Is the immune network a complex network?

Biological networks have been recently found to exhibit many topological properties of the so-called complex networks. It has been reported that they are, in general, both highly skewed and directed. In this paper, we report on the dynamics of a Michaelis-Menten like model when the topological features of the underlying network resemble those of real biological networks. Specifically, instead of using a random graph topology, we deal with a complex heterogeneous network chara...

Pattern-diluted associative networks were introduced recently as models for the immune system, with nodes representing T-lymphocytes and stored patterns representing signalling protocols between T- and B-lymphocytes. It was shown earlier that in the regime of extreme pattern dilution, a system with $N_T$ T-lymphocytes can manage a number $N_B!=!\order(N_T^\delta)$ of B-lymphocytes simultaneously, with $\delta!<!1$. Here we study this model in the extensive load regime $N_B!=!...

We present a new approach to the simulation and analysis of immune system behavior. The simulations that can be done with our software package called SIMMUNE are based on immunological data that describe the behavior of immune system agents (cells, molecules) on a microscopial (i.e. agent-agent interaction) scale by defining cellular stimulus-response mechanisms. Since the behavior of the agents in SIMMUNE can be very flexibly configured, its application is not limited to imm...

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment...

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 ...

Almost every biological, economic and social system is a complex adaptive system (CAS). Mathematical and computer models are relevant to CAS. Some approaches to modeling CAS are given. Applications in vaccination and the immune system are studied. Mathematical topics motivated by CAS are discussed.

We consider the mutual interactions, via cytokine exchanges, among helper lymphocytes, B lymphocytes and killer lymphocytes, and we model them as a unique system by means of a tripartite network. Each part includes all the different clones of the same lymphatic subpopulation, whose couplings to the others are either excitatory or inhibitory (mirroring elicitation and suppression by cytokine). First of all, we show that this system can be mapped into an associative neural netw...

We investigate a model where idiotypes (characterizing B-lymphocytes and antibodies of an immune system) and anti-idiotypes are represented by complementary bitstrings of a given length d allowing for a number of mismatches (matching rules). In this model, the vertices of the hypercube in dimension d represent the potential repertoire of idiotypes. A random set of (with probability p) occupied vertices corresponds to the expressed repertoire of idiotypes at a given moment. Ve...

The immune system protects the body against health-threatening entities, known as antigens, through very complex interactions involving the antigens and the system's own entities. One remarkable feature resulting from such interactions is the immune system's ability to improve its capability to fight antigens commonly found in the individual's environment. This adaptation process is called the evolution of specificity. In this paper, we introduce a new mathematical model for ...

Modeling the immune system so that its essential functionalities stand out without the need for every molecular or cellular interaction to be taken into account has been challenging for many decades. Two competing approaches have been the clonal selection theory and the idiotypic-network theory, each stemming from a relatively separate set of principles. One recent perspective holding the promise of unification is that of immunity as computation, that is, of immunity as the p...