G-CSF control of neutrophils dynamics in the blood.

White blood cell neutrophil is a key component in the fast initial immune response against bacterial and fungal infections. Granulocyte colony stimulating factor (G-CSF) which is naturally produced in the body, is known to control the neutrophils production in the bone marrow and the neutrophils delivery into the blood. In oncological practice, G-CSF injections are widely used to treat neutropenia (dangerously low levels of neutrophils in the blood) and to prevent the infectious complications that often follow chemotherapy. However, the accurate dynamics of G-CSF neutrophil interaction has not been fully determined and no general scheme exists for an optimal G-CSF application in neutropenia. Here we develop a two-dimensional ordinary differential equation model for the G-CSF-neutrophil dynamics in the blood. The model is built axiomatically by first formally defining from the biology the expected properties of the model, and then deducing the dynamic behavior of the resulting system. The resulting model is structurally stable, and its dynamical features are independent of the precise form of the various rate functions. Choosing a specific form for these functions, three complementary parameter estimation procedures for one clinical (training) data set are utilized. The fully parameterized model (6 parameters) provides adequate predictions for several additional clinical data sets on time scales of several days. We briefly discuss the utility of this relatively simple and robust model in several clinical conditions.

How growth affects the fate of cellular metabolites.

Cellular metabolites frequently have more than a single function in the cell. For example they may be sources of energy as well as building blocks for several macromolecules. The relative cellular needs for these different functions depend on environmental and intracellular factors. The intermediary products of phosphorylation of pyruvate by mitochondria, for example, are used for growth, while the released ATP is used for both growth and maintenance. Since maintenance has priority over growth, and maintenance is proportional to a cell's mass, a cell's need for ATP vs. building blocks depends on the growth rate, and hence on substrate availability. We show how the concept of Synthesising Units (SUs) in linear and cyclic pathways takes care of the correct variation of the ATP/building block ratio in the context of the Dynamic Energy Budget (DEB) theory. This can only be achieved by an interaction between subsequent SUs in transferring metabolites. Apart from this interaction we also needed an essential feature of the performance of the pathway in the DEB context: the relative amount of enzymes varies with the growth rate in a special way. We solved an important consistency problem between the DEB model at the whole-cell level and a model for pathway dynamics. We observe that alternative whole-cell models, such as the Marr-Pirt model, that keep the relative amount of enzymes constant, and hence independent of the growth rate, will have problems in explaining how pathways can meet cells' growth-dependent needs for building blocks vs. ATP.

One-vesicle hypothesis for neurotransmitter release: a possible molecular mechanism.

Neurotransmitter-containing vesicles are clustered in release sites. Although a given site can contain tens of vesicles, there is evidence that under a wide range of conditions, following an action potential, rarely is more than one vesicle released from each site. Such findings led to the one vesicle hypothesis, for which this paper suggests a molecular mechanism. The release of a vesicle from a site provides a transient high concentration of transmitter in that site. It is proposed here that the local high transmitter concentration interrupts further vesicle releases from the same release site. The suggested mechanism for this 'release interruption' is based on a theory of release control by the authors wherein inhibitory transmitter autoreceptors play a central role. (That transmitter binding to these autoreceptors can inhibit release on a fast time scale has recently been shown experimentally.) A detailed kinetic scheme is presented for the proposed mechanism. Stochastic simulations of this scheme demonstrate how the mechanism accounts for the one vesicle hypothesis. In agreement with recent experiments, the simulations also show that changes in conditions that affect the release process can cause frequent release of more than one vesicle per site.

Controlling the immune system: diffuse feedback via a diffuse informational network.

Diffuse feedback is defined to be a process by which a system in some sense improves its performance with respect to a variety of conflicting and even contradictory goals. In the immune system, such feedback is mediated by scores of extracellular chemicals (cytokines), each of which participates in achieving several goals. Progress toward any given goal is mediated by several cytokines. The 'immunoinformatics' of this diffuse informational network will be discussed. It will be shown how diffuse feedbacks, based on this network, can improve the performance of a given type of immune effector cell, and can cause the preferential amplification of more potent effectors. It will be argued that diffuse feedback also acts in other biological systems ranging from the metabolic system to ant colonies.

Th1 or Th2: how an appropriate T helper response can be made.

Two types of T helper (Th) cells have been defined on the basis of their cytokine secretion patterns. The decision of a naive T cell to differentiate into Th1 or Th2 is crucial, since to a first approximation it determines whether a cell-mediated or humoral immune response is triggered against a particular pathogen, which profoundly influences disease outcome. Here we show that the internal behaviour of the T helper system, which emerges from regulatory mechanisms 'built into' the T helper system, itself can usually select the appropriate T helper response. This phenomenon arises from an initial Th1 bias together with the induction of Th1-->Th2 switches when Th1 effectors do not lead to efficient antigen clearance. The occurrence of these shifts is based on the antigen dose dependence of T helper differentiation, which is a consequence of asymmetries in cross-suppression. Critical for this feature is the rate with which Th2 cells undergo antigen-induced cell death.

Generation of oscillations by the p53-Mdm2 feedback loop: a theoretical and experimental study.

The intracellular activity of the p53 tumor suppressor protein is regulated through a feedback loop involving its transcriptional target, mdm2. We present a simple mathematical model suggesting that, under certain circumstances, oscillations in p53 and Mdm2 protein levels can emerge in response to a stress signal. A delay in p53-dependent induction of Mdm2 is predicted to be required, albeit not sufficient, for this oscillatory behavior. In line with the predictions of the model, oscillations of both p53 and Mdm2 indeed occur on exposure of various cell types to ionizing radiation. Such oscillations may allow cells to repair their DNA without risking the irreversible consequences of continuous excessive p53 activation.

Theory for the feedback inhibition of fast release of neurotransmitter.

Autoinhibition of neurotransmitter release occurs via binding of transmitter to appropriate receptors. Experiments have provided evidence suggesting that the control of neurotransmitter release in fast systems is mediated by these inhibitory autoreceptors. Earlier, the authors formulated and analysed a mathematical model for a theory of release control in which these autoreceptors played a key role. The key experimental findings on which the release-control theory is based are: (i) the inhibitory autoreceptor has high affinity for transmitter under rest potential and shifts to low affinity upon depolarization; (ii) the bound (with transmitter) autoreceptor associates with exocytotic machinery Ex and thereby blocks it, preventing release of neurotransmitter. Release commences when depolarization shifts the autoreceptor to a low-affinity state and thereby frees Ex from its association with the autoreceptors. Here we extend the model that describes control of release so that it also accounts for release autoinhibition. We propose that inhibition is achieved because addition of transmitter, above its rest level, causes transition of the complex of autoreceptor and Ex to a state of stronger association. Relief of Ex from this state requires higher depolarization than from the weakly associated complex. In contrast to the weakly associated complex that only requires binding of transmitter to the autoreceptor to be formed, the transition to the strongly associated complex is induced by a second messenger, which is produced as a result of the receptor binding to transmitter. The theory explains the following experimental results (among others): for inhibition via transmitter or its agonists, the magnitude of inhibition decreases with depolarization; a plot of inhibition as a function of the concentration of muscarine (an acetylcholine agonist) yields an S-shaped curve that shifts to the right for higher depolarizations; the time course of release does not change when transmitter is added; the time course of release also does not change when transmitter antagonists are added, although quantal content increases; however, addition of acetylcholine esterase (an enzyme that hydrolyses acetylcholine) prolongs release.

On the role of feedback in promoting conflicting goals of the adaptive immune system.

We explored here the implications of two premises. 1) In their response over days or weeks to pathogen invasion, cells of the immune system combine several overlapping and perhaps contradictory goals. 2) The immune system has ways to monitor progress toward these goals via receptors that bind chemicals whose concentrations are related to such progress. We illustrate with simple mathematical models how such monitoring can lead to feedbacks that improve the efficiency of a given effector type in accomplishing its specialized task, and also how feedbacks can shift the balance among a variety of effectors toward a preponderance of the more effective. Specific suggestions are given for feedback molecules.

Multiple attractors in immunology: theory and experiment.

This selective survey discusses the relative merits of various modeling approaches in immunology that exhibit multiple attractors, and also assesses the ability of the different models to contribute to deeper biological understanding. The first topic is global anti-idiotypic network models, which, like Hopfield neural network models, exhibit a large number of steady states that are identified with memory. It is shown that a 'reverse engineering approach' to T-cell vaccination for autoimmunity, featuring steady states corresponding respectively to 'normality', 'vaccination' and 'disease', is able to spur new experiments, in spite of the model's deliberate neglect of almost all biological detail. Mention is made of several other T-cell models that feature bistability for Th1 or Th2 dominance, or for activation and unresponsiveness.

On the role of a possible dialogue between cytokine and TCR-presentation mechanisms in the regulation of autoimmune disease.

Autoimmune diseases are thought to occur through some weakness in an active process of autoregulation. Two different regulatory mechanisms have been proposed separately during the years: a "non-specific" mechanism, via Th1-Th2 non-specific cytokines, and a "specific" one-on-one mechanism, via presentation of peptides, i.e., T cell receptor (TCR) peptides, by the T cells themselves. Several anti-idiotypic models rely on the latter to explain the effects of "T-cell-vaccination" therapy. We present and analyse a model for the interaction between both regulatory mechanisms within an ensemble composed of Th1 and Th2 cells. Our model shows how both TCR presentation and non-specific Th1/2 signals can cooperate in the choice of the prevailing Th1 or Th2 response. We show how TCR presentation can foster regulation, without necessitating a particular "suppressor" agent, of the type that some have assumed to play a central role in the regulation of autoimmunity. Our results suggest an important role for the cells' sensitivities to Th1 and Th2 derived cytokines; only for certain sensitivity ranges, is it possible to switch dominance between subtypes. It is argued that memory is sustained via modulation of sensitivities to cytokines, not only to antigens. The results and hypotheses also suggest one possible reason for the known correlation between standard and autoimmune diseases. Several therapies and informative experiments are suggested. We argue, for example, that administering a non-relevant peptide while increasing the ratio between the clones reactive to it and other clones in the pancreas, might cure autoimmune diabetes. Moreover, we predict that disease could be prevented by administering an autoimmune peptide at an early age while forcing the system to react in a Th2 fashion.

Modeling immunotherapy for allergy.

Type I hypersensitivity, which functions to protect the organism from parasites, is caused by binding of antigen to IgE antibodies pre-attached to the cell surface of tissue mast cells and their circulating counterparts, the basophils. In "allergy," type I hypersensitivity is inappropriately induced by protein-based foreign substances (such as pollen) or protein components of insect stings, which in the normal course of events would be cleared from the organism without causing any damage. Paradoxically, a successful clinical treatment of allergy involves repeated immunization of allergic persons with low doses of the allergen--immunotherapy. Investigation of the available experimental evidence leads to the conclusion that the phenomena of immunotherapy are best addressed in terms of the interplay among the mechanism(s) of immune memory--Th1/Th2 cross-regulation--and the physical compartmentalization of the immune system. These conclusions are illustrated with a numerical simulation.

Extending the quasi-steady state approximation by changing variables.

The parameter domain for which the quasi-steady state assumption is valid can be considerably extended merely by a simple change of variable. This is demonstrated for a variety of biologically significant examples taken from enzyme kinetics, immunology and ecology.

A quantitative model of autoimmune disease and T-cell vaccination: does more mean less?

According to a simple mathematical model, the activated effector T cells that cause an autoimmune disorder can also cure the disease if administered in large doses. This prediction has been tested in the nonobese diabetic (NOD) mouse model and demonstrates that administration of intermediate doses of a diabetogenic T-cell clone caused early hyperglycemia, whereas a higher dose cured the disease. As discussed here by Lee Segel and colleagues, the proposed application of T-cell vaccination to treat clinical disease obliges immunologists to consider the quantitative complexities of regulation.

Reverse engineering: a model for T-cell vaccination.

A class of minimal models is constructed that can exhibit several salient phenomena associated with T-cell inoculations that prevent and cure autoimmune disease. The models consist of differential equations for the magnitude of two populations, the effectors E (which cause the disease), and an interacting regulator population R. In these models, normality, vaccination and disease are identified with stable steady-states of the differential equations. Thereby accommodated by the models are a variety of findings such as the induction of vaccination or disease, depending on the size of the effector inoculant. Features such as spontaneous acquisition of disease and spontaneous cure require that the models be expanded to permit slow variation of their coefficients and hence slow shifts in the number of steady-states. Other extensions of the basic models permit them to be relevant to vaccination by killed cells or by antigen, or to the interaction of a larger number of cell types. The discussion includes an indication of how the highly simplified approach taken here can serve as a first step in a modeling program that takes increasing cognizance of relevant aspects of known immunological physiology. Even at its present stage, the theory leads to several suggestions for experiments.

A basic biophysical model for bursting neurons.

Presented here is a basic biophysical cell model for bursting, an extension of our previous model (Av-Ron et al. 1991) for excitability and oscillations. By changing a limited set of model parameters, one can describe different patterns of bursting behavior in terms of the burst cycle, the durations of oscillation and quiescence, and firing frequency.

Plasmid copy number control: a case study of the quasi-steady-state assumption.

Perelson & Brendel (1989, J. molec. Biol. 208, 245-255) have proposed kinetic models for the control of plasmid copy number, based on experiments by J. Tomizawa and his associates. The quasi-steady-state assumptions (QSSA) made in the analysis of these models are justified in the present paper, thereby providing an example of how QSSA can provide a powerful and reliable tool in the analysis of biological kinetics.

Local probes and heterogeneous catalysis: a case study of a mitochondria-luciferase-hexokinase coupled system.

Biological systems are characterized by a high degree of structural organization. In the intracellular context, this introduces physical constraints which are not considered in the standard biochemical analysis of isolated systems, aimed towards mechanistic studies. A major challenge in cellular biology is thus to integrate the structural and mechanistic information and reach an adequate representation of the modes of operation in situ. We present an approach to this problem which takes advantage of a localized probe to study heterogeneous coupled system, as minimal models for cellular operation. The system consists of ATP production at the surface of mitochondria, and ATP consumption in solution by the hexokinase reaction. Soluble or biologically localized firefly luciferase is used to continuously monitor ATP concentration either in the bulk solution or at the surface of the organelle, respectively. The general system of a surface source and a bulk sink is mathematically modeled, and an analytic steady-state solution for local and bulk ATP is presented. The results are validated by experiment and differ from the expected behavior of an equivalent homogeneous system in solution. The model is further adapted to evaluate the effect of mixing. In addition, two limiting cases of heterogeneous distribution of hexokinase are analyzed, in which the soluble enzyme adsorbs non-specifically to mitochondria, or binds selectively to the site of ATP appearance on the membrane. The results are discussed in terms of their significance to the analysis of bulk measurements in vitro and their relevance to better description of cellular situations.

Pattern formation in one- and two-dimensional shape-space models of the immune system.

A large-scale model of the immune network is analyzed, using the shape-space formalism. In this formalism, it is assumed that the immunoglobulin receptors on B cells can be characterized by their unique portions, or idiotypes, that have shapes that can be represented in a space of a small finite dimension. Two receptors are assumed to interact to the extent that the shapes of their idiotypes are complementary. This is modeled by assuming that shapes interact maximally whenever their coordinates in the space-space are equal and opposite, and that the strength of interaction falls off for less complementary shapes in a manner described by a Gaussian function of the Euclidean "distance" between the pair of interacting shapes. The degree of stimulation of a cell when confronted with complementary idiotypes is modeled using a log bell-shaped interaction function. This leads to three possible equilibrium states for each clone: a virgin, an immune, and a suppressed state. The stability properties of the three possible homogeneous steady states of the network are examined. For the parameters chosen, the homogeneous virgin state is stable to both uniform and sinusoidal perturbations of small amplitude. A sufficiently large perturbation will, however, destabilize the virgin state and lead to an immune reaction. Thus, the virgin system is both stable and responsive to perturbations. The homogeneous immune state is unstable to both uniform and sinusoidal perturbations, whereas the homogeneous suppressed state is stable to uniform, but unstable to sinusoidal, perturbations. The non-uniform patterns that arise from perturbations of the homogeneous states are examined numerically. These patterns represent the actual immune repertoire of an animal, according to the present model. The effect of varying the standard deviation sigma of the Gaussian is numerically analyzed in a one-dimensional model. If sigma is large compared to the size of the shape-space, the system attains a fixed non-uniform equilibrium. Conversely if sigma is small, the system attains one out of many possible non-uniform equilibria, with the final pattern depending on the initial conditions. This demonstrates the plasticity of the immune repertoire in this shape-space model. We describe how the repertoire organizes itself into large clusters of clones having similar behavior. These results are extended by analyzing pattern formation in a two-dimensional (2-D) shape-space.(ABSTRACT TRUNCATED AT 400 WORDS)