Energy landscape reveals that the budding yeast cell cycle is a robust and adaptive multi-stage process.
ABSTRACT: Quantitatively understanding the robustness, adaptivity and efficiency of cell cycle dynamics under the influence of noise is a fundamental but difficult question to answer for most eukaryotic organisms. Using a simplified budding yeast cell cycle model perturbed by intrinsic noise, we systematically explore these issues from an energy landscape point of view by constructing an energy landscape for the considered system based on large deviation theory. Analysis shows that the cell cycle trajectory is sharply confined by the ambient energy barrier, and the landscape along this trajectory exhibits a generally flat shape. We explain the evolution of the system on this flat path by incorporating its non-gradient nature. Furthermore, we illustrate how this global landscape changes in response to external signals, observing a nice transformation of the landscapes as the excitable system approaches a limit cycle system when nutrients are sufficient, as well as the formation of additional energy wells when the DNA replication checkpoint is activated. By taking into account the finite volume effect, we find additional pits along the flat cycle path in the landscape associated with the checkpoint mechanism of the cell cycle. The difference between the landscapes induced by intrinsic and extrinsic noise is also discussed. In our opinion, this meticulous structure of the energy landscape for our simplified model is of general interest to other cell cycle dynamics, and the proposed methods can be applied to study similar biological systems.
Project description:A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths-the rare trajectories that transit between the folded and unfolded ensembles-using only thermodynamic information, such as a low-dimensional equilibrium free-energy landscape. However, commonly used one-dimensional landscapes typically fall short of this aim, because an empirical coordinate-dependent diffusion coefficient has to be fit to transition-path trajectory data in order to reproduce the transition-path dynamics. We show that an alternative, first-principles free-energy landscape predicts transition-path statistics that agree well with simulations and single-molecule experiments without requiring dynamical data as an input. This "topological configuration" model assumes that distinct, native-like substructures assemble on a time scale that is slower than native-contact formation but faster than the folding of the entire protein. Using only equilibrium simulation data to determine the free energies of these coarse-grained intermediate states, we predict a broad distribution of transition-path transit times that agrees well with the transition-path durations observed in simulations. We further show that both the distribution of finite-time displacements on a one-dimensional order parameter and the ensemble of transition-path trajectories generated by the model are consistent with the simulated transition paths. These results indicate that a landscape based on transient folding intermediates, which are often hidden by one-dimensional projections, can form the basis of a predictive model of protein-folding transition-path dynamics.
Project description: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.
Project description:Microbial communities often perform important functions that depend on inter-species interactions. To improve community function via artificial selection, one can repeatedly grow many communities to allow mutations to arise, and "reproduce" the highest-functioning communities by partitioning each into multiple offspring communities for the next cycle. Since improvement is often unimpressive in experiments, we study how to design effective selection strategies in silico. Specifically, we simulate community selection to improve a function that requires two species. With a "community function landscape", we visualize how community function depends on species and genotype compositions. Due to ecological interactions that promote species coexistence, the evolutionary trajectory of communities is restricted to a path on the landscape. This restriction can generate counter-intuitive evolutionary dynamics, prevent the attainment of maximal function, and importantly, hinder selection by trapping communities in locations of low community function heritability. We devise experimentally-implementable manipulations to shift the path to higher heritability, which speeds up community function improvement even when landscapes are high dimensional or unknown. Video walkthroughs: https://go.nature.com/3GWwS6j ; https://online.kitp.ucsb.edu/online/ecoevo21/shou2/ .
Project description:Elucidating the relationship between the folding landscape of enzymes and their catalytic power has been one of the challenges of modern enzymology. The present work explores this issue by using a simplified folding model to generate the free-energy landscape of an enzyme and then to evaluate the activation barriers for the chemical step in different regions of the landscape. This approach is used to investigate the recent finding that an engineered monomeric chorismate mutase exhibits catalytic efficiency similar to the naturally occurring dimer even though it exhibits the properties of an intrinsically disordered molten globule. It is found that the monomer becomes more confined than its native-like counterpart upon ligand binding but still retains a wider catalytic region. Although the overall rate acceleration is still determined by reduction of the reorganization energy, the detailed contribution of different barriers yields a more complex picture for the chemical process than that of a single path. This work provides insight into the relationship between folding landscapes and catalysis. The computational approach used here may also provide a powerful strategy for modeling single-molecule experiments and designing enzymes.
Project description:Protein folding has been viewed as a difficult problem of molecular self-organization. The search problem involved in folding however has been simplified through the evolution of folding energy landscapes that are funneled. The funnel hypothesis can be quantified using energy landscape theory based on the minimal frustration principle. Strong quantitative predictions that follow from energy landscape theory have been widely confirmed both through laboratory folding experiments and from detailed simulations. Energy landscape ideas also have allowed successful protein structure prediction algorithms to be developed. The selection constraint of having funneled folding landscapes has left its imprint on the sequences of existing protein structural families. Quantitative analysis of co-evolution patterns allows us to infer the statistical characteristics of the folding landscape. These turn out to be consistent with what has been obtained from laboratory physicochemical folding experiments signaling a beautiful confluence of genomics and chemical physics.
Project description:Cell cycles, essential for biological function, have been investigated extensively. However, enabling a global understanding and defining a physical quantification of the stability and function of the cell cycle remains challenging. Based upon a mammalian cell cycle gene network, we uncovered the underlying Mexican hat landscape of the cell cycle. We found the emergence of three local basins of attraction and two major potential barriers along the cell cycle trajectory. The three local basins of attraction characterize the G1, S/G2, and M phases. The barriers characterize the G1 and S/G2 checkpoints, respectively, of the cell cycle, thus providing an explanation of the checkpoint mechanism for the cell cycle from the physical perspective. We found that the progression of a cell cycle is determined by two driving forces: curl flux for acceleration and potential barriers for deceleration along the cycle path. Therefore, the cell cycle can be promoted (suppressed), either by enhancing (suppressing) the flux (representing the energy input) or by lowering (increasing) the barrier along the cell cycle path. We found that both the entropy production rate and energy per cell cycle increase as the growth factor increases. This reflects that cell growth and division are driven by energy or nutrition supply. More energy input increases flux and decreases barrier along the cell cycle path, leading to faster oscillations. We also identified certain key genes and regulations for stability and progression of the cell cycle. Some of these findings were evidenced from experiments whereas others lead to predictions and potential anticancer strategies.
Project description:Kinetic bulk and single molecule folding experiments characterize barrier properties but the shape of folding landscapes between barrier top and native state is difficult to access. Here, we directly extract the full free energy landscape of a single molecule of the GCN4 leucine zipper using dual beam optical tweezers. To this end, we use deconvolution force spectroscopy to follow an individual molecule's trajectory with high temporal and spatial resolution. We find a heterogeneous energy landscape of the GCN4 leucine zipper domain. The energy profile is divided into two stable C-terminal heptad repeats and two less stable repeats at the N-terminus. Energies and transition barrier positions were confirmed by single molecule kinetic analysis. We anticipate that deconvolution sampling is a powerful tool for the model-free investigation of protein energy landscapes.
Project description:It is an outstanding problem to clarify how the RNA sequence is related to its structure and biological functions. We developed a simplified definition of a metric for tree representation of RNA secondary structures and analyzed the conformational energy landscapes of human spliceosomal snRNAs. We discuss the structural properties of the biological sequence by calculating the conformational energy landscapes based on the structural distance between each of the pairs in the set of suboptimal structures. The new index value is introduced for estimating the shapes of distribution patterns in conformational energy landscapes. We apply our method to the five human snRNAs and show that U1 snRNA has a multi-valley profile of the landscape, whereas the landscapes of the other four snRNAs have one steep valley. This result reflects different biological functions of these snRNAs in the pre-mRNA splicing process. The results of analyzing tRNAs and rRNAs show that the conformational energy landscapes of these sequences have multi-valley profiles.
Project description:Macromolecular function is rooted in energy landscapes, where sequence determines not a single structure but an ensemble of conformations. Hence, evolution modifies a protein's function by altering its energy landscape. Here, we recreate the evolutionary pathway between two modern human oncogenes, Src and Abl, by reconstructing their common ancestors. Our evolutionary reconstruction combined with x-ray structures of the common ancestor and pre-steady-state kinetics reveals a detailed atomistic mechanism for selectivity of the successful cancer drug Gleevec. Gleevec affinity is gained during the evolutionary trajectory toward Abl and lost toward Src, primarily by shifting an induced-fit equilibrium that is also disrupted in the clinical T315I resistance mutation. This work reveals the mechanism of Gleevec specificity while offering insights into how energy landscapes evolve.
Project description:To traverse complex three-dimensional terrain with large obstacles, animals and robots must transition across different modes. However, the most mechanistic understanding of terrestrial locomotion concerns how to generate and stabilize near-steady-state, single-mode locomotion (e.g. walk, run). We know little about how to use physical interaction to make robust locomotor transitions. Here, we review our progress towards filling this gap by discovering terradynamic principles of multi-legged locomotor transitions, using simplified model systems representing distinct challenges in complex three-dimensional terrain. Remarkably, general physical principles emerge across diverse model systems, by modelling locomotor-terrain interaction using a potential energy landscape approach. The animal and robots' stereotyped locomotor modes are constrained by physical interaction. Locomotor transitions are stochastic, destabilizing, barrier-crossing transitions on the landscape. They can be induced by feed-forward self-propulsion and are facilitated by feedback-controlled active adjustment. General physical principles and strategies from our systematic studies already advanced robot performance in simple model systems. Efforts remain to better understand the intelligence aspect of locomotor transitions and how to compose larger-scale potential energy landscapes of complex three-dimensional terrains from simple landscapes of abstracted challenges. This will elucidate how the neuromechanical control system mediates physical interaction to generate multi-pathway locomotor transitions and lead to advancements in biology, physics, robotics and dynamical systems theory.