Stochastic theory of compartments: An open,two compartment,reversible system with independent poisson arrivals

This paper discusses two compartment models with interaction allowed between the compartments. The total number of particles in the system at any time is discussed along with the number to the found in each separate compartment. An interesting result is that the number of particles in each of the two compartments areindependent random variables. Some asymptotic results are also given. The paper is a continuation of some earlier work by the author.     

Stochastic theory of compartments

The stochastic model of a compartment developed by Thakur, Rescigno and Schafer is discussed without using generating functions. The behavior of the mean and variance of the number of particles present as a function of time is also discussed. We also allow both the input and output to be time dependent.     

Stochastic P systems and the simulation of biochemical processes with dynamic compartments

We introduce a sequential rewriting strategy for P systems based on Gillespie's stochastic simulation algorithm, and show that the resulting formalism of stochastic P systems makes it possible to simulate biochemical processes in dynamically changing, nested compartments. Stochastic P systems have been implemented using the spatially explicit programming language MGS. Implementation examples include models of the Lotka-Volterra auto-catalytic system, and the life cycle of the Semliki Forest virus.     

On the stochastic theory of compartments: II. Multi-compartment systems

A stochastic model is developed for a system of interconnected compartments. The generating function of the random variable of any compartment can be constructed from a flow graph involving the expectations of the random variables of all compartments of the system.     

On the stochastic theory of compartments: The leaving process of the two-compartment systems

In this paper three stochastic models are developed for a class of two-compartment systems to analyse the randomness of the leaving process of the particles in the system. Results in closed form for the distribution of the leaving process of the particles in the system are given both for general and exponential sojourn time distributions and also in association with forward recurrence time distributions with and without Poisson input.     

The use of two radiotracers for transfer-rate determinations in closed two compartment systems

The sensitivity and “specificity” of measurements for the determination of transferates are enhanced by the use of an additional radiotracer, serving to trace the unlabelled substance. This method presents advantages mostly in systems outside their steady state but only exeptionally in steady state systems.     

The use of two radiotracers for transfer-rate determinations in closed two compartment systems

The sensitivity and “specificity” of measurements for the determination of transferates are enhanced by the use of an additional radiotracer, serving to trace the unlabelled substance. This method presents advantages mostly in systems outside their steady state but only exeptionally in steady state systems. This paper is an outgrowth of work supported by grant AI 02457 from the National Institute of Allergy and Infectious Diseases, U.S. Public Health Service.     

On the stochastic theory of compartments: Solution forn-compartment systems with irreversible,time-dependent transition probabilities

The bivariate distribution of a two-compartment stochastic system with irreversible, time-dependent transition probabilities is obtained for any point in time. The mean and variance of the number of particles in any compartment and the covariance between the number of particles in each of the two compartments are exhibited and compared to existing results. The two-compartment system is then generalized to ann-compartment catenary and to ann-compartment mammillary system. The multivariate distributions of these two systems are obtained under two sets of initial conditions: (1) the initial distribution is known; and (2) the number of particles in each compartment of the system at timet=0 is determined. The moments of these distributions are also produced and compared with existing results.     

The calculation of transfer rates in two compartment systems not in dynamic equilibrium

Dynamic equilibrium in a biological system implies that the compartment under study does not change in size during the period of observation. In many biological systems there are, however, net changes with time and this report deals with the mathematical treatment necessary to calculate unequal rates of inflow and outflow. A method is presented for the calculation of transfer rates in a two compartment system when the rates of flow between these compartments are unequal but constant. Equations were developed to calculate the amount of material transported per unit time derived from measurements of specific activity and compartment size. The problems of (1) sampling from the pool and (2) the effects of analytical errors on the estimation of rate have been evaluated. An example has been presented in which the derived equations have been applied to a study of the simultaneous passage of sodium into and out of a permanently isolated loop of bowel.     

Stochastic and deterministic models for the kinetic behavior of certain structured enzyme systems II: consecutive two enzyme systems.

This paper contains extensions of results from a previous paper regarding structured one enzyme systems to a more complicated structured two enzyme system. A stochastic model and a deterministic model are developed for such systems and their steady state reaction kinetics are compared. These comparisons are in the form of graphs of the reaction kinetics versus substrate concentration. Two quantities are proposed as indications of lack of agreement between the two models. This lack of agreement corresponds to situations in which the model systems are more highly non-linear, in accord with Jensen's inequalities. Implications of these results, relative to experimental procedures are briefly discussed.     

Liver stem cells: a two compartment system

Hepatocytes and biliary epithelia are phenotypically very dissimilar, but share a common ancestry. Hepatocytes regenerate very efficiently, and their division potential indicates that many of them are functional stem cells. When hepatocyte-damaging agents also impair the regenerative ability of surviving hepatocytes, a potential stem cell system of biliary origin is activated to generate new hepatocytes — a reversal of ontogeny. Now both bile duct derived cells and hepatocytes can be isolated from the liver, genetically modified in vitro and returned to their in vivo origins where, after considerable population expansion, they can function as hepatocytes — paving the way for ex vivo gene therapy.     

Stochastic theory of population genetics

Stochastic models of population genetics are studied with special reference to the biological interest. Mathematical methods are described for treating some simple models and their modifications aimed at the problems of the molecular evolution. Unified theory for treating different quantities is extensively developed and applied to some typical problems of current interest in genetics. Mathematical methods for treating geographically structured populations are given. Approximation formulae and their accuracy are discussed. Some criteria are given for a structured population to behave almost like a panmictic population of the same total size. Some quantities are shown to be independent of the geographical structure and their dynamics are described.     

Two-chamber AFM: probing membrane proteins separating two aqueous compartments

Biological membranes compartmentalize and define physical borders of cells. They are crowded with membrane proteins that fulfill diverse crucial functions. About one-third of all genes in organisms code for, and the majority of drugs target, membrane proteins. To combine structure and function analysis of membrane proteins, we designed a two-chamber atomic force microscopy (AFM) setup that allows investigation of membranes spanned over nanowells, therefore separating two aqueous chambers. We imaged nonsupported surface layers (S layers) of Corynebacterium glutamicum at sufficient resolution to delineate a 15 A-wide protein pore. We probed the elastic and yield moduli of nonsupported membranes, giving access to the lateral interaction energy between proteins. We combined AFM and fluorescence microscopy to demonstrate the functionality of proteins in the setup by documenting proton pumping by Halobacterium salinarium purple membranes.     

On the stochastic theory of compartments: I. A single-compartment system

A stochastic model is developed for a compartment with a single time-dependent input, and generalized to include inputs from several sources. With the number of particles of a given molecular species in the compartment as the random variable, the mean, variance and third central moment of this variable are calculated from its generating function, and compared with previous results. The behavior of the calculated moments is discussed, and the possibility of applying the model to chemical and biological systems is considered.     

Stochastic theory of a selection game

The stochastic theory of a nonlinear game is presented which incorporates some of the essential properties of living systems: metabolism, reproduction and mutability. The steady state distribution function as well as the complete time development are given explicitly. The second law of thermodynamics is generalized to a certain class of nonequilibrium systems. An order parameter is introduced as a measure of the system's internal organization. From the point of view of phase transition theory, the model exhibits a transition at the absolute zero of temperature, with critical behaviour showing up in the low temperature region.     

Generation of nonidentical compartments in vesicular transport systems

How can organelles communicate by bidirectional vesicle transport and yet maintain different protein compositions? We show by mathematical modeling that a minimal system, in which the basic variables are cytosolic coats for vesicle budding and membrane-bound soluble N-ethyl-maleimide–sensitive factor attachment protein receptors (SNAREs) for vesicle fusion, is sufficient to generate stable, nonidentical compartments. A requirement for establishing and maintaining distinct compartments is that each coat preferentially packages certain SNAREs during vesicle budding. Vesicles fuse preferentially with the compartment that contains the highest concentration of cognate SNAREs, thus further increasing these SNAREs. The stable steady state is the result of a balance between this autocatalytic SNARE accumulation in a compartment and the distribution of SNAREs between compartments by vesicle budding. The resulting nonhomogeneous SNARE distribution generates coat-specific vesicle fluxes that determine the size of compartments. With nonidentical compartments established in this way, the localization and cellular transport of cargo proteins can be explained simply by their affinity for coats.     

On some metric properties of the systems of compartments

Rules for the enumeration of the strong components of a graph and for the calculation of its variable adjacency matrix are presented. A new method is given to calculate the transfer function of a graphy by analyzing the strong components of the graph, the elementary paths between two nodes, and the linear subgraphs.     

On some topological properties of the systems of compartments

Compartment systems are often used as models for tracer and drug kinetics. The structure of a compartment system is here analyzed by means of theory of graphs methods. In particular the precursor-successor relationship between any two compartments is classified according to the structure of the graph of the system and to the values of the elements of the matrix associated with it. Supported jointly by NASA and AEC.