Self-organizing behavior in a lattice model for co-evolution of virus and immune systems

COMPLEX BIOLOGICAL IMMUNE SYSTEM THROUGH THE EYES OF DUAL-PHASE EVOLUTION

Dual-phase evolution (DPE) and the network theory help to analyze prominent properties of the complex adaptive systems (CASs) such as emergence and self-organization that are caused due to the phase transitions. These transitions are observed because of the increase and decrease in the number of system components and their interactions. The immune system, which is one of the CASs, provides an adaptive response to the foreign molecules. Prior to this response, the immune system is present in the circulation state and during the response, it moves into the growth state, where the number of immune cells and their cell–cell contacts increase rapidly. The phase transitions from the circulation state to the growth state and then back to the circulation state cause the emergence and self-organization of the immune system, respectively. There is a need to understand these complex cellular dynamics during the immune response. In this paper, we have proposed an integrated model of DPE, network theory, and the immune system that has helped to understand and analyze the phases and properties of the immune system. Analysis of the growth phase network is provided and it is concluded that this network exhibits scale-free nature following power law for the degree distribution of nodes.

Amplitude ratios for critical systems in the c=-2 universality class

We study the finite-size corrections of the critical dense polymer (CDP) and the dimer models on ∞×N rectangular lattice. We find that the finite-size corrections in the CDP and dimer models depend in a crucial way on the parity of N, and a change of the parity of N is equivalent to the change of boundary conditions. We present a set of universal amplitude ratios for amplitudes in finite-size correction terms of critical systems in the universality class with central charge c=-2. The results are in perfect agreement with a perturbated conformal field theory under the assumption that all analytical corrections coming from the operators which belongs to the tower of the identity. Our results inspire many interesting problems for further studies.

Short-time evolution in the adaptive immune system

We exploit a simple model to numerically and analytically investigate the effect of enforcing a time constraint for achieving a system-wide goal during an evolutionary dynamics. This situation is relevant to finding antibody specificities in the adaptive immune response as well as to artificial situations in which an evolutionary dynamics is used to generate a desired capability in a limited number of generations. When the likelihood of finding the target phenotype is low, we find that the optimal mutation rate can exceed the error threshold, in contrast to conventional evolutionary dynamics. We also show how a logarithmic correction to the usual inverse scaling of population size with mutation rate arises. Implications for natural and artificial evolutionary situations are discussed.

Asymptotic shape of the region visited by an Eulerian walker

We study an Eulerian walker on a square lattice, starting from an initial randomly oriented background using Monte Carlo simulations. We present evidence that, for a large number of steps N , the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as N1/3, for large N , and the width of the boundary region grows as Nalpha/3, with alpha=0.40+/-0.06 . If we introduce stochasticity in the evolution rules, the mean-square displacement of the walker, <RN2> approximately <RN2> approximately N2nu, shows a crossover from the Eulerian (nu=1/3) to a simple random-walk (nu=1/2) behavior.