International Workshop on Quantitative Biology 2012

Complex dynamics of a wide range of biophysical systems, such as the opened/closed gating of ion channels, the On/Off fluorescent kinetics in single enzymatic turnovers, are often probed experimentally in the form of time series with finite discrete levels. Statistics of the dwell-time time series, the stationary state distributions (SSDs) associated with the chronological sequence of the lengths of time that the system dwells at each level, have been studied to infer the underlying dynamics and kinetics of the system. However, it is well known that the underlying kinetic scheme, a hidden Markov model (HMM) composed of states and state transitions, cannot be identified uniquely from the SSDs of dwell-times because some states and the associated transitions of the underlying HMM are hidden and cannot be resolved by finite-level measurements. Here, I present an information-theoretic framework to quantify the amount of excessive information contained in a given HMM that is not warranted by the measured dwell-time statistics. In this framework, the HMM with minimum excessive information can be uniquely identified and it is regarded as the most objective representation one can extract from the observed data. The minimum excessive information enables us to compare the degree of identifiability of the underlying HMM for measurements of the same system using different observables. The method is applied to a single molecule (SM) enzymatic turnover experiment, and the origin of dynamic disorder is discussed in terms of the network properties of the HMM.

High Density cultures of yeast auto-synchronize their physiology, resulting in a demarcation of anabolic and catabolic processes. Here, I present our recent data on quantifying chromatin, membrane, metabolite and flux dynamics. How these data are integrated and our modeling approaches will be discussed.

Data assimilation (DA) is a fundamental technique that combines numerical simulation models and observational/experimental data through a Bayesian estimation of continuously changing status behind target systems. DA was originally developed in geophysical areas, especially in meteorology and oceanology, and is nowadays applied in other various fields of science such as space, life and industrial sciences. The eventual goal of DA is to provide next-generation simulation models that can predict future statuses. In this study, DA is applied for the first time to the intracellular fluid dynamics focusing on the cytoplasmic streaming in Caenorhabditis elegans embryo, which is observed shortly after the fertilization. Niwayama et al. [Proc. Natl. Acad. Sci., 2011] proposed a hydrodynamic simulation model that qualitatively reproduces the velocity distribution in the cell measured by the particle image velocimetry. The purpose of the present work is to quantitatively obtain the spatial and temporal distributions of the force generated by the molecular motors, which is considered to drive the cytoplasmic streaming. A number of ''particles'', each of which is a realization of a set of model parameters, are sampled from an assumed prior distribution function associated with the apparent velocity structure along the cell wall starting from the anterior to the posterior. Then the hydrodynamic simulation calculates a likelihood function, which is a measure of how the simulation well explains the observation, for each particle. Finally, the targeting posterior distribution function is obtained on the basis of the Bayes’ theorem. The estimated force distribution that is reconstituted from the maximum-a-posteriori solution, which attains the posterior distribution function maximum, is found no longer to be proportional to the velocity distribution. This fact may indicate strong forces are generated even at region where the streaming is slow. In the presentation, we introduce the foundations of DA and discuss the new findings associated with the relation between the driving force and the velocity distributions associated with the cytoplasmic streaming in C. elegans embryo.

The quality of sensing and response to external stimuli constitutes a basic element in the selective performance of living organisms. Here we consider the response of Escherichia coli to chemical stimuli. For moderate amplitudes, the bacterial response to generic profiles of sensed chemicals is reconstructed from its response function to an impulse, which then controls the efficiency of bacterial motility. We introduce a method for measuring the impulse response function based on coupling microfluidic experiments and inference methods: The response function is inferred using Bayesian methods from the observed trajectories of bacteria swimming in microfluidically controlled chemical fields. The notable advantages are that the method is based on the bacterial swimming response, it is noninvasive, without any genetic and/or mechanical preparation, and assays the behavior of the whole flagella bundle. We exploit the inference method to measure responses to aspartate and α-methylaspartate—measured previously by other methods—as well as glucose, leucine, and serine. The response to the attractant glucose is shown to be biphasic and perfectly adapted, as for aspartate. The response to the attractant serine is shown to be biphasic yet imperfectly adapted, that is, the response function has a nonzero (positive) integral. The adaptation of the response to the repellent leucine is also imperfect, with the sign of the two phases inverted with respect to serine. The diversity in the bacterial population of the response function and its dependency upon the background concentration are quantified.

Post-translational protein modifications play a fundamental role in gene regulation, but the dynamics of these modifications remain difficult to quantify in living cells. Part of the problem is that standard labeling techniques based on permanent fluorescent fusion tags such as GFP are unable to distinguish modified forms of the same protein. For example, although GFP has been used to visualize the live-cell dynamics of RNA polymerase II (pol II), it has been difficult to distinguish actively elongating forms of pol II (phosphorylated at serine 2) from freely diffusing (unphosphorylated) or initiated but stationary forms (phosphorylated at serine 5). This complicates the analysis of pol II transcription dynamics and leaves some doubt about deduced results. Here we overcome this difficulty using FabLEM (Fab-based Live Endogenous Modification labeling), a recently developed technique utilizing fluorescent antigen binding fragments (Fab) to reversibly label protein modifications in living cells with minimal disturbance [1]. Specifically, we are visualizing pol II phosphorylation in conjunction with histone acetylation at an activated gene array in single living cells. By timing the recruitment of these modifications to the gene array, this work is the first to distinguish in vivo transcription initiation kinetics from recruitment and elongation kinetics. This data place tight constraints on quantitative models for pol II transcription and enable unbiased and accurate estimates of model parameters. In contrast to previous live-cell analyses of pol II kinetics, our data now argue that the transition from initiation to elongation is highly efficient, approaching values over 80%. This efficient promoter escape appears to be driven by histone H3K27 acetylation, as elongating forms of pol II accumulate more quickly at arrays with more acetylation. Surprisingly, initiated forms of pol II accumulate at the same rate regardless of array acetylation level, indicating that enhanced array accessibility is not the main factor contributing to the high transcription efficiency. Our data therefore demonstrate that, in addition to facilitating chromatin decondensation, histone acetylation can also regulate distinct steps of the pol II transcription cycle.

[1] Y. Hayashi-Takanaka, K. Yamagata, T. Wakayama, T.J. Stasevich, T. Kainuma, T. Tsurimoto, M. Tachibana, Y. Shinkai, H. Kurumizaka, N. Nozaki, and H. Kimura, ''Tracking epigenetic histone modifications in single cells using Fab-based live endogenous modification labeling,'' Nucleic Acids Res., 39, 6475-6488 (2011).

Successful partitioning of chromosomes in mitosis relies on the bipolar attachment of sister chromatids (chromosome bi-orientation). At the center of paired kinetochores (the inner centromere), shugoshin Sgo1 protects centromeric cohesin from dissociation by a prophase pathway, and the CPC (chromosomal passenger complex) plays a crucial role in correcting erroneous microtubule-kinetochore attachment. Sgo1 and CPC form a complex at the inner centromeres depending on two histone phosphorylations, H2A-pT120 and H3-pT3, which are mediated by kinetochore-associated kinase Bub1 and cohesin-associated kinase Haspin, respectively. Because Sgo1 favors H2A-pT120-enriched sites, Sgo1 redistributes from the inner centromeres to kinetochores at the metaphase-anaphase transition. This redistribution of Sgo1 is essential for de-protecting cohesin and separating chromosomes at anaphase. Moreover, we reveal that the centromeric heterochromatin plays a crucial role in limiting Sgo1 redistribution during metaphase, a disorder of that might be the major reason for the chromosomal instability widely observed in cancer cells.