Biomedical subjects

David B Saakian

Publications and source records attributed to David B Saakian.

6 recordsLinked to original sources

PubMed2006

Quasispecies theory for multiple-peak fitness landscapes.

We use a path integral representation to solve the Eigen and Crow-Kimura molecular evolution models for the case of multiple fitness peaks with arbitrary fitness and degradation functions. In the general case, we find that the solution to these molecular evolution models can be written as the optimum of a fitness function, with constraints enforced by Lagrange multipliers and with a term accounting for the entropy of the spreading population in sequence space. The results for the Eigen model are applied to consider virus or cancer proliferation under the control of drugs or the immune system.

Biological Evolution↗

PubMed2006

Exact solution of the Eigen model with general fitness functions and degradation rates.

We present an exact solution of Eigen's quasispecies model with a general degradation rate and fitness functions, including a square root decrease of fitness with increasing Hamming distance from the wild type. The found behavior of the model with a degradation rate is analogous to a viral quasispecies under attack by the immune system of the host. Our exact solutions also revise the known results of neutral networks in quasispecies theory. To explain the existence of mutants with large Hamming distances from the wild type, we propose three different modifications of the Eigen model: mutation landscape, multiple adjacent mutations, and frequency-dependent fitness in which the steady-state solution shows a multicenter behavior.

Biological Evolution↗

PubMed2005

Error threshold in optimal coding, numerical criteria, and classes of universalities for complexity.

The free energy of the random energy model at the transition point between the ferromagnetic and spin glass phases is calculated. At this point, equivalent to the decoding error threshold in optimal codes, the free energy has finite size corrections proportional to the square root of the number of degrees. The response of the magnetization to an external ferromagnetic phase is maximal at values of magnetization equal to one-half. We give several criteria of complexity and define different universality classes. According to our classification, at the lowest class of complexity are random graphs, Markov models, and hidden Markov models. At the next level is the Sherrington-Kirkpatrick spin glass, connected to neuron-network models. On a higher level are critical theories, the spin glass phase of the random energy model, percolation, and self-organized criticality. The top level class involves highly optimized tolerance design, error thresholds in optimal coding, language, and, maybe, financial markets. Living systems are also related to the last class. The concept of antiresonance is suggested for complex systems.

Journal Article↗

PubMed2004

Solvable biological evolution models with general fitness functions and multiple mutations in parallel mutation-selection scheme.

In a recent paper [Phys. Rev. E 69, 046121 (2004)]], we used the Suzuki-Trottere formalism to study a quasispecies biological evolution model in a parallel mutation-selection scheme with a single-peak fitness function and a point mutation. In the present paper, we extend such a study to evolution models with more general fitness functions or multiple mutations in the parallel mutation-selection scheme. We give some analytical equations to define the error thresholds for some general cases of mean-field-like or symmetric mutation schemes and fitness functions. We derive some equations for the dynamics in the case of a point mutation and polynomial fitness functions. We derive exact dynamics for two-point mutations, asymmetric mutations, and the four-value spin model with a single-peak fitness function. The same method is applied for the model with a royal road fitness function. We derive the steady-state distribution for the single-peak fitness function.

Biological Evolution↗

PubMed2004

Solvable biological evolution model with a parallel mutation-selection scheme.

Based on the connection between a quantum spin model and an asexual biological evolution model with a single-peak fitness function in parallel mutation-selection scheme, we solve exactly both static and dynamics of the evolution model. We find that relaxation in such a parallel scheme is faster than that in a connected scheme of Eigen model. Our method can also be extended to other fitness functions.

Journal Article↗

PubMed2003

Approximate calculation of the ground-state energy for Potts spin-glass models.

We consider the q-state Potts spin-glass model, with quenched couplings taking two different values only. As an approximation for this model a proper generalization of the random energy model is derived. Formulas of the resulting diluted generalized random energy model (DGREM) are applied to calculate the ground-state energy for the two-dimensional Potts spin-glass model. The semianalytical results are compared with numerical determinations of the ground-state energy, using multicanonical, random cost, and simulated annealing techniques.

Journal Article↗