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. This work was supported in part by the United States Atomic Energy Commission and the National Aeronautics and Space Administration.     

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.     

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.     

Glutamate dehydrogenase: some properties of the rat brain enzyme from different cellular compartments

1. Differences in the GDH activity of neuronal, glial cells and synaptosomes were detected. 2. The enzyme was measured in both directions: synthesis and degradation of glutamate. 3. Synaptosomes were the region with the highest GDH activity. 4. ADP plays an important role in the regulation of the reaction sense. 5. This effector produced higher activation on the enzyme measured in the direction of glutamate synthesis than in the sense of its degradation. 6. The enhancement produced by ADP was dependent on the enzyme localization. The ADP effect is discussed.     

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.     

On the stock estimation for some fishery systems

In this work we address the stock estimation problem for two fishery models. We show that a tool from nonlinear control theory called “observer” can be helpful to deal with the resource stock estimation in the field of renewable resource management. It is often difficult or expensive to measure all the state variables characterising the evolution of a given population system, therefore the question arises whether from the observation of certain indicators of the considered system, the whole state of the population system can be recovered or at least estimated. The goal of this paper is to show how some techniques of control theory can be applied for the approximate estimation of the unmeasurable state variables using only the observed data together with the dynamical model describing the evolution of the system. More precisely we shall consider two fishery models and we shall show how to built for each model an auxiliary dynamical system (the observer) that uses the available data (the total of caught fish) and which produces a dynamical estimation of the unmeasurable stock state x(t). Moreover the convergence speed of towards x(t) can be chosen.     

On some basic laws in physiological systems

Summary By the application of a new concept of activity, which is an extension of excitability in physiology, it was possible to establish the activity cycle in relation to the interstimulus interval as an extension of excitability cycle. It was proved also that the response area and audiogram in the auditory system, as well as the spectral response curve in the visual system can be described in uniform fashion as a special situation of activity.It was further found that Fechner's law and Stevens' power function are none other than one of the laws of activity in the semi-logarithmic and in the double logarithmic domains, respectively.     

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.     

Temporal properties of some biological systems and their fractal attractors

In this paper we analyse time series data as the growth of organisms using markers such as treerings and otolith deposits (fish). The series studied belong to two tree species (Pinus uncinata, Fagus sylvatica) and one fish species (Dicentrarchus labrax). Spectral analyses of the time series growth show that the main frequencies of fluctuation may be due to variations of the energy input. However, any causal explanation must consider the internal continuous readjustment in the system as reported by the corresponding chaotic properties of the asymptotic decay of the spectra time structure. Since the output of noisy and chaotic systems tend to show similar spectral densities, an attempt to differentiate them has been carried out. The chaotic behaviour has been characterized by the study of the attractors. The dimmensions of these multiple topologies were 3.2 and 3.4 for the tree species and 2.3 for the fish species. Therefore, we are dealing with fractal attractors and the minimum number of variables that can be used to describe the systems are 4 and 3 respectively. It is suggested that some of the variables that most influence growth are those obtained by the response functions in the case of trees.     

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 vesicles and membrane compartments

Summary Two different mechanisms have been proposed to explain transport along the endocytic and biosynthetic transport routes in cells. The first involves stable compartments connected by vesicular traffic while the second argues that the key organelles (early endosomes or the cis Golgi) form de novo by fusion of vesicles and subsequently mature into later forms. In the first part of this article, I propose a classification that distinguishes between stable, preexisting membrane compartments and vesicles that are, by definition, transient organelles. In this scheme, compartments, but not vesicles, are capable of homotypic fusion while vesicles, but not compartments, are able to mature, a process defined as an irreversible set of biochemical events which lead to a physiologically distinct end-state of the vesicle prior to its vectorial fusion with a target compartment. In the second part, I summarize my current ideas about the ultrastructural organization of the ER-Golgi region. Finally, I review the cell biology of selected examples of different vesicle types in order to exemplify the fascinating diversity of functions that this class of membrane organelles has evolved.Abbreviations COP coatomer - ECV endosome carrier vesicle - ER endoplasmic reticulum - HRP horseradish peroxidase - IC intermediate compartment between ER and Golgi - MVB multivesicular body - NSF N-ethyl maleimide sensitive factor - SNAPS soluble NSF associated proteins - TGN trans Golgi network Dedicated to Professor Eldon H. Newcomb in recognition of his contributions to cell biology