Promiscuous Enzyme Activity as a Driver of Allo and Iso Convergent Evolution, Lessons from the β-Lactamases

The probability of the evolution of a character depends on two factors: the probability of moving from one character state to another character state and the probability of the new character state fixation. The more the evolution of a character is probable, the more the convergent evolution will be witnessed, and consequently, convergent evolution could mean that the convergent character evolution results as a combination of these two factors. We investigated this phenomenon by studying the convergent evolution of biochemical functions. For the investigation we used the case of β-lactamases. β-lactamases hydrolyze β-lactams, which are antimicrobials able to block the DD-peptidases involved in bacterial cell wall synthesis. β-lactamase activity is present in two different superfamilies: the metallo-β-lactamase and the serine β-lactamase. The mechanism used to hydrolyze the β-lactam is different for the two superfamilies. We named this kind of evolution an allo-convergent evolution. We further showed that the β-lactamase activity evolved several times within each superfamily, a convergent evolution type that we named iso-convergent evolution. Both types of convergent evolution can be explained by the two evolutionary mechanisms discussed above. The probability of moving from one state to another is explained by the promiscuous β-lactamase activity present in the ancestral sequences of each superfamily, while the probability of fixation is explained in part by positive selection, as the organisms having β-lactamase activity allows them to resist organisms that secrete β-lactams. Indeed, an organism that has a mutation that increases the β-lactamase activity will be selected, as the organisms having this activity will have an advantage over the others.

Promiscuous Enzyme Activity as a Driver of Allo and Iso Convergent Evolution, Lessons from the β-lactamases

The probability of the evolution of a character depends on two factors: the probability of moving from one character state to another character state and the probability of the new character state fixation. More the evolution of a character is probable more convergent evolution will be witnessed, consequently, convergent evolution could mean that the convergent character evolution result as a combination of these two factors. We investigate this phenomenon by studying the convergent evolution of biochemical functions. We use for the investigation the case of β-lactamases. β-lactamases hydrolyzes β-lactams which are antimicrobials able to block the DD-peptidases involved in bacterial cell wall synthesis. β-lactamase activity is present in two different superfamilies: the metallo-β-lactamase and the serine β-lactamase superfamily. The mechanism used to hydrolyze the β-lactam is different for the two superfamilies. We named this kind of evolution an allo-convergent evolution. We further show that the β-lactamase activity evolved several times within each superfamily, a convergent evolution type that we named iso-convergent evolution. Both types of convergent evolution can be explained by the two evolutionary mechanisms discussed above. The probability of moving from one state to another is explaining the promiscuous β-lactamase activity present in the ancestral sequences of each superfamily, while the probability of fixation is explained in part, by positive selection as the organisms having β-lactamase activity allows them to resist to organism secreting β-lactams. Indeed a mutation increasing the β-lactamases activity will be selected as the organisms having this activity will have an advantage over the others.

On the Two-phase Fractional Stefan Problem

The classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion. We start the paper by reviewing the main properties of the classical problem that are of interest to us. Then we introduce the fractional Stefan problem and develop the basic theory. After that we center our attention on selfsimilar solutions, their properties and consequences. We first discuss the results of the one-phase fractional Stefan problem, which have recently been studied by the authors. Finally, we address the theory of the two-phase fractional Stefan problem, which contains the main original contributions of this paper. Rigorous numerical studies support our results and claims.

Global Attractors for the Higher-Order Evolution Equation

In this paper, we obtain the existence of a global attractor for the higher-order evolution type equation. Moreover, we discuss the asymptotic behavior of global solution.

Singular Perturbation of Nonlinear Systems with Regular Singularity

We extend Balser-Kostov method of studying summability properties of a singularly perturbed inhomogeneous linear system with regular singularity at origin to nonlinear systems of the form εzf′=Fε,z,f with F a Cν-valued function, holomorphic in a polydisc D-ρ×D-ρ×D-ρν. We show that its unique formal solution in power series of ε, whose coefficients are holomorphic functions of z, is 1-summable under a Siegel-type condition on the eigenvalues of Ff(0,0,0). The estimates employed resemble the ones used in KAM theorem. A simple lemma is applied to tame convolutions that appear in the power series expansion of nonlinear equations. Applications to spherical Bessel functions and probability theory are indicated. The proposed summability method has certain advantages as it may be applied as well to (singularly perturbed) nonlinear partial differential equations of evolution type.