Jacques Rene Hiernaux

Models for cell differentiation and generation of polarity in diffusion-governed morphogenetic fields

Models based on molecular mechanisms are presented for pattern formation in developing organisms. It is assumed that there exists a diffusion governed gradient in the morphogenetic field. It is shown that cellular differentiation and the subsequent pattern formation result from the interaction of the diffusing morphogen with the genetic regulatory mechanism of cells. In a second stage it is shown that starting from a homogeneous distribution of morphogen, polarity can be generated spontaneously in the morphogenetic field giving rise to the establishment of a gradient. The stability of these gradients is demonstrated. The onset of a morphogenetic gradient and pattern formation are combined in a single coherent model. Size invariance and its biological implications are discussed.

Some remarks on the stability of the idiotypic network

Abstract The regulation of the immune response is a complex phenomenon whose details are not yet well known. Recently, Jerne has described the immune system as a complex idiotypic network. He has proposed that the interactions between elements involved in the latter are responsible for the main regulatory patterns of the immune system. Some experimental results are in favour of this hypothesis. A few theoretical models have been developed to described more precisely the nature of the interactions between the lymphocytes and the antibodies inside the network as well as their implications. In such a model, the time evolution of the concentration of those elements is described by kinetic equations whose integration over time can reproduce roughly the dynamic behaviour of the immune system. Those theoretical models should at least account for phenomena such as a memory or tolerance, which implies the maintenance of a stationary state. This latter statement can be directly related to the mathematical concept of stability. We illustrate this point on various models. More precisely, we show how each mode of the immune response may be interpreted as a transition from one steady state to another one, following antigenic or any other stimulation.

On the kinetics and optimal specificity of cytotoxic reactions mediated by T-lymphocyte clones

Using the chromium release assay and the single cell assay in agarose, we study the cytotoxic reaction of the MHC-restricted T lymphocyte clones P89:15 and P1:3, which recognize distinct but specific tumour antigens on the surface of syngeneic P815 mastocytoma cells. We propose a mathematical model which describes these experiments, accounts for the strongly non-Michaelian behaviour of the reaction and permits us to estimate the kinetic parameters characterizing effector-target conjugation and lethal hit delivery. The results show that the binding and lytic activity of effector cells is modulated by the number of targets bound to them. The binding of a second target by an effector having already a target bound is facilitated; on the other hand, an effector having bound two targets delivers a lethal hit more slowly than one with a single target bound. We investigate the role of these kinetic properties in the competition between the process of tumour progression due to cancer cell replication and the process of tumour regression due to T lymphocyte cytotoxic activity. For both clones, we estimate the effector-target ratio beyond which rejection prevails. This ratio is nine times larger for P1:3 than for P89:15. Furthermore, our analysis suggests that there exists an optimal specificity minimizing this ratio. Deviations from this optimum, be it in the sense of an increase or decrease of specificity, tendsto stabilize the tumoural state: a situation which in the broader context of the immune response evolution and regulation can be viewed as animmune response dilemma.

Lack of involvement of auto-anti-idiotypic antibody in the regulation of oscillations and tolerance in the antibody response to levan

Abstract Bacterial levan (BL) induces a cyclic (oscillatory) antibody response in both euthymic and athymic BALB/c mice. Significant numbers of plaque-forming cells (PFC) making auto-anti-idiotypic antibody directed against a major cross-reactive idiotype expressed on antibodies specific for BL were detected in euthymic—but not athymic—mice. This suggests that auto-anti-idiotypic antibody, the formation of which requires the participation of mature T cells, does not play a decisive role in generating the cyclic patterns observed. However, such antibody might still influence the proportion of PFC making antibody of complementary idiotype. No relationship between the suppressive property of auto-anti-idiotypic antibody and either the induction or maintenance of immunological tolerance to BL was evident.

Transition from polar to duplicate patterns

AbstractThe existence of symmetric nonuniform solutions in nonlinear reaction-diffusion systems is examined. In the first part of the paper, we establish systematically the bifurcation diagram of small amplitude solutions in the vicinity of the two first bifurcation points. It is shown that:i)The system can adopt a stable symmetric solution (basic wave number 2) if the value of the bifurcation parameter is changed or if the initial polar structure (basic wave number 1) is sufficiently perturbed.ii)This behavior is independent of the particular reaction-diffusion model proposed and of the number of intermediate components (⩾2) involved. In the second part of the paper, analogies are established between the possibilities offered by the bifurcation diagrams, involving only the two first primary branches, and the observation that in the early development of different organisms, appropriate experimental manipulations may switch the normal (polar) developmental pattern to a duplicate structure.

Kinetics of cellular cytotoxicity mediated by cloned cytotoxic T lymphocytes.

Kinetic methods can provide significant information concerning the mechanism of cellular cytotoxicity reactions. Previous kinetic studies of cytotoxic T lymphocytes (Tc) have been hampered by the heterogeneity of the effector cell population tested. We therefore examined the kinetics of lysis mediated by cloned, IL 2 and antigen-dependent murine Tc cells with strong cytotoxic activity that is restricted to distinct tumor-associated antigens on P815 mastocytoma target cells. Initial velocity measurements for cytotoxicity mediated by these clones fit a simple Michaelian kinetic model. Specific activity values obtained from these initial rate measurements are compared to those obtained for polyclonal Tc preparations, NK cells, and activated killer cells. Whereas the initial rate of lytic programming mediated by these cloned cells was very rapid, the rate of cytolysis mediated by the cloned cells decreased significantly within one hour. Since this decrease was observed over a wide range of E:T ratios, it is unlikely to result from product inhibition or a significant decrease in the concentration of unlysed target cells, but may be due to a decrease in the rate of programming and/or effector cell recycling. These results indicate that a simple Michaelian kinetic model is not adequate for tumor cell cytolysis by Tc cells in vitro.

Chemical patterns in circular morphogenetic fields

A model of morphogenetic pattern formation recently proposed by Frenchet al. (1976) is investigated in relation to the properties of reaction-diffusion systems operating on two-dimensional circular medium. One of the basic requirements of this model is the existence of a circular morphogenetic gradient exhibiting no discontinuity. We explain how bifur-cation theory may account for the generation of such a spatial pattern through reaction-diffusion processes. For this, we study the emergence of multiple-order bifurcations.

Dissipation in Embryogenesis

The non-linear Thermodynamics of Irreversible Processes is used to evaluate dissipation during embryogenesis. Simple model systems for cell differentiation and pattern formation are presented. The dissipation in these systems is evaluated by computing the entropy production per unit mass. It is shown that for those models there is an increase in dissipation during the early stages of development.

Model for the positional differentiation of the cap in Acetabularia

A late stage during the biological cycle of the unicellular alga Acetabularia is the differentiation of a cap at the apical end of the stalk. A minimal model of the spatio-temporal regulation of this event is proposed on the basis of biological data available and current hypotheses. This involves the interaction between a diffusing inhibitor specific to the translation of cap mRNAs and a graded distribution of these messengers. The model accounts for delayed protein synthesis which occurs preferably at the apex and is likely to initiate the formation of the cap. The biological and theoretical implications are discussed.

On some stochastic models for protein biosynthesis

Abstract The stability of the solutions of a model proposed by Gibbs et al to describe the protein biosynthesis is studied in terms of the relative values of the kinetic parameters characterizing the three main steps of the polymerization process, i.e., initiation, elongation and termination. When the rate of initiation is equal to the rate of termination, the stationary state is unstable and depends thus on the perturbations imposed to the system. A comparison with results established by Vassart et al. suggests that initiation could be the rate determining step in protein biosynthesis.