Immune networks: multi-tasking capabilities near saturation

Many components of the IS are constructed as modular units which do not need to communicate with each other such that the number of components increases but the size remains constant. However, a sub-modular IS architecture in which lymph node number and size both increase sublinearly with body size is shown to efficiently balance the requirements of communication and migration, consistent with experimental data. We hypothesize that the IS architecture optimizes the tradeoff b...

Biological systems, unlike physical or chemical systems, are characterized by the very inhomogeneous distribution of their components. The immune system, in particular, is notable for self-organizing its structure. Classically, the dynamics of natural systems have been described using differential equations. But, differential equation models fail to account for the emergence of large-scale inhomogeneities and for the influence of inhomogeneity on the overall dynamics of biolo...

Complex mathematical models of interaction networks are routinely used for prediction in systems biology. However, it is difficult to reconcile network complexities with a formal understanding of their behavior. Here, we propose a simple procedure (called $\bar \varphi$) to reduce biological models to functional submodules, using statistical mechanics of complex systems combined with a fitness-based approach inspired by $\textit{in silico}$ evolution. $\bar \varphi$ works by ...

In this paper we made a review of some papers about probabilistic regulatory networks (PRN), in particular we introduce our concept of homomorphisms of PRN with an example of projection of a regulatory network to a smaller one. We apply the model PRN (or Probabilistic Boolean Network) to the immune system, the PRN works with two functions. The model called ""The B/T-cells interaction"" is Boolean, so we are really working with a Probabilistic Boolean Network. Using Markov Cha...

Immune system is the most important defense system to resist human pathogens. In this paper we present an immune model with bipartite graphs theory. We collect data through COPE database and construct an immune cell- mediators network. The act degree distribution of this network is proved to be power-law, with index of 1.8. From our analysis, we found that some mediators with high degree are very important mediators in the process of regulating immune activity, such as TNF-al...

In this work we use belief-propagation techniques to study the equilibrium behaviour of a minimal model for the immune system comprising interacting T and B clones. We investigate the effect of the so-called idiotypic interactions among complementary B clones on the system's activation. Our result shows that B-B interactions increase the system's resilience to noise, making clonal activation more stable, while increasing the cross-talk between different clones. We derive anal...

We study the influence of network topology on retrieval properties of recurrent neural networks, using replica techniques for diluted systems. The theory is presented for a network with an arbitrary degree distribution $p(k)$ and applied to power law distributions $p(k) \sim k^{-\gamma}$, i.e. to neural networks on scale-free graphs. A bifurcation analysis identifies phase boundaries between the paramagnetic phase and either a retrieval phase or a spin glass phase. Using a po...

The biological immune system is a robust, complex, adaptive system that defends the body from foreign pathogens. It is able to categorize all cells (or molecules) within the body as self-cells or non-self cells. It does this with the help of a distributed task force that has the intelligence to take action from a local and also a global perspective using its network of chemical messengers for communication. There are two major branches of the immune system. The innate immune ...

The repertoire of lymphocyte receptors in the adaptive immune system protects organisms from diverse pathogens. A well-adapted repertoire should be tuned to the pathogenic environment to reduce the cost of infections. We develop a general framework for predicting the optimal repertoire that minimizes the cost of infections contracted from a given distribution of pathogens. The theory predicts that the immune system will have more receptors for rare antigens than expected from...

Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another interesting feature of these networks is their connection to the attention mechanism which is part of the Transformer architectures widely applied in deep learning. In this work, we study a generic family of pattern ensembles using a statist...