A scale-free behavior has been observed in many living systems at micro- and macro-scales. These systems continue to stimulate the interests in theoretical studies, including the understanding of aging and specifically of immunosenescence. The immune system represents the major system with a large cellular component dedicated to the generation of adaptive memory to pathogens. It is this component of immunity which is the most instructive in understanding the life stages of humans.

In the experimental studies of the adaptive immune system, we had observed a scale-free network governing the repertoire of memory T-cells (Naumov et al, 2003). At the molecular level, we observe that a memory immune response to influenza virus becomes diverse upon repeated exposures to the virus that can be modeled as a fractal self-similar system. Theoretical explanation of experimental findings has been described by the small-world construction (Ruskin and Burns, 2006) as a special case of the scale-free network (Albert and Barabasi, 2002). We then simulated the fractal behavior mimicking immune memory - its generation, maintenance and senescence (Naumova et al, 2008) and experimentally illustrated the general stability of the power-law structures and age-related changes. Our recent theoretical work confirms the assumptions that multiple expansion-contraction cycles define the robustness of immune response and correspond to memory formation (Saito and Narikiyo, 2011). Saito and Narikiyo had proposed the dynamical network of the adaptive immune system as a self-organized critical state in which the avalanche feedback reinforcement may reduce immunosenescence.
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At the population level, we also observed the evidence of exposure to influenza as a marker of “immunological age.” In the cohort of healthy donors, each encounter with an infectious agent was unique for every person. Yet, the commonality in responses formed “immunological kinship” among all affected individuals, manifested by a preserved T-cell clonal pool. The diverse responses to flu and changes in diversity allow us to make an inference to “immunological kinship” and “immunological age.” Our experimental data indicate that at a certain point the continuing exposures to influenza begin to decrease the diversity of immune response. These observations lead us to explore theoretical conditions governing the “stable” and “volatile” components of the T-cell repertoires via dynamic neural networks. Such separation allowed us to detect a condition indicative of acceleration of immune aging. We derived the initial network parameters based on a specially designed anchored power-law regression fit of experimental data from middle-aged and older donors over time and illustrated age acceleration and immunosenescence in humans.

References:
Albert, R., and Barabási, A.L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics 74, 47-97.
Naumov, Y.N., Naumova, E.N., Hogan, K.T., Selin, L.K., and Gorski, J. (2003). A fractal clonotype distribution in the CD8+ memory T cell repertoire could optimize potential for immune responses. J Immunol 170, 3994-4001
Naumova, E.N., Gorski, J., and Naumov, Y.N. (2008). Simulation studies for a multistage dynamic process of immune memory response to influenza: experiment in silico. Ann Zool Fennici 45, 369-
384.
Ruskin, H.J., and Burns, J. (2006). Weighted networks in immune system shape space. Physica A: Statistical Mechanics and its Applications 365, 549-555.
Saito, S., and O. Narikiyo, O. (2011). Scale-free dynamics of somatic adaptability in immune system. Biosystems 103: 420-424.

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