On the distribution of the epoch of the first contact of immunocompetent cell with antigen

A hypothesis on the dynamics of the immune reaction at a cellular level is considered, as was presented by Šterzl (1967). According to this hypothesis, the onset of the immune response depends on the first contact of a so-called virgin immunocompetent cell with the antigen. In the present paper a conditional probability distribution of the epoch of this first contact is derived, assuming that such a contact occurs at all (probability of non-occurrence of the contact being, in the general case, positive); the density of this distribution (7) is then specified (8) for the case that decrease of the quantity of an active antigen follows an exponential curve, and moments of this distribution are calculated (12).     

On contacts of immunocompetent cells with antigen (Note on a probability model)

This communication continues with the mathematical formulation and solution of some problems connected with the beginning of the immunological reaction. This paper generalizes some previous results concerning the probability of the event that such a contact of an immunocompetent cell (ICC) with antigen, which is followed by the differentiation of this cell towards the antibody forming cell (AbFC), takes place. Previous papers considered the onset of the differentiation of an ICC caused by the contact of this cell with at least a certain threshold amount of antigen (assuming that these contacts form a non-homogeneous Poisson process). This paper is based on the more general and more realistic assumption thatn such contacts are necessary for the stimulation of ICC differentiation (this new assumption has its origin in some new biological findings on the nature of the contact considered, and corresponds with the idea that the diffentiation of ICC does not begin until the antigen is bound on a certain fixed number of receptors on the cell surface). Under this assumption, the probability of the event that the differentiation of the cell begin at all (i.e. that at leastn contacts will take place), and the probability distribution of the epoch of the beginning of the differentiation (i.e. of the epoch at which thenth contact take place), are derived.— If necessary, these new forms of probability distributions may be used (instead of previous ones) as building stones in models of ICC differentiation.     

Cyclic kinetics and mathematical expression of the primary immune response to soluble antigen

The conveyer hypothesis is based on the fact that because of clone predetermination, antibody production takes place in an organism without the presence of antigen as a result of natural cell differentiation. Soluble antigen is an analogue of a specific mitogen which gives rise to reproduction mainly of cells carrying on their surface the immunoglobulin receptors to the given antigen. The mathematical model of the conveyer hypothesis takes into account the initial conditions, among them the background level of antibody-producing cells before injection of a soluble antigen, migration of precursor cells in the draining lymphoid organ, and the rate of precursor differentiation, including the rate of the change of the immunoglobulin receptor number on the cell surface. Changes of antigen concentration in blood determine the intensity of precursor proliferation. Comparison of real experiments (intraperitoneal injection of capsular antigen ofPasteurella pestis into inbred mice) with calculations done on the basis of the developed mathematical model shows a definite qualitative resemblance with the kinetics of antibody-producing cells and free antibodies as well as with the decrease of free antigen concentration in blood. In spite of some differences between model experiments and real experiments the conveyer hypothesis and its mathematical model appear suitable for describing the primary immune response of mice immunized with low doses of capsular antigen ofPasteurella pestis.     

The number of immunologically activated cells after repeated immunization (A mathematical model)

Using a mathematical model, the effect of the dose of antigen and of the rate of its elimination on the number of immunologically activated cells, derived from a single immunocompetent cell, that are prepared for the change into antibody-producing cells under the condition that further antigenic stimulus takes place, was studied. The following results were obtained under certain assumptions that are explained and discussed in our present work: (1) The shape of the dependence of the number of immunologically activated cells afterk-fold immunization on the immunizing dose and the rate of elimination of antigen was established. (2) In studies on the influence of the magnitude of a single antigen dose on the readiness for the secondary reaction (expressed as the number of immunologically activated cells present at the time of injection of the secondary antigen dose), we found that with increasing antigen dose the number of immunologically activated cells increases until it reaches its peak at the optimum antigen dose; then a decrease starts to occur. The range of doses of antigen causing approximately similar (and high) readiness for the secondary response is broader with antigens that are eliminated faster from the organism. (3) A method for the estimation of the optimum dose of antigen and of the number of persisting immunologically activated cells after this antigen dose is presented. This method can be used provided certain knowledge concerning the particular experimental system is available.     

Characteristics of serotonin binding by the cells of immunocompetent tissues and synaptosomes

The ratio of surface and intracellular serotonin binding by the cells of immunocompetent tissues and synaptosomes of immunized and intact CBA mice was studied by treatment with imipramine inhibiting serotonin penetration through the cytoplasmic membrane. As early as 5 minutes after the antigen injection the content of intracellular amine increased with changes in its binding by the cytoplasmic membrane. The probability of the functional interconnection between the reaction of immunocompetent tissues to the antigen and two forms of serotonin binding by the cells of these tissues is discussed.     

Nets with distance bias

A distance bias is imposed on the probability of direct connection between every pair of points in a random net. The probability that there exists a path from a given point in the net to another point is now a function of both the axone density and the distance between the points. A recursion formula is derived in terms of which this probability can be computed. The rate of spread of an epidemic where probability of contact depends on the distance between the individuals can also be computed from the recursion formula.     

Stem cell potential for type 1 diabetes therapy

Stem cells have been considered as a useful tool in Regenerative Medicine due to two main properties: high rate of self-renewal, and their potential to differentiate into all cell types present in the adult organism. Depending on their origin, these cells can be grouped into embryonic or adult stem cells. Embryonic stem cells are obtained from the inner cell mass of blastocyst, which appears during embryonic day 6 of human development. Adult stem cells are present within various tissues of the organism and are responsible for their turnover and repair. In this sense, these cells open new therapeutic possibilities to treat degenerative diseases such as type 1 diabetes. This pathology is caused by the autoimmune destruction of pancreatic β-cells, resulting in the lack of insulin production. Insulin injection, however, cannot mimic β-cell function, thus causing the development of important complications. The possibility of obtaining β-cell surrogates from either embryonic or adult stem cells to restore insulin secretion will be discussed in this review.     

Growth of cell populations with arbitrarily distributed cycle durations. I. basic model

A discrete model is proposed describing the growth of cell populations with arbitrary frequency distributions of cycle durations. The model assumes that each cell divides into two cells at the end of its cycle, and that each new cell is assigned an individual cycle duration according to a probability distribution that can be arbitrarily defined. The increase in the cell number is calculated, either from the numbers of cells at earlier time points or from the initial conditions of the population, by a recurrence formula; it is also approximated by the optimal exponential function, whose parameters are determined by the initial conditions. The appropriate average cycle duration is shown not to be the arithmetic or geometric mean, but rather the solution to a more complex equation. Age distributions are calculated and compared with those found in the literature. The results of the model calculations are compared with computer simulations and with observed data on populations of the ciliate Tetrahymena geleii.     

A murine B cell lymphoma expressing human HER2/neu undergoes spontaneous tumor regression and elicits antitumor immunity

 In the present study we describe a novel murine tumor model in which the highly malignant murine B cell lymphoma 38C13 has been transduced with the cDNA encoding human tumor-associated antigen HER2/neu. This new cell line (38C13-HER2/neu) showed stable surface expression but not secretion of human HER2/neu. It also maintained expression of the idiotype (Id) of the surface immunoglobulin of 38C13, which serves as another tumor-associated antigen. Surprisingly, spontaneous tumor regression was observed following s.c. but not i.v. injection of 38C13-HER2/neu cells in immunocompetent syngeneic mice. Regression was more frequently observed with larger tumor cell challenges and was mediated through immunological mechanisms because it was not observed in syngeneic immunodeficient mice. Mice that showed complete tumor regression were immune to challenge with the parental cell line 38C13 and V1, a variant of 38C13 that does not express the Id. Immunity could be transferred with sera, suggesting that an antibody response mediated rejection and immunity. Continuously growing s.c. tumors as well as metastatic tumors obtained after the i.v. injection of 38C13-HER2/neu maintained expression of human HER2/neu, which can serve as a target for active immunotherapy. As spontaneous tumor regression has not been observed in other human murine models expressing human HER2/neu, our results illustrate the enormous differences that can exist among different murine tumors expressing the same antigen. The present model provides a useful tool for the study of the mechanisms of protective immunity to B cell lymphoma and for the evaluation of different therapeutic approaches based on the stimulation or suppression of the immune response. Received: 2 August 2000 / Accepted: 20 September 2000     

Computing 3D Chromatin Configurations from Contact Probability Maps by Inverse Brownian Dynamics

The three-dimensional (3D) organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state—accessibility and amount of gene expression—of the chromatin. Recent advances in chromosome conformation capture experiments provide partial information on the chromatin organization in a cell population, namely the contact count between any segment pairs, but not on the interaction strength that leads to these contact counts. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In this work, a novel inverse Brownian dynamics method based on a coarse-grained bead-spring chain model has been proposed to compute the optimal interaction strengths between different segments of chromatin such that the experimentally measured contact count probability constraints are satisfied. Applying this method to the α-globin gene locus in two different cell types, we predict the 3D organizations corresponding to active and repressed states of chromatin at the locus. We show that the average distance between any two segments of the region has a broad distribution and cannot be computed as a simple inverse relation based on the contact probability alone. The results presented for multiple normalization methods suggest that all measurable quantities may crucially depend on the nature of normalization. We argue that by experimentally measuring predicted quantities, one may infer the appropriate form of normalization.     

An age-dependent stochastic model of population growth

A stochastic model of population growth is treated using the Bellman-Harris theory of agedependent stochastic branching processes. The probability distribution for the population size at any time and the expectation are obtained when it is assumed that there is probability (1−σ), 0≤σ<1, of the organism dividing into two at the end of its lifetime, and probability σ that division will not take place.     

Fitness and Propensity’s Annulment?

Recent debate on the nature of probabilities in evolutionary biology has focused largely on the propensity interpretation of fitness (PIF), which defines fitness in terms of a conception of probability known as “propensity”. However, proponents of this conception of fitness have misconceived the role of probability in the constitution of fitness. First, discussions of probability and fitness have almost always focused on organism effect probability, the probability that an organism and its environment cause effects. I argue that much of the probability relevant to fitness must be organism circumstance probability, the probability that an organism encounters particular, detailed circumstances within an environment, circumstances which are not the organism’s effects. Second, I argue in favor of the view that organism effect propensities either don’t exist or are not part of the basis of fitness, because they usually have values close to 0 or 1. More generally, I try to show that it is possible to develop a clearer conception of the role of probability in biological processes than earlier discussions have allowed.     

Cyclic kinetics and mathematical expression of the primary immune response to soluble antigen

The injected dose of antigen determines not only the duration of its persistence in the injection site but also the intensity of plasma cell response in the regional lymph node. It was found that the logarithmic sum of antigen quantity in the injection site was related to the sum of cell response values, the correlation coefficient approaching 1. The antigen-lymphoid system interrelations appear to obey Weber-Fechner’s law for afferent systems of the organism. The sum of plasma cells appeared to be in direct connection with the logarithm of the dose injected, with antigen persistence in the injection site and also with the tangent of the acute angle adjoining the ordinate. The basic components of the primary immune response of the organism to soluble antigen,viz. logarithm of the dose injected, antigen persistence in the injection place, plasma cell quantity, tangent of the acute angle, transition modulus from antigen to plasma cells, are interconnected by rather simple equations, which represent the structural elements of the mathematical model described in the text.     

Outline of a mathematical approach to the cancer problem

The fact that the growth of every organism, as it develops through cell multiplication from the ovum, eventually ceases, makes plausible the hypothesis that each cell of an organism exerts some kind of inhibitory influence upon the growth and multiplication of every other cell through the medium of some factorj. Each cell, however, is considered to possess an amount of a “growth factor”g, the activity of which is inhibited byj. In the course of development, most cells differentiate. A number of them remains relatively undifferentiated, and those are used for repairs of natural tear and wear as well as for healing of wounds. With age either the number of those cells or their “potency” decreases, which accounts for a general decrease in the speed of wound healing. Due to statistical fluctuations, the amount of theg is not uniformly distributed amongst the cells. Some of them have accidentally a greater amount than others. As the number or potency of the undifferentiated cells decreases with age, so does their inhibitory influence upon other cells. Therefore, those cells which do have an accidental dental excess ofg-factor will begin to grow and multiply, producing neoplasms. Putting the above assumptions into mathematical form, it is possible to derive a relation which gives theprobability of cancer incidence as a function of age. The theoretical relation is compared to the rather inadequate empirical data and found in agreement with them. A relation for the speed of wound healing as a function of age is also derived, and also found in general agreement with the rather scant data. Several other conclusions are discussed and possibilities of their practical applications pointed out.     

Contribution to the mathematical theory of contagion and spread of information: I. Spread through a thoroughly mixed population

An equation is derived from the spread of a “state” by contact through a thoroughly mixed population, in which the probability of transmission depends both on the over-all duration of the process and on the time an individual has been in the “state.” Cases in which this probability is a function of only one or the other of the two “times” are worked out. It is shown that in the case of dependence on “private time” alone the asymptotic value of the fraction of the population effected is the same as that derived by the random net approach.     

Modulation of the helper activity of educated T cells to the synthetic polypeptide poly(Tyr,Glu)-poly(dlAla)-poly(Lys) by adherent cell-bound antigen

The effects of culturing in vivo- or in vitro-activated helper cells on antigen-pulsed splenic adherent cells were studied. In vivo T cells educated to the synthetic polypeptide (T,G)-A-L were obtained by the transfer of thymocytes into lethally irradiated mice. When the activation process was suboptimal, resulting in a low helper function of the cell preparation, incubation of the educated cells on (T,G)-A-L-pulsed splenic adherent cells for 24 hr potentiated their activity, and efficient helper cells were obtained. This process was found to be antigen specific, it did not involve de novo education of naive cells or selection of specific T lymphocytes, but rather completion of the education procedure, which had already started in vivo. It seems that a physical contact between the educated T cells and the antigen-presenting cells is essential for inducing the enhanced helper effect. It is also apparent that during this 24-hr culture on antigen-pulsed macrophages T cells did not proliferate, but rather differentiated into immunocompetent helper cells. On the contrary, when the initial education step was efficient the subsequent culture of the activated T cells on antigen-pulsed splenic adherent cells resulted in a marked decay in the helper function of the cells, while control monolayers were inert. Thus, macrophage-bound antigen differentially modulates the helper function of educated T cells, a procedure which is probably dependent on the degree of maturation or differentiation of the T lymphocyte.     

Life,information theory,probability, and physics

A purely information-theoretical approach to the problem of self-replication of elementary living units implies that pure chance is the determining factor in the formation of the first living unit. The probability of such a spontaneous formation can be calculated from the minimum amount of information which an organism must possess in order to replicate itself. An estimation of this amount of information is made here by two different methods. First by a “paper and pencil experiment” which indicates the minimum amount of information needed on a printed page in order that with given tools the page could be reproduced. Second—by an analytical consideration of some hypothetical molecular mechanisms. A general method for handling such problems is suggested. On the basis of estimated information contents it is shown that under most favorable conditions the probability of a spontaneous generation by pure chance during the lifetime of the earth is vanishingly small. It is concluded that dynamic factors, which may reduce tremendously the information content, must play a role in the genesis of life on earth.     

Morphological findings in the liver of diabetic rats after intraportal transplantation of neonatal isologous pancreatic islets

Morphological (light microscopical, immunohistological and electron microscopical) findings in the recipient liver of rats with streptozotocin-induced diabetes, obtained 9 months after intraportal injection of neonatal isologous pancreatic islets, are described and their significance discussed. - The results support the assumption of active ingrowth of nonmyelinated nerve fibers into the islet isografts. - The hepatocytes surrounding the islet isografts contain-obviously owing to the influence of unusually high and locally variable concentrations of insulin-a focally increased number of enlarged mitochondria, abundant glycogen and a smaller amount of neutral fat droplets. Furthermore, hepatocytes and cells looking like hepatocytes (hepato-cyte-like cells) with typically structured cytoplasmic beta(insulin)granules were found bordering the islet isografts. These results could be interpreted as an expression of arteficial or nonarteficial fusion of beta cells with hepatocytes, i.e. formation of hybrid cells (“in vivo hybridization”). Alternatively, they might reflect insulin uptake and storage in the hepatocytes. In addition, these findings suggest that contact between neonatal islet tissue and liver tissue could be a trigger for the in vivo transformation (modulation) of differentiated cells of similar embryonic development in the adult organism.     

Modularity and reliability in the organization of organisms

An organism persists only if it satisfies internal and external constraints. Within the organism networks of processes meet the constraints. In such networks a principle of matching often obtains: the pattern of coupling among processes matches the correlation among constraints. That is, a module—a cluster of coupled processes—meets a constraint. Dissociable modules meet dissociàble constraints. A hierarchy of modules meets a hierarchy of constraints. We have inquired whether such matching is predicted by an optimality criterion in a simple example. We find that in an ensemble of networks with unreliable processes, the networks that meet the constraints with highest reliability obey the principle of matching. The difference in reliability between modular and nonmodular networks that meet the same constraints is a function of the probability of success per process. Our results suggest that this difference is maximal at a probability of success that increases monotonically with the number of processes in the network.