Chun-Biu Li

Multiscale complex network of protein conformational fluctuations in single-molecule time series

Conformational dynamics of proteins can be interpreted as itinerant motions as the protein traverses from one state to another on a complex network in conformational space or, more generally, in state space. Here we present a scheme to extract a multiscale state space network (SSN) from a single-molecule time series. Analysis by this method enables us to lift degeneracy—different physical states having the same value for a measured observable—as much as possible. A state or node in the network is defined not by the value of the observable at each time but by a set of subsequences of the observable over time. The length of the subsequence can tell us the extent to which the memory of the system is able to predict the next state. As an illustration, we investigate the conformational fluctutation dynamics probed by single-molecule electron transfer (ET), detected on a photon-by-photon basis. We show that the topographical features of the SSNs depend on the time scale of observation; the longer the time scale, the simpler the underlying SSN becomes, leading to a transition of the dynamics from anomalous diffusion to normal Brownian diffusion.

Topographical complexity of multidimensional energy landscapes

A scheme for visualizing and quantifying the complexity of multidimensional energy landscapes and multiple pathways is presented employing principal component-based disconnectivity graphs and the Shannon entropy of relative “sizes” of superbasins. The principal component-based disconnectivity graphs incorporate a metric relationship between the stationary points of the system, which enable us to capture not only the actual assignment of the superbasins but also the size of each superbasin in the multidimensional configuration space. The landscape complexity measure quantifies the degree of topographical complexity of a multidimensional energy landscape and tells us at which energy regime branching of the main path becomes significant, making the system more likely to be kinetically trapped in local minima. The path complexity measure quantifies the difficulty encountered by the system to reach a connected local minimum by the path in question, implying that the more significant the branching points along the path the more difficult it is to end up in the desired local minimum. As an illustrative example, we apply this analysis to two kinds of small model protein systems exhibiting a highly frustrated and an ideal funnel-like energy landscape.

Fast Step Transition and State Identification (STaSI) for Discrete Single-Molecule Data Analysis

We introduce a step transition and state identification (STaSI) method for piecewise constant single-molecule data with a newly derived minimum description length equation as the objective function. We detect the step transitions using the Student’s t test and group the segments into states by hierarchical clustering. The optimum number of states is determined based on the minimum description length equation. This method provides comprehensive, objective analysis of multiple traces requiring few user inputs about the underlying physical models and is faster and more precise in determining the number of states than established and cutting-edge methods for single-molecule data analysis. Perhaps most importantly, the method does not require either time-tagged photon counting or photon counting in general and thus can be applied to a broad range of experimental setups and analytes.

New Quantification of Local Transition Heterogeneity of Multiscale Complex Networks Constructed from Single-Molecule Time Series

A new measure is presented to quantify the local topographical feature, i.e., diversity in transitions from a state to the others, on complex networks. This measure is composed of two contributions: one is related to the number of outgoing links from a state (known as degree) and the other is related to heterogeneity in transition probabilities from a state to the others associated with the links. To illustrate the potential of the new measure, we apply it to the multiscale state space networks (SSNs) extracted directly from the single-molecule time series of protein fluctuation of the NADH:flavin oxidoreductase complex by using a recently developed technique [Li, C. B.; Yang, H.; Komatsuzaki, T. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 536]. We find that the multiscale SSN network structures dependent on the time scale of observation are not differentiated significantly in the topological feature of the SSNs where the connectivity pattern among the nodes is solely taken into account, but instead in the weighted properties of the network including the heterogeneous strengths of transitions and the resident probabilities of the nodes. The relationship of the transition heterogeneity with the anomalous diffusion observed in the single-molecule measurement is also discussed.

Bifurcation of no-return transition states in many-body chemical reactions

A new method is presented to study bifurcation of no-return transition states (TSs) at potential saddles for systems of many degrees of freedom (dof). The method enables us to investigate analytically when and how the no-return TS bifurcates. Our method reveals a new aspect of bifurcation for systems of many dof, i.e., the action variables of the bath dof play a role of control parameters as long as they remain approximately conserved. As an illustrative example, we demonstrate our new method by using a three atomic exchange reaction. The bifurcation of no-return TSs gives rise to a short-lived intermediate state at the saddle, which results in the overestimation of the reaction rate. Hence, the understanding of the bifurcation of the no-return TS is crucial to capture the complexity in kinetics and dynamics of the reactions. The definability of no-return TSs in many-body chemical reactions is also addressed under the occurrence of bifurcation above the reaction threshold.

Time-Resolved Single Molecule Fluorescence Spectroscopy of an alpha-Chymotrypsin Catalyzed Reaction

Single molecule fluorescence spectroscopy offers great potential for studying enzyme kinetics. A number of fluorescence reporter systems allow for monitoring the sequence of individual reaction events with a confocal microscope. When using a time-correlated single photon counting (TCSPC) detection scheme, additional information about the fluorescence lifetimes of the fluorophores can be obtained. We have applied a TCSPC detection scheme for studying the kinetics of α-chymotrypsin hydrolyzing a double-substituted rhodamine 110-based fluorogenic substrate in a two-step reaction. On the basis of the lifetime information, it was possible to discriminate the intermediate and the final product. At the high substrate concentration used, only the formation of the intermediate was observed. No rebinding of the intermediate followed by rhodamine 110 formation occurred at these high concentrations. We have further found no alterations in the fluorescence lifetime of this intermediate that would indicate changes in the local environment of the fluorophore originating from strong interactions with the enzyme. Our results clearly show the power of using lifetime-resolved measurements for investigating enzymatic reactions at the single molecule level.

Dynamical Hierarchy in Transition States of Reactions

Abstract.We present a partial normalization procedure of Lie canonical perturbation theory to elucidate the phase space geometry of the transition state in the multidimensional phase space for a wide range of energy above the threshold. State selectivity and dynamical correlation along the evolution of reactions will also be discussed.

Reactivity boundaries for chemical reactions associated with higher-index and multiple saddles

Yutaka Nagahata, Hiroshi Teramoto, 2 Chun-Biu Li, 3, 4 Shinnosuke Kawai, 2 and Tamiki Komatsuzaki 2, 4, ∗ Graduate School of Life Science, Hokkaido University, Kita 12, Nishi 6,Kita-ku, Sapporo 060-0812, Japan Molecule and Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan Graduate School of Science, Department of Mathematics, Hokkaido University, Kita 12, Nishi 6,Kita-ku, Sapporo 060-0812, Japan Research Center for Integrative Mathematics, Hokkaido University, Kita 20, Nishi 10, Kita-Ku, Sapporo, Hokkaido, 001-0020, Japan (Dated: May 11, 2014)

Error-based Extraction of States and Energy Landscapes from Experimental Single-Molecule Time-Series

Characterization of states, the essential components of the underlying energy landscapes, is one of the most intriguing subjects in single-molecule (SM) experiments due to the existence of noise inherent to the measurements. Here we present a method to extract the underlying state sequences from experimental SM time-series. Taking into account empirical error and the finite sampling of the time-series, the method extracts a steady-state network which provides an approximation of the underlying effective free energy landscape. The core of the method is the application of rate-distortion theory from information theory, allowing the individual data points to be assigned to multiple states simultaneously. We demonstrate the methods proficiency in its application to simulated trajectories as well as to experimental SM fluorescence resonance energy transfer (FRET) trajectories obtained from isolated agonist binding domains of the AMPA receptor, an ionotropic glutamate receptor that is prevalent in the central nervous system.

Why plants make puzzle cells, and how their shape emerges

The shape and function of plant cells are often highly interdependent. The puzzle-shaped cells that appear in the epidermis of many plants are a striking example of a complex cell shape, however their functional benefit has remained elusive. We propose that these intricate forms provide an effective strategy to reduce mechanical stress in the cell wall of the epidermis. When tissue-level growth is isotropic, we hypothesize that lobes emerge at the cellular level to prevent formation of large isodiametric cells that would bulge under the stress produced by turgor pressure. Data from various plant organs and species support the relationship between lobes and growth isotropy, which we test with mutants where growth direction is perturbed. Using simulation models we show that a mechanism actively regulating cellular stress plausibly reproduces the development of epidermal cell shape. Together, our results suggest that mechanical stress is a key driver of cell-shape morphogenesis.