Statistical mechanics of transport in disordered lattices and reaction-diffusion systems

This thesis is the report of a study of several different problems in statistical physics. The first two are about random walks in a disordered lattice, with applications to a biological system, the third is about reaction-diffusion systems, particularly the phenomena of front propagation and pattern formation, and the last is about a special kind of evolving complex networks, the addition-deletion network. The motivation for the first of the two random walk investigations is provided by the diffusion of molecules in cell membranes. A mathematical model is constructed in order to predict molecular diffusion phenomena relating to the so-called compartmentalized view of the cell membrane. The theoretical results are compared with experimental observations available in the literature. The second random walk part in the thesis contains contributions to the analysis of transport in disordered systems via effective medium theory. Calculation of time-dependent transport quantities are presented along with discussion of effects of finite system size, significance of long-range memory functions, and consequences of correlated disorder. The investigation of reaction-diffusion systems that deals with front propagation is concerned with providing a method of studying transient dynamics in such systems whereas the study of pattern formation focuses on determining necessary conditions for such patterns to arise in situations wherein sub- and super-diffusion are present in addition to simple diffusion. In the network study, results are reported on cluster size distribution in addition-deletion networks, on the basis of both numerical and analytic investigations

Development of ultrafast camera-based single fluorescent-molecule imaging for cell biology

細胞膜上の分子がバレエの群舞のように見えてきた： 1蛍光分子の感度で、究極速度で撮像できるカメラを開発. 京都大学プレスリリース. 2023-06-06.The spatial resolution of fluorescence microscopy has recently been greatly enhanced. However, improvements in temporal resolution have been limited, despite their importance for examining living cells. Here, we developed an ultrafast camera system that enables the highest time resolutions in single fluorescent-molecule imaging to date, which were photon-limited by fluorophore photophysics: 33 and 100 µs with single-molecule localization precisions of 34 and 20 nm, respectively, for Cy3, the optimal fluorophore we identified. Using theoretical frameworks developed for the analysis of single-molecule trajectories in the plasma membrane (PM), this camera successfully detected fast hop diffusion of membrane molecules in the PM, previously detectable only in the apical PM using less preferable 40-nm gold probes, thus helping to elucidate the principles governing the PM organization and molecular dynamics. Furthermore, as described in the companion paper, this camera allows simultaneous data acquisitions for PALM/dSTORM at as fast as 1 kHz, with 29/19 nm localization precisions in the 640 × 640 pixel view-field

Ultrafast single-molecule imaging reveals focal adhesion nano-architecture and molecular dynamics

細胞膜上の分子がバレエの群舞のように見えてきた： 1蛍光分子の感度で、究極速度で撮像できるカメラを開発. 京都大学プレスリリース. 2023-06-06.Using our newly developed ultrafast camera described in the companion paper, we reduced the data acquisition periods required for photoactivation/photoconversion localization microscopy (PALM, using mEos3.2) and direct stochastic reconstruction microscopy (dSTORM, using HMSiR) by a factor of ≈30 compared with standard methods, for much greater view-fields, with localization precisions of 29 and 19 nm, respectively, thus opening up previously inaccessible spatiotemporal scales to cell biology research. Simultaneous two-color PALM-dSTORM and PALM-ultrafast (10 kHz) single fluorescent-molecule imaging-tracking has been realized. They revealed the dynamic nanoorganization of the focal adhesion (FA), leading to the compartmentalized archipelago FA model, consisting of FA-protein islands with broad diversities in size (13–100 nm; mean island diameter ≈30 nm), protein copy numbers, compositions, and stoichiometries, which dot the partitioned fluid membrane (74-nm compartments in the FA vs. 109-nm compartments outside the FA). Integrins are recruited to these islands by hop diffusion. The FA-protein islands form loose ≈320 nm clusters and function as units for recruiting FA proteins

Confined diffusion of transmembrane proteins and lipids induced by the same actin meshwork lining the plasma membrane.

The mechanisms by which the diffusion rate in the plasma membrane (PM) is regulated remain unresolved, despite their importance in spatially regulating the reaction rates in the PM. Proposed models include entrapment in nanoscale noncontiguous domains found in PtK2 cells, slow diffusion due to crowding, and actin-induced compartmentalization. Here, by applying single-particle tracking at high time resolutions, mainly to the PtK2-cell PM, we found confined diffusion plus hop movements (termed "hop diffusion") for both a nonraft phospholipid and a transmembrane protein, transferrin receptor, and equal compartment sizes for these two molecules in all five of the cell lines used here (actual sizes were cell dependent), even after treatment with actin-modulating drugs. The cross-section size and the cytoplasmic domain size both affected the hop frequency. Electron tomography identified the actin-based membrane skeleton (MSK) located within 8.8 nm from the PM cytoplasmic surface of PtK2 cells and demonstrated that the MSK mesh size was the same as the compartment size for PM molecular diffusion. The extracellular matrix and extracellular domains of membrane proteins were not involved in hop diffusion. These results support a model of anchored TM-protein pickets lining actin-based MSK as a major mechanism for regulating diffusion

Confining Domains Lead to Reaction Bursts: Reaction Kinetics in the Plasma Membrane

Confinement of molecules in specific small volumes and areas within a cell is likely to be a general strategy that is developed during evolution for regulating the interactions and functions of biomolecules. The cellular plasma membrane, which is the outermost membrane that surrounds the entire cell, was considered to be a continuous two-dimensional liquid, but it is becoming clear that it consists of numerous nano-meso-scale domains with various lifetimes, such as raft domains and cytoskeleton-induced compartments, and membrane molecules are dynamically trapped in these domains. In this article, we give a theoretical account on the effects of molecular confinement on reversible bimolecular reactions in a partitioned surface such as the plasma membrane. By performing simulations based on a lattice-based model of diffusion and reaction, we found that in the presence of membrane partitioning, bimolecular reactions that occur in each compartment proceed in bursts during which the reaction rate is sharply and briefly increased even though the asymptotic reaction rate remains the same. We characterized the time between reaction bursts and the burst amplitude as a function of the model parameters, and discussed the biological significance of the reaction bursts in the presence of strong inhibitor activity

Effects of confinement on the statistics of encounter times: exact analytical results for random walks in a partitioned lattice

We study the effects of temporarily and permanently confining domains on the statistics of first-passage times in finite lattices in one and two dimensions. We present exact results for the mean and variance of the first-passage time between arbitrary sites in the following: (1) a finite one-dimensional lattice partitioned into temporarily confining domains and (2) a finite two-dimensional lattice with reflecting boundaries for a single random walker and an immobile target. In the one-dimensional case, we also present the full first-passage time distribution via numerical inversion of Laplace transforms

Exact Green's functions for a Brownian particle reversibly binding to a fixed target in a finite, two-dimensional, circular domain

Despite the apparent need to study reversible reactions between molecules confined to a two-dimensional space such as the cell membrane, exact Green's functions for this case have not been reported. Here we present exact analytical Green's functions for a Brownian particle reversibly reacting with a fixed reaction center in a finite two-dimensional circular region with reflecting or absorbing boundaries, considering either a spherically symmetric initial distribution or a particle that is initially bound. We show that Green's function can be used to predict the effect of measurement uncertainties on the outcome of single-particle/molecule-tracking experiments in which molecular interactions are investigated. Hence, we bridge the gap between previously known solutions in one dimension (Agmon 1984 J. Chem. Phys. 81 2811) and three dimensions (Kim and Shin 1999 Phys. Rev. Lett. 82 1578), and provide an example of how the knowledge of Green's function can be used to predict experimentally accessible quantities

Observing the rotational diffusion of nanodiamonds with arbitrary nitrogen vacancy center configurations

We present theoretical results on the relationship between the rotational diffusion coefficient of a nanodiamond undergoing Brownian motion and the configuration of nitrogen vacancy centers (NVCs) contained in the particle. Through exact calculations and simulations, we obtain the fluorescence intensity autocorrelation function that is measured in optically detected magnetic resonance experiments conducted at single-particle level. We relate the autocorrelation function to the rotational diffusion coefficient and discuss the influence of different NVC configurations on the outcome of measurements. We believe that our results can be useful in interpreting observations on nanodiamonds that contain multiple nitrogen vacancy centers