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Protein structures strongly influence molecular evolution. In particular, the evolutionary rate of a protein site depends on the number of its native contacts. Stability-constrained models of protein evolution consider this influence of protein structure on evolution by predicting the effect of mutations on the stability of the native state, but they currently neglect how mutations affect the protein structure. These models predict that buried protein sites with more native contacts are more constrained by natural selection and less variable, as observed. Nevertheless, previous work did not consider the stability against compact misfolded conformations, although it is known that the negative design that destabilizes these misfolded conformations influences protein evolution significantly. Here, we show that stability-constrained models that consider misfolding predict that site-specific sequence entropy and substitution rate peak at amphiphilic sites with an intermediate number of contacts, as these sites are less constrained than exposed sites with few contacts whose hydrophobicity must be limited. This result holds both for a mean-field model with independent sites and for a pairwise model that takes as a reference the wild-type sequence, but it contrasts with the observations that indicate that the entropy and the substitution rate decrease monotonically with the number of contacts. Our work suggests that stability-constrained models overestimate the tolerance of amphiphilic sites against mutations, either because of the limits of the free energy function or, more importantly in our opinion, because they do not consider how mutations perturb the native protein structure.

In this work, we aim to study the well-posedness of a deterministic problem consisting of the non-linear heat equation of gradient type. The evolution equation emerges by projecting the Laplace operator with Dirichlet boundary conditions and polynomial nonlinearity of degree 2n − 1, onto the tangent space of the sphere M in a Hilbert space H. We are going to deal with the question of existence and uniqueness based on the Faedo-Galerkin compactness method.

A recent analysis of evolutionary rates in >500 globular soluble enzymes revealed pervasive conservation gradients toward catalytic residues. By looking at amino acid preference profiles rather than evolutionary rates in the same data set, we quantified the effects of active sites on site-specific constraints for physicochemical traits. We found that conservation gradients respond to constraints for polarity, hydrophobicity, flexibility, rigidity and structure in ways consistent with fold polarity principles; while sites far from active sites seem to experience no physicochemical constraint, rather being highly variable and favoring amino acids of low metabolic cost. Globally, our results highlight that amino acid variation contains finer information about protein structure than usually regarded in evolutionary models, and that this information is retrievable automatically with simple fits. We propose that analyses of the kind presented here incorporated into models of protein evolution should allow for better description of the physical chemistry that underlies molecular evolution.

Phenotypic variation is the raw material of adaptive Darwinian evolution. The phenotypic variation found in organismal development is biased towards certain phenotypes, but the molecular mechanisms behind such biases are still poorly understood. Gene regulatory networks have been proposed as one cause of constrained phenotypic variation. However, most pertinent evidence is theoretical rather than experimental. Here, we study evolutionary biases in two synthetic gene regulatory circuits expressed in Escherichia coli that produce a gene expression stripe—a pivotal pattern in embryonic development. The two parental circuits produce the same phenotype, but create it through different regulatory mechanisms. We show that mutations cause distinct novel phenotypes in the two networks and use a combination of experimental measurements, mathematical modelling and DNA sequencing to understand why mutations bring forth only some but not other novel gene expression phenotypes. Our results reveal that the regulatory mechanisms of networks restrict the possible phenotypic variation upon mutation. Consequently, seemingly equivalent networks can indeed be distinct in how they constrain the outcome of further evolution. Synopsis Analyses in synthetic circuits show that mutations result in distinct novel phenotypes in two circuits that showed the same phenotype before mutation. This constrained phenotypic variation is caused by differences in the circuits’ regulatory mechanisms. Two synthetic circuits expressed in E. coli that produce the same phenotype, but through different regulatory mechanisms, are used to study the molecular mechanisms underlying constrained phenotypic variation during evolution. The two networks create different spectra of novel phenotypes after mutation. A combination of experimental measurements, mathematical modeling and DNA sequencing shows that the regulatory mechanisms restrict the phenotypic variation that becomes accessible upon mutation. Graphical Abstract Analyses in synthetic circuits show that mutations result in distinct novel phenotypes in two circuits that showed the same phenotype before mutation. This constrained phenotypic variation is caused by differences in the circuits’ regulatory mechanisms.

A continuum model of the two dimensional low angle grain boundary motion and the dislocation structure evolution on the grain boundaries has been developed in [L. Zhang and Y. Xiang, J. Mech. Phys. Solids, 117 (2018), pp. 157-178]. The model is based on the motion and reaction of the constituent dislocations of the grain boundaries. The long-range elastic interaction between dislocations is included in the continuum model, and it maintains a stable dislocation structure described by Frank's formula for grain boundaries. In this paper, we develop a new continuum model for the coupling and sliding motions of grain boundaries that avoids the time-consuming calculation of the long-range elastic interaction. In this model, the long-range elastic interaction is replaced by a constraint of Frank's formula. The constrained evolution problem in our new continuum model is further solved by using the projection method. Effects of the coupling and sliding motions in our new continuum model and relationship with the classical motion by curvature model are discussed. The continuum model is validated by comparisons with discrete dislocation dynamics model and the early continuum model [L. Zhang and Y. Xiang, J. Mech. Phys. Solids, 117 (2018), pp. 157-178] in which the long-range dislocation interaction is explicitly calculated.

Macro-hybrid multidomain optimal control of dual evolution mixed variational transport flow processes through elastoviscoplastic porous media, with intrinsic control mechanisms, are formulated and analyzed as evolutionary mixed subpotential maximal monotone variational inclusions. Existence results for the state systems as well as optimality conditions are established in reflexive Banach real functional frameworks via resolvent fixed point characterizations. Macro-hybrid mixed variational optimality conditions, as well as primal, dual and Lagrangean mixed optimization results are determined, applying perturbation conjugate duality methods, recently developed by the author.

Optimal power allocation (OPA), which can be transformed into an optimization problem with constraints, plays a key role in wireless sensor networks (WSNs). In this paper, inspired by ant colony optimization, an improved multioperator-based constrained adaptive differential evolution (namely, IMO-CADE) is proposed for the OPA. The proposed IMO-CADE can be featured as follows: (i) to adaptively select the proper operator among different operators, the feedback of operators and the status of individuals are considered simultaneously to assign the selection probability; (ii) the constrained reward assignment is used to measure the feedback of operators; (iii) the parameter adaptation is used for the parameters of differential evolution. To extensively evaluate the performance of IMO-CADE, it is used to solve the OPA for both the independent and correlated observations with different numbers of sensor nodes. Compared with other advanced methods, simulation results clearly indicate that IMO-CADE yields the best performance on the whole. Therefore, IMO-CADE can be an efficient alternative for the OPA of WSNs, especially for WSNs with a large number of sensor nodes.

Optimal power flow is a complex and highly non-linear problem in which steady-state parameters are needed to find a network’s efficient and economical operation. In addition, the difficulty of the Optimal power flow problem becomes enlarged when new constraints are added, and it is also a challenging task for the power system operator to solve the constrained Optimal power flow problems efficiently. Therefore, this paper presents a constrained composite differential evolution optimization algorithm to search for the optimum solution to Optimal power flow problems. In the last few decades, numerous evolutionary algorithm implementations have emerged due to their superiority in solving Optimal power flow problems while considering various objectives such as cost, emission, power loss, etc. evolutionary algorithms effectively explore the solution space unconstrainedly, often employing the static penalty function approach to address the constraints and find solutions for constrained Optimal power flow problems. It is a drawback that combining evolutionary algorithms and the penalty function approach requires several penalty parameters to search the feasible space and discard the infeasible solutions. The proposed a constrained composite differential evolution algorithm combines two effective constraint handling techniques, such as feasibility rule and ɛ constraint methods, to search in the feasible space. The proposed approaches are recognized on IEEE 30, 57, and 118-bus standard test systems considering 16 study events of single and multi-objective optimization functions. Ultimately, simulation results are examined and compared with the many recently published techniques of Optimal power flow solutions owing to show the usefulness and performance of the proposed a constrained composite differential evolution algorithm.

Many engineering problems can be categorized into constrained optimization problems (COPs). The engineering design optimization problem is very important in engineering industries. Because of the complexities of mathematical models, it is difficult to find a perfect method to solve all the COPs very well. \\[\\varepsilon \\] constrained differential evolution (\\[\\varepsilon \\]DE) algorithm is an effective method in dealing with the COPs. However, \\[\\varepsilon \\]DE still cannot obtain more precise solutions. The interaction between feasible and infeasible individuals can be enhanced, and the feasible individuals can lead the population finding optimum around it. Hence, in this paper we propose a new algorithm based on \\[\\varepsilon \\] feasible individuals driven local search called as \\[\\varepsilon \\] constrained differential evolution algorithm with a novel local search operator (\\[\\varepsilon \\]DE-LS). The effectiveness of the proposed \\[\\varepsilon \\]DE-LS algorithm is tested. Furthermore, four real-world engineering design problems and a case study have been studied. Experimental results show that the proposed algorithm is a very effective method for the presented engineering design optimization problems.

Water inrush in roadways frequently occurs in coal mines when the rock mass is enriched with underground water. To avoid underground water flow into the roadway and guarantee the stability of the roadway, grouting and cables are commonly used to prevent water inrush and guarantee the stability of the roadway. In this work, FLAC3D (fast lagrangian analysis of continua 3 dimension) numerical simulation software was used, and the fluid‒mechanical coupling effects were considered. In combination with the CMOEAD (constrained multi-objective evolution algorithm based on decomposition) optimization method, the optimal grouting area and cable distribution were determined: the center point of the ellipse (grouting area) is (0.01, 1.59), the long axis length is 4.73 m, the short axis length is 4.60 m, and the inclination angle of the ellipse is 53.15°. The cable length is 6.51 m, the total number of cables is 11. The grouting area and cable distribution design from numerical simulation results were applied to engineering practice, the degree of water inrush was markedly reduced, and the displacement of the roadway was within control, indicating that the proposed method is workable and reliable.