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Register a new userA graph model for the evolution of specificity in humoral immunity
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The immune system protects the body against health-threatening entities, known as antigens, through very complex interactions involving the antigens and the systems own entities. One remarkable feature resulting from such interactions is the immune systems ability to improve its capability to fight antigens commonly found in the individuals environment. This adaptation process is called the evolution of specificity. In this paper, we introduce a new mathematical model for the evolution of specificity in humoral immunity, based on Jernes functional, or idiotypic, network. The evolution of specificity is modeled as the dynamic updating of connection weights in a graph whose nodes are related to the networks idiotypes. At the core of this weight-updating mechanism are the increase in specificity caused by clonal selection and the decrease in specificity due to the insertion of uncorrelated idiotypes by the bone marrow. As we demonstrate through numerous computer experiments, for appropriate choices of parameters the new model correctly reproduces, in qualitative terms, several immune functions.
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We consider the problem of self tolerance in the frame of a minimalistic model of the idiotypic network. A node of this network represents a population of B lymphocytes of the same idiotype which is encoded by a bit string. The links of the network connect nodes with (nearly) complementary strings. The population of a node survives if the number of occupied neighbours is not too small and not too large. There is an influx of lymphocytes with random idiotype from the bone marrow. Previous investigations have shown that this system evolves toward highly organized architectures, where the nodes can be classified into groups according to their statistical properties. The building principles of these architectures can be analytically described and the statistical results of simulations agree very well with results of a modular mean field theory. In this paper we present simulation results for the case that one or several nodes, playing the role of self, are permanently occupied. We observe that the group structure of the architecture is very similar to the case without self antigen, but organized such that the neighbours of the self are only weakly occupied, thus providing self tolerance. We also treat this situation in mean field theory which give results in good agreement with data from simulation.
We present a discrete stochastic model which represents many of the salient features of the biological process of wound healing. The model describes fronts of cells invading a wound. We have numerical results in one and two dimensions. In one dimension we can give analytic results for the front speed as a power series expansion in a parameter, p, that gives the relative size of proliferation and diffusion processes for the invading cells. In two dimensions the model becomes the Eden model for p near 1. In both one and two dimensions for small p, front propagation for this model should approach that of the Fisher-Kolmogorov equation. However, as in other cases, this discrete model approaches Fisher-Kolmogorov behavior slowly.
We consider self-tolerance and its failure -autoimmunity- in a minimal mathematical model of the idiotypic network. A node in the network represents a clone of B-lymphocytes and its antibodies of the same idiotype which is encoded by a bitstring. The links between nodes represent possible interactions between clones of almost complementary idiotype. A clone survives only if the number of populated neighbored nodes is neither too small nor too large. The dynamics is driven by the influx of lymphocytes with randomly generated idiotype from the bone marrow. Previous work has revealed that the network evolves towards a highly organized modular architecture, characterized by groups of nodes which share statistical properties. The structural properties of the architecture can be described analytically, the statistical properties determined from simulations are confirmed by a modular mean-field theory. To model the presence of self we permanently occupy one or several nodes. These nodes influence their linked neighbors, the autoreactive clones, but are themselves not affected by idiotypic interactions. The architecture is very similar to the case without self, but organized such that the neighbors of self are only weakly occupied, thus providing self-tolerance. This supports the perspective that self-reactive clones, which regularly occur in healthy organisms, are controlled by anti-idiotypic clones. We discuss how perturbations, like an infection with foreign antigen, a change in the influx of new idiotypes, or the random removal of idiotypes, may lead to autoreactivity and devise protocols which cause a reconstitution of the self-tolerant state. The results could be helpful to understand network and probabilistic aspects of autoimmune disorders.
The comment mostly concerns mis-representation of my position on Quantum Biology, by stating that I am reducing cells behavior to quantum particles inside the cell. I contrast my position with that of McFadden-Al-Khalili, as well as with the position of Asano et al. I also advertise an idea, described in our latest paper (Bordonaro, Ogryzko. Quantum Biology at the Cellular level - elements of the research program, BioSystems, 2013), for the need of synthetic biology in testing some predictions that follow from our approach.
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