Reaction-diffusion kinetics on lattice at the microscopic scale

Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME), can simulate for extended spatial and temporal scales but cannot directly account for the microscopic effects in the cell such as volume exclusion and diffusion-influenced reactions. Nonetheless, schemes based on the high-resolution microscopic lattice method (MLM) can directly simulate these effects by representing each finite-sized molecule explicitly as a random walker on fine lattice voxels. The theory and consistency of MLM in simulating diffusion-influenced reactions have not been clarified in detail. Here, we examine MLM in solving diffusion-influenced reactions in 3D space by employing the Spatiocyte simulation scheme. Applying the random walk theory, we construct the general theoretical framework underlying the method and obtain analytical expressions for the total rebinding probability and the effective reaction rate. By matching Collins-Kimball and lattice-based rate constants, we obtained the exact expressions to determine the reaction acceptance probability and voxel size. We found that the size of voxel should be about 2% larger than the molecule. MLM is validated by numerical simulations, showing good agreement with the off-lattice particle-based method, eGFRD. MLM run time is more than an order of magnitude faster than eGFRD when diffusing macromolecules with typical concentrations in the cell. MLM also showed good agreements with eGFRD and mean-field models in case studies of two basic motifs of intracellular signaling, the protein production-degradation process and the dual phosphorylation cycle. Moreover, when a reaction compartment is populated with volume-excluding obstacles, MLM captures the non-classical reaction kinetics caused by anomalous diffusion of reacting molecules

Flexible and dynamic nucleosome fiber in living mammalian cells

© Landes Bioscience, 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Nucleus 4 (2013): 349-356, doi:10.4161/nucl.26053.Genomic DNA is organized three dimensionally within cells as chromatin and is searched and read by various proteins by an unknown mechanism; this mediates diverse cell functions. Recently, several pieces of evidence, including our cryomicroscopy and synchrotron X-ray scattering analyses, have demonstrated that chromatin consists of irregularly folded nucleosome fibers without a 30-nm chromatin fiber (i.e., a polymer melt-like structure). This melt-like structure implies a less physically constrained and locally more dynamic state, which may be crucial for protein factors to scan genomic DNA. Using a combined approach of fluorescence correlation spectroscopy, Monte Carlo computer simulations, and single nucleosome imaging, we demonstrated the flexible and dynamic nature of the nucleosome fiber in living mammalian cells. We observed local nucleosome fluctuation (~50 nm movement per 30 ms) caused by Brownian motion. Our in vivo-in silico results suggest that local nucleosome dynamics facilitate chromatin accessibility and play a critical role in the scanning of genome information.This work was supported by a grant-in-aid for a MEXT grant, JST CREST, Yamada Science Foundation and Takeda Science Foundation. Nozaki T and Hihara A are JSPS fellows

Density imaging of heterochromatin in live cells using orientation-independent-DIC microscopy

© The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Molecular Biology of the Cell 28 (2017): 3349-3359, doi:10.1091/mbc.E17-06-0359.In eukaryotic cells, highly condensed inactive/silenced chromatin has long been called “heterochromatin.” However, recent research suggests that such regions are in fact not fully transcriptionally silent and that there exists only a moderate access barrier to heterochromatin. To further investigate this issue, it is critical to elucidate the physical properties of heterochromatin such as its total density in live cells. Here, using orientation-independent differential interference contrast (OI-DIC) microscopy, which is capable of mapping optical path differences, we investigated the density of the total materials in pericentric foci, a representative heterochromatin model, in live mouse NIH3T3 cells. We demonstrated that the total density of heterochromatin (208 mg/ml) was only 1.53-fold higher than that of the surrounding euchromatic regions (136 mg/ml) while the DNA density of heterochromatin was 5.5- to 7.5-fold higher. We observed similar minor differences in density in typical facultative heterochromatin, the inactive human X chromosomes. This surprisingly small difference may be due to that nonnucleosomal materials (proteins/RNAs) (∼120 mg/ml) are dominant in both chromatin regions. Monte Carlo simulation suggested that nonnucleosomal materials contribute to creating a moderate access barrier to heterochromatin, allowing minimal protein access to functional regions. Our OI-DIC imaging offers new insight into the live cellular environments.This work was supported by MEXT and Japan Society for the Promotion of Science (JSPS) grants (Nos. 23115005 and 16H04746, respectively), as well as a Japan Science and Technology Agency (JST) CREST grant (No. JPMJCR15G2). R.I. and T.N. are JSPS Fellows. R.I. was supported by the SOKENDAI Short-Stay Study Abroad Program in fiscal year 2016

A comprehensive molecular interaction map of the budding yeast cell cycle

With the accumulation of data on complex molecular machineries coordinating cell-cycle dynamics, coupled with its central function in disease patho-physiologies, it is becoming increasingly important to collate the disparate knowledge sources into a comprehensive molecular network amenable to systems-level analyses. In this work, we present a comprehensive map of the budding yeast cell-cycle, curating reactions from ∼600 original papers. Toward leveraging the map as a framework to explore the underlying network architecture, we abstract the molecular components into three planes—signaling, cell-cycle core and structural planes. The planar view together with topological analyses facilitates network-centric identification of functions and control mechanisms. Further, we perform a comparative motif analysis to identify around 194 motifs including feed-forward, mutual inhibitory and feedback mechanisms contributing to cell-cycle robustness. We envisage the open access, comprehensive cell-cycle map to open roads toward community-based deeper understanding of cell-cycle dynamics

Fragilities Caused by Dosage Imbalance in Regulation of the Budding Yeast Cell Cycle

Cells can maintain their functions despite fluctuations in intracellular parameters, such as protein activities and gene expression levels. This commonly observed biological property of cells is called robustness. On the other hand, these parameters have different limitations, each reflecting the property of the subsystem containing the parameter. The budding yeast cell cycle is quite fragile upon overexpression of CDC14, but is robust upon overexpression of ESP1. The gene products of both CDC14 and ESP1 are regulated by 1∶1 binding with their inhibitors (Net1 and Pds1), and a mathematical model predicts the extreme fragility of the cell cycle upon overexpression of CDC14 and ESP1 caused by dosage imbalance between these genes. However, it has not been experimentally shown that dosage imbalance causes fragility of the cell cycle. In this study, we measured the quantitative genetic interactions of these genes by performing combinatorial “genetic tug-of-war” experiments. We first showed experimental evidence that dosage imbalance between CDC14 and NET1 causes fragility. We also showed that fragility arising from dosage imbalance between ESP1 and PDS1 is masked by CDH1 and CLB2. The masking function of CLB2 was stabilization of Pds1 by its phosphorylation. We finally modified Chen's model according to our findings. We thus propose that dosage imbalance causes fragility in biological systems