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Yayın Dissipative dynamics and the statistics of energy states of a Hookean model for protein folding(Kluwer Academic Publishers-Plenum Publishers, 2000-07) Tüzel, Erkan; Erzan, AyşeA generic model of a random polypeptide chain, with discrete torsional degrees of freedom and Hookean spring connecting pails or hydrophobic residues, reproduces the energy probability distribution of real proteins over a very large range of energies. We show that this system with harmonic interactions, under dissipative dynamics driven by random noise, leads to a distribution of energy states obeying a modified one-dimensional Ornstein-Uhlenbeck process and giving rise Lo the so-called Wigner distribution. A tunably fine- or coarse-grained sampling of the energy landscape yields a family of distributions for the energies and energy spacings.Yayın Spectral renormalization group for the Gaussian model and 𝜓4 theory on nonspatial networks(American Physical Society, 2015-08-06) Tuncer, Aslı; Erzan, AyşeWe implement the spectral renormalization group on different deterministic nonspatial networks without translational invariance. We calculate the thermodynamic critical exponents for the Gaussian model on the Cayley tree and the diamond lattice and find that they are functions of the spectral dimension, (d) over tilde. The results are shown to be consistent with those from exact summation and finite-size scaling approaches. At (d) over tilde = 2, the lower critical dimension for the Ising universality class, the Gaussian fixed point is stable with respect to a psi(4) perturbation up to second order. However, on generalized diamond lattices, non-Gaussian fixed points arise for 2 < <(d)over tilde> < 4.Yayın Strategies for the evolution of sex(American Institute of Physics Inc., 2001-12) Tüzel, Erkan; Sevim, Volkan; Erzan, AyşeThe maintenance of a macroscopic sexual population is addressed. As a scenario, the mechanism of random conversion to sex, in the presence of a constant rate of mutation is examined. This scenario is very closely related to "coevolution of cell senescence and diploid sexual reproduction in unicellular organisms." In this work, a "senescence clock" ticks off a finite lifetime for each bit string. Sexual reproduction resets the senescence of clock; unless this happens after a number of generations of cloning, the offspring stop dividing and die.Yayın Evolutionary route to diploidy and sex(National Academy of Sciences, 2001-11-20) Tüzel, Erkan; Sevim, Volkan; Erzan, AyşeBy using a bit-string model of evolution, we find a successful route to diploidy and sex in simple organisms. Allowing the sexually reproducing diploid individuals to also perform mitosis, as they do in a haploid-diploid cycle, leads to the complete takeover of the population by sexual diploids. This mechanism is so robust that even the accidental conversion and pairing of only two diploids give rise to a sexual population.Yayın The statistics of energy states of a Hookean model for proteins(TÜBİTAK, 2000) Erzan, Ayşe; Tüzel, ErkanA generic model of a random polypeptide chain, with discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobia residues, reproduces the energy probability distribution of real proteins over a very large range of energies. We show that this system with harmonic interactions, under dissipative dynamics driven by random noise, leads to a distribution of energy states obeying a modified one-dimensional Ornstein-Uhlenbeck process with reflecting boundary conditions, and giving rise to distributions of the Wigner or inverse Gaussian form. A continuum approximation leads to a path integral formulation of the problem.Yayın Testing a hypothesis for the evolution of sex(World Scientific Publishing Company, 2000-07-11) Örçal, Bora; Tüzel, Erkan; Sevim, Volkan; Jan, Naeem; Erzan, AyşeAn asexual set of primitive bacteria is simulated with a lit-string Penna model with a Fermi function for survival. A recent hypothesis by Jan, Stauffer, and Moseley on the evolution of sex from asexual cells as a strategy for trying to escape the effects of deleterious mutations is checked. This strategy is found to provide a successful scenario for the evolution of a stable macroscopic sexual population.Yayın Strategies for the evolution of sex(American Physical Soc, One Physics Ellipse, 2001-12) Tüzel, Erkan; Sevim, Volkan; Erzan, AyşeWe find that the hypothesis made by Jan, Stauffer, and Moseley [Theory Biosci. 119, 166 (2000)] for the evolution of sex, namely, a strategy devised to escape extinction due to too many deleterious mutations, is sufficient but not necessary for the successful evolution of a steady state population of sexual individuals within a finite population. Simply allowing for a finite probability for conversion to sex in each generation also gives rise to a stable sexual population, in the presence of an upper limit on the number of deleterious mutations per individual. For large values of this probability, we find a phase transition to an intermittent, multistable regime. On the other hand, in the limit of extremely slow drive. another transition takes place to a different steady state distribution. with fewer deleterious mutations within the population.
