Dynamic stability in random and scale-free B-lymphocyte networks

The Oral Tolerance as a Complex Network Phenomenon

The phenomenon of oral tolerance refers to a local and systemic state of tolerance induced in the gut after its exposure to innocuous antigens. Recent findings have shown the interrelationship between cellular and molecular components of oral tolerance, but its representation through a network of interactions has not been investigated. Our work aims at identifying the causal relationship of each element in an oral tolerance network, and also to propose a phenomenological model that's capable of predicting the stochastic behavior of this network when under manipulation. We compared the changes of a "healthy" network caused by "knock-outs" (KOs) in two approaches: an analytical approach by the Perron Frobenius theory; and a computational approach, which we describe within this work in order to find numerical results for the model. Both approaches have shown the most relevant immunological components for this phenomena, that happens to corroborate the empirical results from animal models. Besides explain in a intelligible fashion how the components interacts in a complex manner, we also managed to describe and quantify the importance of KOs that hasn't been empirically tested.

Randomly evolving idiotypic networks: structural properties and architecture

We consider a minimalistic dynamic model of the idiotypic network of B lymphocytes. A network node represents a population of B lymphocytes of the same specificity (idiotype), which is encoded by a bit string. The links of the network connect nodes with complementary and nearly complementary bit strings, allowing for a few mismatches. A node is occupied if a lymphocyte clone of the corresponding idiotype exists; otherwise it is empty. There is a continuous influx of new B lymphocytes of random idiotype from the bone marrow. B lymphocytes are stimulated by cross-linking their receptors with complementary structures. If there are too many complementary structures, steric hindrance prevents cross-linking. Stimulated cells proliferate and secrete antibodies of the same idiotype as their receptors; unstimulated lymphocytes die. Depending on few parameters, the autonomous system evolves randomly towards patterns of highly organized architecture, where the nodes can be classified into groups according to their statistical properties. We observe and describe analytically the building principles of these patterns, which make it possible to calculate number and size of the node groups and the number of links between them. The architecture of all patterns observed so far in simulations can be explained this way. A tool for real-time pattern identification is proposed.

Organization and evolution of synthetic idiotypic networks

We introduce a class of weighted graphs whose properties are meant to mimic the topological features of idiotypic networks, namely, the interaction networks involving the B core of the immune system. Each node is endowed with a bit string representing the idiotypic specificity of the corresponding B cell, and the proper distance between any couple of bit strings provides the coupling strength between the two nodes. We show that a biased distribution of the entries in bit strings can yield fringes in the (weighted) degree distribution, small-world features, and scaling laws, in agreement with experimental findings. We also investigate the role of aging, thought of as a progressive increase in the degree of bias in bit strings, and we show that it can possibly induce mild percolation phenomena, which are investigated too.