acase@tulane.edu / 1 / Kui Zhang

No description available.

Diffusion can be classified as either normal or anomalous. A variety of experimental systems are evaluated to classify diffusion. Potential regressions and step size distributions are analysed. Nor-mal diffusion holds except where flocculation takes place, or where concentrations of cationic starches are high or with cationic starches and latex together. In these cases, subdiffusion takes place. Furthermore, limiting values are used to calculate diffusion coefficients. Diffusion of non-spherical particles is covered as well, here tested on microcrystalline cellulose.

Many crucial cellular processes take place at the plasma membrane. The latter is a complex, two-dimensional medium exhibiting significant lateral structure. As a result, a number of non-classical processes, including anomalous diffusion, compartimentalisation and fractal kinetics take place at the membrane surface. The evaluation of various hypotheses and theories about the membrane is currently very difficult because no general modelling framework is available. In this thesis, we present a stochastic, spatially explicit Monte Carlo model for the plasma membrane that accounts for illmixedness, mobile lipid microdomains, fixed proteins, cytoskeletal fence structures and other interactions. We interrogate this model to obtain three classes of results, regarding (1) the effect of lipid microdomains on protein dynamics on the membrane (2) the effects of microdomains, cytoskeletal fences and fixed proteins on the nature of the (anomalous) diffusion on the membrane and (3) the effects of obstructed diffusion on reaction kinetics at the membrane. We find that the presence of lipid microdomains can lead to nonclassical phenomena such as increased collision rates and differences between long-range and short-range diffusion coefficients. Our results also suggest that experimental techniques measuring long-range diffusion may not be sufficiently discriminating and hence cannot be used to infer quantitative information about the presence and characteristics of microdomains. With regard to anomalous diffusion in particular, we find that to explain this phenomenon at the levels observed in vivo, a number of interactions are required, including (but not necessarily limited to) obstacle-induced diffusion and segregation, or exclusion from microdomains. The effects of these different interactions upon the nature of the diffusion appear to be approximately additive. Finally, we show that a widely used non-spatial method, the Stochastic Simulation Algorithm, can be modified to take into account anomalous diffusion and that this significantly increases its predictive accuracy. The model presented in this thesis is expected to be of future value in evaluating different models of cell surface processes.

Many crucial cellular processes take place at the plasma membrane. The latter is a complex, two-dimensional medium exhibiting significant lateral structure. As a result, a number of non-classical processes, including anomalous diffusion, compartimentalisation and fractal kinetics take place at the membrane surface. The evaluation of various hypotheses and theories about the membrane is currently very difficult because no general modelling framework is available. In this thesis, we present a stochastic, spatially explicit Monte Carlo model for the plasma membrane that accounts for illmixedness, mobile lipid microdomains, fixed proteins, cytoskeletal fence structures and other interactions. We interrogate this model to obtain three classes of results, regarding (1) the effect of lipid microdomains on protein dynamics on the membrane (2) the effects of microdomains, cytoskeletal fences and fixed proteins on the nature of the (anomalous) diffusion on the membrane and (3) the effects of obstructed diffusion on reaction kinetics at the membrane. We find that the presence of lipid microdomains can lead to nonclassical phenomena such as increased collision rates and differences between long-range and short-range diffusion coefficients. Our results also suggest that experimental techniques measuring long-range diffusion may not be sufficiently discriminating and hence cannot be used to infer quantitative information about the presence and characteristics of microdomains. With regard to anomalous diffusion in particular, we find that to explain this phenomenon at the levels observed in vivo, a number of interactions are required, including (but not necessarily limited to) obstacle-induced diffusion and segregation, or exclusion from microdomains. The effects of these different interactions upon the nature of the diffusion appear to be approximately additive. Finally, we show that a widely used non-spatial method, the Stochastic Simulation Algorithm, can be modified to take into account anomalous diffusion and that this significantly increases its predictive accuracy. The model presented in this thesis is expected to be of future value in evaluating different models of cell surface processes.

Many crucial cellular processes take place at the plasma membrane. The latter is a complex, two-dimensional medium exhibiting significant lateral structure. As a result, a number of non-classical processes, including anomalous diffusion, compartimentalisation and fractal kinetics take place at the membrane surface. The evaluation of various hypotheses and theories about the membrane is currently very difficult because no general modelling framework is available. In this thesis, we present a stochastic, spatially explicit Monte Carlo model for the plasma membrane that accounts for illmixedness, mobile lipid microdomains, fixed proteins, cytoskeletal fence structures and other interactions. We interrogate this model to obtain three classes of results, regarding (1) the effect of lipid microdomains on protein dynamics on the membrane (2) the effects of microdomains, cytoskeletal fences and fixed proteins on the nature of the (anomalous) diffusion on the membrane and (3) the effects of obstructed diffusion on reaction kinetics at the membrane. We find that the presence of lipid microdomains can lead to nonclassical phenomena such as increased collision rates and differences between long-range and short-range diffusion coefficients. Our results also suggest that experimental techniques measuring long-range diffusion may not be sufficiently discriminating and hence cannot be used to infer quantitative information about the presence and characteristics of microdomains. With regard to anomalous diffusion in particular, we find that to explain this phenomenon at the levels observed in vivo, a number of interactions are required, including (but not necessarily limited to) obstacle-induced diffusion and segregation, or exclusion from microdomains. The effects of these different interactions upon the nature of the diffusion appear to be approximately additive. Finally, we show that a widely used non-spatial method, the Stochastic Simulation Algorithm, can be modified to take into account anomalous diffusion and that this significantly increases its predictive accuracy. The model presented in this thesis is expected to be of future value in evaluating different models of cell surface processes.

Many crucial cellular processes take place at the plasma membrane. The latter is a complex, two-dimensional medium exhibiting significant lateral structure. As a result, a number of non-classical processes, including anomalous diffusion, compartimentalisation and fractal kinetics take place at the membrane surface. The evaluation of various hypotheses and theories about the membrane is currently very difficult because no general modelling framework is available. In this thesis, we present a stochastic, spatially explicit Monte Carlo model for the plasma membrane that accounts for illmixedness, mobile lipid microdomains, fixed proteins, cytoskeletal fence structures and other interactions. We interrogate this model to obtain three classes of results, regarding (1) the effect of lipid microdomains on protein dynamics on the membrane (2) the effects of microdomains, cytoskeletal fences and fixed proteins on the nature of the (anomalous) diffusion on the membrane and (3) the effects of obstructed diffusion on reaction kinetics at the membrane. We find that the presence of lipid microdomains can lead to nonclassical phenomena such as increased collision rates and differences between long-range and short-range diffusion coefficients. Our results also suggest that experimental techniques measuring long-range diffusion may not be sufficiently discriminating and hence cannot be used to infer quantitative information about the presence and characteristics of microdomains. With regard to anomalous diffusion in particular, we find that to explain this phenomenon at the levels observed in vivo, a number of interactions are required, including (but not necessarily limited to) obstacle-induced diffusion and segregation, or exclusion from microdomains. The effects of these different interactions upon the nature of the diffusion appear to be approximately additive. Finally, we show that a widely used non-spatial method, the Stochastic Simulation Algorithm, can be modified to take into account anomalous diffusion and that this significantly increases its predictive accuracy. The model presented in this thesis is expected to be of future value in evaluating different models of cell surface processes.

Diffusion and random walks have been studied for more than 100 years. However, there are still details in the methodology that are overlooked, and more information can be extracted from the typical data that is studied. In this thesis, I simulate random walks on two dimensional lattices with immobile obstacles configured in a variety of ways: periodic, random, and "Fuzzy" (a cross intermediate state of disorder between periodic and random). The primary goal is to develop a deeper understanding of "Fuzzy" systems by designing different ways of generating tunable disorder. An example of this is the universal Fz parameter that we developed to unify the natural disorder parameters of the various disorder generation methods we developed. Often times the importance of analysing the transient/anomalous regime with more precision and consistency is overlooked. In our work, we expand on random walk dynamics by applying non-standard probabilities, and justify our choice analytically and through a comparison of results. Furthermore we discuss how the transient regime should be analyzed so that there is consistency in the field. Other than discussing semantics of algorithms and analysis, we study the connection between the transient regime and the steady-state. We introduce two measures of the width of the transient/anomalous regime, and compare them to the crossover time. Using the width of the transient/anomalous regime we are able to provide an estimate of the steady-state diffusion coefficient without access to the steady-state simulation data.

We address the problem of the DNA sequences developing a "dynamical" method based on the assumption that the statistical properties of DNA paths are determined by the joint action of two processes, one deterministic, with long-range correlations, and the other random and delta correlated. The generator of the deterministic evolution is a nonlinear map, belonging to a class of maps recently tailored to mimic the processes of weak chaos responsible for the birth of anomalous diffusion. It is assumed that the deterministic process corresponds to unknown biological rules which determine the DNA path, whereas the noise mimics the influence of an infinite-dimensional environment on the biological process under study. We prove that the resulting diffusion process, if the effect of the random process is neglected, is an a-stable Levy process with 1 < a < 2. We also show that, if the diffusion process is determined by the joint action of the deterministic and the random process, the correlation effects of the "deterministic dynamics" are cancelled on the short-range scale, but show up in the long-range one. We denote our prescription to generate statistical sequences as the Copying Mistake Map (CMM). We carry out our analysis of several DNA sequences, and of their CMM realizations, with a variety of techniques, and we especially focus on a method of regression to equilibrium, which we call the Onsager Analysis. With these techniques we establish the statistical equivalence of the real DNA sequences with their CMM realizations. We show that long-range correlations are present in exons as well as in introns, but are difficult to detect, since the exon "dynamics" is shown to be determined by theentaglement of three distinct and independent CMM's. Finally we study the validity of the stationary assumption in DNA sequences and we discuss a biological model for the short-range random process based on a folding mechanism of the nucleic acid in the cell nucleus.

The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the motion is Fickian with a diffusion coefficient D that depends on the concentration and type of obstacles present in the system. For intermediate times, the mean-square displacement of the particle often increases approximately as t α , with α < 1, typical of what is generally called anomalous diffusion. However, it is not clear how one can identify or choose a time or displacement interval that would give a reliable estimate of α. In this paper, we use two exact numerical approaches to obtain diffusion data for a simple Lattice Monte Carlo model in both time limits. This allows us to propose an objective definition of the transient regime and a unique value for α. Furthermore, our methodology directly gives us the length scale over which the transient regime switches to the steady-state regime. We test our proposed approach using several types of obstacle systems, and we introduce the novel concept of excess diffusion lengths. Finally, we show that the values of the parameters describing the anomalous transient regime depend on the Monte Carlo moves used to describe the dynamics of the particle, and we propose a new algorithm that correctly models the short time diffusion of a particle on a lattice.