Fixation Probability Of Mutant Research Articles

Counterintuitive properties of evolutionary measures: A stochastic process study in cyclic population structures with periodic environments

Local environmental interactions are a major factor in determining the success of a new mutant in structured populations. Spatial variations in the concentration of genotype-specific resources change the fitness of competing strategies locally and thus can drastically change the outcome of evolutionary processes in unintuitive ways. The question is how such local environmental variations in network population structures change the condition for selection and fixation probability of an advantageous (or deleterious) mutant. We consider linear graph structures and focus on the case where resources have a spatial periodic pattern. This is the simplest model with two parameters, length scale and fitness scales, representing heterogeneity. We calculate fixation probability and fixation times for a constant population birth–death process as fitness heterogeneity and period vary. Fixation probability is affected by not only the level of fitness heterogeneity but also spatial scale of resources variations set by period of distribution T. We identify conditions for which a previously a deleterious mutant (in a uniform environment) becomes beneficial as fitness heterogeneity is increased. We observe cases where the fixation probability of both mutant and resident types are more than their neutral value, 1/N, simultaneously. This coincides with exponential increase in time to fixation which points to potential coexistence of resident and mutant types. Finally, we discuss the effect of the ‘fitness shift’ where the fitness function of two types has a phase difference. We observe significant increases (or decreases) in the fixation probability of the mutant as a result of such phase shift.

Modeling dynamics of mutants in heterogeneous stem cell niche

Studying the stem cell (SC) niche architecture is a crucial step for investigating the process of oncogenesis and obtaining an effective stem cell therapy for various cancers. Recently, it has been observed that there are two groups of SCs in the SC niche collaborating with each other to maintain tissue homeostasis: border stem cells (BSCs), which are responsible in controlling the number of non-stem cells as well as stem cells, and central stem cells (CeSCs), which regulate the SC niche. Here, we develop a bi-compartmental stochastic model for the SC niche to study the spread of mutants within the niche. The analytic calculations and numeric simulations, which are in perfect agreement, reveal that in order to delay the spread of mutants in the SC niche, a small but non-zero number of SC proliferations must occur in the CeSC compartment. Moreover, the migration of BSCs to CeSCs delays the spread of mutants. Furthermore, the fixation probability of mutants in the SC niche is independent of types of SC division as long as all SCs do not divide fully asymmetrically. Additionally, the progeny of CeSCs have a much higher chance than the progeny of BSCs to take over the entire niche.

The duality of spatial death–birth and birth–death processes and limitations of the isothermal theorem

Evolutionary models on graphs, as an extension of the Moran process, have two major implementations: birth–death (BD) models (or the invasion process) and death–birth (DB) models (or voter models). The isothermal theorem states that the fixation probability of mutants in a large group of graph structures (known as isothermal graphs, which include regular graphs) coincides with that for the mixed population. This result has been proved by Lieberman et al. (2005 Nature 433, 312–316. (doi:10.1038/nature03204)) in the case of BD processes, where mutants differ from the wild-types by their birth rate (and not by their death rate). In this paper, we discuss to what extent the isothermal theorem can be formulated for DB processes, proving that it only holds for mutants that differ from the wild-type by their death rate (and not by their birth rate). For more general BD and DB processes with arbitrary birth and death rates of mutants, we show that the fixation probabilities of mutants are different from those obtained in the mass-action populations. We focus on spatial lattices and show that the difference between BD and DB processes on one- and two-dimensional lattices is non-small even for large population sizes. We support these results with a generating function approach that can be generalized to arbitrary graph structures. Finally, we discuss several biological applications of the results.

Universal distribution of protein evolution rates as a consequence of protein folding physics

The hypothesis that folding robustness is the primary determinant of the evolution rate of proteins is explored using a coarse-grained off-lattice model. The simplicity of the model allows rapid computation of the folding probability of a sequence to any folded conformation. For each robust folder, the network of sequences that share its native structure is identified. The fitness of a sequence is postulated to be a simple function of the number of misfolded molecules that have to be produced to reach a characteristic protein abundance. After fixation probabilities of mutants are computed under a simple population dynamics model, a Markov chain on the fold network is constructed, and the fold-averaged evolution rate is computed. The distribution of the logarithm of the evolution rates across distinct networks exhibits a peak with a long tail on the low rate side and resembles the universal empirical distribution of the evolutionary rates more closely than either distribution resembles the log-normal distribution. The results suggest that the universal distribution of the evolutionary rates of protein-coding genes is a direct consequence of the basic physics of protein folding.

Effect of dominance on heterozygosity and the fixation probability in a subdivided population.

Under the assumptions of a subdivided population and the presence of dominance for fitness, the expected sum of heterozygosity in the total population during the lifetime of mutant was investigated. It was shown analytically and by computer simulations that in the island model the effect of dominance on the expected sum of heterozygosity decreases as the migration rate decreases and is lost almost completely when the migration rate is very low. In addition to the expected sum of heterozygosity, the fixation probability of mutant was also investigated. The effect of dominance on the fixation probability also decreases as the migration rate decreases but is not completely lost when the migration rate is very low.