A Family of Fitness Landscapes Modeled through Gene Regulatory Networks

Fitness landscapes are a powerful metaphor for understanding the evolution of biological systems. These landscapes describe how genotypes are connected to each other through mutation and related through fitness. Empirical studies of fitness landscapes have increasingly revealed conserved topographical features across diverse taxa, e.g., the accessibility of genotypes and “ruggedness”. As a result, theoretical studies are needed to investigate how evolution proceeds on fitness landscapes with such conserved features. Here, we develop and study a model of evolution on fitness landscapes using the lens of Gene Regulatory Networks (GRNs), where the regulatory products are computed from multiple genes and collectively treated as phenotypes. With the assumption that regulation is a binary process, we prove the existence of empirically observed, topographical features such as accessibility and connectivity. We further show that these results hold across arbitrary fitness functions and that a trade-off between accessibility and ruggedness need not exist. Then, using graph theory and a coarse-graining approach, we deduce a mesoscopic structure underlying GRN fitness landscapes where the information necessary to predict a population’s evolutionary trajectory is retained with minimal complexity. Using this coarse-graining, we develop a bottom-up algorithm to construct such mesoscopic backbones, which does not require computing the genotype network and is therefore far more efficient than brute-force approaches. Altogether, this work provides mathematical results of high-dimensional fitness landscapes and a path toward connecting theory to empirical studies.     

Gaussian Amplitude Amplification for Quantum Pathfinding

We study an oracle operation, along with its circuit design, which combined with the Grover diffusion operator boosts the probability of finding the minimum or maximum solutions on a weighted directed graph. We focus on the geometry of sequentially connected bipartite graphs, which naturally gives rise to solution spaces describable by Gaussian distributions. We then demonstrate how an oracle that encodes these distributions can be used to solve for the optimal path via amplitude amplification. And finally, we explore the degree to which this algorithm is capable of solving cases that are generated using randomized weights, as well as a theoretical application for solving the Traveling Salesman problem.     

Multicomponent Polymers of Poly(Lactic Acid) Macromonomers with Methacrylate Terminal and Copolymers of Poly(2-Hydroxyethyl Methacrylate)

Abstract

Poly(lactic acid) macromonomers with methacrylate terminal functionality have been synthesized from the cyclic dimer of lactic acid (referred to as lactide) with 2-hydroxyethyl methacrylate (HEMA) as initiator and stannous 2-ethyl hexanoate as catalyst. The macromonomers were characterized with FT-IR, NMR, GPC, DSC, WAXS, and CD. The molecular weights of the macromonomers ranging from M _n 1425 to 19,169 are predictable from the lactide/HEMA ratio in the polymerization feeds. The properties of the macromonomers vary with the stereochemistry of the lactide and the composition. Circular dichroism measurements demonstrate that there is little racemization during polymerization.     

A semiempirical approach to ligand‐binding affinities: Dependence on the Hamiltonian and corrections

We present a combination of semiempirical quantum‐mechanical (SQM) calculations in the conductor‐like screening model with the MM/GBSA (molecular‐mechanics with generalized Born and surface‐area solvation) method for ligand‐binding affinity calculations. We test three SQM Hamiltonians, AM1, RM1, and PM6, as well as hydrogen‐bond corrections and two different dispersion corrections. As test cases, we use the binding of seven biotin analogues to avidin, nine inhibitors to factor Xa, and nine phenol‐derivatives to ferritin. The results vary somewhat for the three test cases, but a dispersion correction is mandatory to reproduce experimental estimates. On average, AM1 with the DH2 hydrogen‐bond and dispersion corrections gives the best results, which are similar to those of standard MM/GBSA calculations for the same systems. The total time consumption is only 1.3–1.6 times larger than for MM/GBSA. © 2012 Wiley Periodicals, Inc.     

One Way Traffic: Base-to-Backbone Hole Transfer in Nucleoside Phosphorodithioate

The directionality of the hole-transfer processes between DNA backbone and base was investigated by using phosphorodithioate [P(S⁻)=S] components. ESR spectroscopy in homogeneous frozen aqueous solutions and pulse radiolysis in aqueous solution at ambient temperature confirmed initial formation of G^.+-P(S⁻)=S. The ionization potential of G-P(S⁻)=S was calculated to be slightly lower than that of guanine in 5′-dGMP. Subsequent thermally activated hole transfer from G^.+ to P(S⁻)=S led to dithiyl radical (P-2S^.) formation on the μs timescale. In parallel, ESR spectroscopy, pulse radiolysis, and density functional theory (DFT) calculations confirmed P-2S^. formation in an abasic phosphorodithioate model compound. ESR investigations at low temperatures and higher G-P(S⁻)=S concentrations showed a bimolecular conversion of P-2S^. to the σ²-σ*¹-bonded dimer anion radical [-P-2S 2S-P-]⁻ [ΔG (150 K, DFT)=−7.2 kcal mol⁻¹]. However, [-P-2S 2S-P-]⁻ formation was not observed by pulse radiolysis [ΔG° (298 K, DFT)=−1.4 kcal mol⁻¹]. Neither P-2S^. nor [-P-2S 2S-P-]⁻ oxidized guanine base; only base-to-backbone hole transfer occurs in phosphorodithioate.     

Highly efficient metal‐free organic catalysts to design new Environmentally‐friendly starch‐based blends

A one‐step process is reported to directly synthesize blends of poly(trimethylene carbonate) (PTMC) with a modified granular starch. Trimethylene Carbonate (TMC) ring‐opening polymerization is performed in the presence of native starch particles in bulk conditions at 150 °C and the efficiency of metal‐free organic catalysts (TBD and phosphazene superbases P1‐t‐Oct, P2‐t‐bu, and P4‐t‐bu) are investigated to replace the organo‐metallic stannous octanoate initiator. TMC monomer is successively converted into PTMC and the robustness of organic catalysts is highlighted with significant activities at very low concentrations (<100 ppm), where stannous octanoate is inefficient. Reactivity of starch toward TMC ROP is deeply investigated by NMR techniques and a starch‐graft‐PTMC is indirectly evidenced. Starch substitution degree reaches 0.9% indicating that PTMC grafting only occurs at the surface of swollen granular starch. PTMC graft length from the starch surface remained low in the range 2–12 and model ROP reactions highlight the role of TMC hydrolysis on PTMC graft length. Despite low PTMC grafts, a fine dispersion of intact starch particles into the PTMC matrix is evidenced. Consequently, metal‐free organic catalysts at low concentrations are promising candidates for synthesizing blends of PTMC with high loadings of surface‐modified starch (32% by weight) in 2 min within a one‐step process. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 493–503