. These modeling insights will be useful in identifying the possible network motifs that may give rise to either Mushroom or Isola bifurcation in other biological systems.

Emergent Bistable Switches from the Incoherent Feed-Forward Signaling of a Positive Feedback Loop

Bistability is intrinsically connected to various decision making processes in living systems. The operating principles of a bistable switch, generated from a positive feedback loop, are well understood both in natural and synthetic settings. However, the fate of dynamic modularity of a positive feedback loop is unknown when it is connected to another dynamically modular signaling motif. In order to address this, here we investigate feed-forward signaling of a positive feedback loop to determine the fate of a bistable switch under such signaling. Using the potential energy based high-throughput bifurcation analysis method, we uncover that in addition to the conventional bistability the hybrid motifs generate various emergent bistable switches, namely mushroom and isola switches, which are not produced by the individual motifs. Using random parameter sampling, network perturbation, and phase plane analysis, we establish the design principles of such emergent behaviors. Incoherent feed-forward signaling of a positive feedback loop with distinct regulatory thresholds of the two arms of the feed-forward loop are the key requirements for such emergent behaviors. Our calculations show that the specific types of atypical bistable responses depend on the logic gate configuration of the signals. However, the emergent bistable behaviors of the hybrid networks do not depend on the nature of the positive feedback loop.

Exact Probability Landscapes of Stochastic Phenotype Switching in Feed-Forward Loops: Phase Diagrams of Multimodality

Feed-forward loops (FFLs) are among the most ubiquitously found motifs of reaction networks in nature. However, little is known about their stochastic behavior and the variety of network phenotypes they can exhibit. In this study, we provide full characterizations of the properties of stochastic multimodality of FFLs, and how switching between different network phenotypes are controlled. We have computed the exact steady-state probability landscapes of all eight types of coherent and incoherent FFLs using the finite-butter Accurate Chemical Master Equation (ACME) algorithm, and quantified the exact topological features of their high-dimensional probability landscapes using persistent homology. Through analysis of the degree of multimodality for each of a set of 10,812 probability landscapes, where each landscape resides over 10⁵–10⁶ microstates, we have constructed comprehensive phase diagrams of all relevant behavior of FFL multimodality over broad ranges of input and regulation intensities, as well as different regimes of promoter binding dynamics. In addition, we have quantified the topological sensitivity of the multimodality of the landscapes to regulation intensities. Our results show that with slow binding and unbinding dynamics of transcription factor to promoter, FFLs exhibit strong stochastic behavior that is very different from what would be inferred from deterministic models. In addition, input intensity play major roles in the phenotypes of FFLs: At weak input intensity, FFL exhibit monomodality, but strong input intensity may result in up to 6 stable phenotypes. Furthermore, we found that gene duplication can enlarge stable regions of specific multimodalities and enrich the phenotypic diversity of FFL networks, providing means for cells toward better adaptation to changing environment. Our results are directly applicable to analysis of behavior of FFLs in biological processes such as stem cell differentiation and for design of synthetic networks when certain phenotypic behavior is desired.