Sequence design of biomimetic copolymers: modeling of membrane proteins and globular proteins with active enzymatic center

The biomimetic approach to the sequence design of synthetic AB‐copolymers has been developed further by means of new series of Monte Carlo computer simulation. The approach is based on using of some particular conformation of a homopolymer chain for “coloring” of monomeric units into two “colors” (or types) A and B depending on the spatial position of particular monomeric unit. We present recent data of our Monte Carlo computer simulation studies of properties of designed AB‐copolymers which mimic membrane proteins, and designed ABC‐copolymers which mimic proteins with active enzymatic center. We have found further evidences for the fact that designed copolymer chain preserves the “memory” about its “parent” spatial conformation and shows the well‐pronounced tendency to restore main features of the “parent” conformation.     

Conformation‐Dependent Sequence Design of HP Copolymers: An Algorithm Based on Sequential Modifications of Monomer Units

We present a new modification of the so‐called conformation‐dependent sequence design scheme for HP copolymers which was proposed several years ago (H and P refer to the hydrophobic and polar monomer units, respectively). New method models the real chemical experiments more realistically. We performed Monte Carlo computer simulations using the bond‐fluctuation model for protein‐like copolymers obtained by means of the new “iterative” method and compared the results with those obtained for originally proposed “instantaneous coloring” procedure. Copolymers designed by the “iterative” method are shown to have better‐optimized functional properties. The investigation of the influence of sequence preparation conditions has revealed that the statistical properties of designed HP sequences depend rather strongly on the density of the parent homopolymer globule but not on the composition of H and P units.     

Dilute solution properties of poly(α-methylstyrene–ethylene) “regular” sequence copolymers

“Regular” sequence copolymers having the structure {[? CH₂? C(CH₃)(C₆H₅)? ]_m(CH₂? CH₂)_n}_p with relatively small values of m and n were prepared by means of “living” polymerization techniques. The intrinsic viscosities of fractions of these copolymers were obtained in various solvents including a theta solvent. The molecular weights of these fractions were determined by the Archibald ultracentrifugal method. The results show that the intrinsic viscosity–molecular weight relations of the regular sequence copolymers are affected not only by the average composition of the copolymer, but also by the sequence length in the copolymer molecule. It is suggested that the effective conformation of a chain element in the copolymer is not always the same as that in the homopolymer.     

Computer modeling of radical copolymerization under unusual conditions

Although recent years have witnessed an impressive confluence of experiments and kinetic and statistical theories, presently there is no comprehensive understanding of the interrelation between chemical sequences in synthetic copolymers and the conditions of synthesis. For this problem, numerical simulations in conjunction with simple models provide a rather detailed answer. A survey is given of the simulation methods as applied to the design of nontrivial chemical sequences in copolymers obtained via heterogeneous radical polymerization. This review is focused on a recently developed approach, called conformation‐dependent sequence design, which takes into account a strong coupling between the conformation and primary structure of copolymers during their synthesis. We consider some applications of this technique, including the following problems and systems: (1) the design of sequences with long‐range correlations via solution radical copolymerization with simultaneous globule formation, (2) radical copolymerization near a chemically homogeneous surface leading to a copolymer with a gradient primary structure, and (3) template copolymerization near chemically patterned surfaces. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5339–5353, 2004     

Theoretical aspects of small-angle neutron scattering from multiphase polymers

A molecular theory for small-angle neutron scattering from polymer mixtures is reviewed and extended to consider multiphase polymer systems such as block copolymers and their blends with homopolymers. Methods are developed for the isolation of scattering functions for individual components in these blends. These methods rely on two contrast-matching techniques: the concept of “composition matching,” where a mixture of deuterium-labeled and protonated species is used to match the contrast of a third component; and the synthesis of “phase-matched” block copolymers, where the contrast of the block copolymer sequences are matched. Methods are discussed specifically for the isolation of single chain and single sequence scattering functions for diblock and triblock copolymers, their blends with homopolymers, and star copolymers.     

Recent advances in the modeling and simulation of metallocene catalysis,sequence distribution,chain conformations,and crystallization of polymers

This article is a review describing the latest advances in modeling and simulation of polymers. Sequence distributions in stereoblock polymers and copolymers greatly affect their chain conformations and thermal transitions. While no theory was able to fully predict the influence of chain conformations on polymer crystallization, modeling techniques have shown good reliance in simulating the conformational behavior of polymeric chains and the related physical properties. This is done by generating representative sequences, and studying the chain conformation and packing of such sequences into crystalline regions in multichain systems. Metallocene catalysts, a class of single site catalysts, also showed unprecedented performance in the polymerization of olefins, most notably their activity, copolymerization capabilities, and potential for precise control of stereostructures. These attributes are among the most important issues in the manufacture of polyolefins and olefin copolymers, and are too good to be ignored. These polymers consist of alternating atactic sequences, which are amorphous and act as elastomeric chains, and ordered isotactic or syndiotactic sequences which, if long enough, will crystallize and act as physical reinforcing crosslinks. Mesoscopic investigation utilizing computer modeling and simulation into the effects of the sequence length and sequence length distribution on the reinforcement of stereoblock and stereoregular polyolefins has also been reviewed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2524–2541, 2006     

Why similar protein sequences encode similar three-dimensional structures?

Evolutionarily related proteins have similar sequences. Such similarity is called homology and can be described using substitution matrices such as Blosum 60. Naturally occurring homologous proteins usually have similar stable tertiary structures and this fact is used in so-called homology modeling. In contrast, the artificial protein designed by the Regan group has 50% identical sequence to the B1 domain of Streptococcal IgG-binding protein and a structure similar to the protein Rop. In this study, we asked the question whether artificial similar protein sequences (pseudohomologs) tend to encode similar protein structures, such as proteins existing in nature. To answer this question, we designed sets of protein sequences (pseudohomologs) homologous to sequences having known three-dimensional structures (template structures), same number of identities, same composition and equal level of homology, according to Blosum 60 substitution matrix as the known natural homolog. We compared the structural features of homologs and pseudohomologs by fitting them to the template structure. The quality of such structures was evaluated by threading potentials. The packing quality was measured using three-dimensional homology models. The packing quality of the models was worse for the “pseudohomologs” than for real homologs. The native homologs have better threading potentials (indicating better sequence-structure fit) in the native structure than the designed sequences. Therefore, we have shown that threading potentials and proper packing are evolutionarily more strongly conserved than sequence homology measured using the Blosum 60 matrix. Our results indicate that three-dimensional protein structure is evolutionarily more conserved than expected due to sequence conservation.     

Template copolymerization near a patterned surface: computer simulation

We perform a Monte Carlo simulation of irreversible template copolymerization near a chemically heterogeneous surface with a regular distribution of discrete adsorption sites that selectively adsorb from solution one of the two polymerizing monomers and the corresponding chain segments. In the polymerization model, the chain propagation process is simulated by adding individual monomers to the end of growing macroradical. We focus in this paper on the influence of polymerization rate, adsorption energy, and the distance between adsorption sites on the chain conformation and the primary sequence of the resulting two-letter (AB) copolymers and, specifically, on the coupling between polymerization and adsorption. The conditions for the realization of conformation-dependent copolymerization are formulated. For this regime, we observe the formation of a quasiregular copolymer with two types of alternating sections. One of them contains randomly distributed A and B segments. The second one consists mainly of strongly adsorbed A segments. It is found that the average length of the random sections is proportional to the distance between the nearest neighbor adsorption sites. The average length of the A-rich sections is determined by the "adsorption capacity" of adsorption site. By varying the strength of the effective monomer-substrate interaction and the distribution of adsorption sites on the substrate, the copolymers with different surface-induced primary sequences can be designed and synthesized in a controlled fashion.     

Characterization of nonbiological antimicrobial polymers in aqueous solution and at water-lipid interfaces from all-atom molecular dynamics

We have applied molecular dynamics to investigate the structural properties and activity of recently synthesized amphiphilic polymethacrylate derivatives, designed to mimic the antimicrobial activity of natural peptides. The composition, molecular weight, and hydrophobicity (ratio of hydrophobic and cationic units) of these short copolymers can be modulated to achieve structural diversity, which is crucial in controlling the antimicrobial activity. We have carried out all-atom molecular dynamics to systematically investigate the conformations adopted by these copolymers in water and at the water-lipid interface as a function of sequence and the chemical nature of the monomers. For two sequences, we observe partial insertion into the bilayer. Formation of strong interactions between the lipid headgroups and the amine groups of the polymers assists in the initial association with the lipids. However, the primary driving force for the observed partial insertion appears to be the hydrophobic effect. Our results indicate sensitive dependence of the overall shape on the sequence, suggesting that experimentally observed changes in activity can be correlated with particular sequences, providing an avenue for rational design.     

Polymer association in poor solvents: from monomolecular micelles to clusters of chains and phase separation

We report some recent results obtained in our laboratory on the poor‐solvent behavior of macromolecules. We first discuss the globular collapse of short chains that, unlike long ones, may form compact ordered states. We then address the collapse of random AB copolymers, which may provide significant clues to understanding biophysical issues such as the protein folding problem or the DNA arrangement in a living cell. Afterwards, we turn to the many‐chain problem of homopolymer aggregation into polymolecular micelles or clusters of chains and eventually phase separation. The unifying feature of our approach consists in the self‐consistent free‐energy minimization with inclusion of intra‐ and inter‐molecular interactions, whenever they are required, that enables us to describe the chain conformation in detail.     

Copolymer Adsorption on Planar Chemically Heterogeneous Substrates: The Interplay between the Monomer Sequence Distribution and Interaction Energies

We use a three‐dimensional self‐consistent field model to study the adsorption of A‐B copolymers from A‐B copolymer/A homopolymer blends on planar substrates comprising two chemically distinct regions C and D. The interplay between the spatial distribution of the surface chemical heterogeneities and the monomer sequence distribution in the copolymer is examined for diblock (A‐B), triblock (A‐B‐A), inverted triblock (B‐A‐B), and alternating (A‐alt‐B) copolymers. Our results demonstrate that when the chemically heterogeneous motifs on the substrate are detected by the copolymer adsorbing segments, the copolymers can transcribe them with high fidelity into three dimensions. The way the surface pattern gets transferred is dictated by the monomer sequence distribution. We show that relative to alternating copolymers, block copolymers are generally better at capturing the chemical pattern shape and transcribing it into the polymer mixture. Moreover, block copolymers with shorter adsorbing blocks are capable of better recognizing the substrate motifs. In order to address the interplay between the monomer sequence distribution in the copolymer and the interaction energies, we systematically vary the repulsion between A and B, and the attraction between B and D. Our calculations reveal that increasing i) the interaction between the copolymer adsorbing segments (B) and the “sticky” points at the substrate (D), and/or ii) the repulsion between the copolymer segments (A and B) increases the total amount of the copolymer adsorbed at the mixture/substrate interface, and decreases (increases) the fidelity of the substrate chemical pattern recognition by compositionally symmetric (asymmetric) copolymers.     

Alternating,gradient, block,and block–gradient copolymers of ethylene and norbornene by Pd–Diimine‐Catalyzed “living” copolymerization

We demonstrate, in this article, the facile synthesis of a broad class of low‐polydispersity ethylene–norbornene (E–NB) copolymers having various controllable comonomer composition distributions, including gradient, alternating, diblock, triblock, and block–gradient, through “living”/quasiliving E–NB copolymerization facilitated with a single Pd – diimine catalyst ( 1 ). This synthesis benefits from two remarkable features of catalyst 1 , its high capability in NB incorporation and high versatility in rendering E–NB “living” copolymerization at various NB feed concentrations ([NB]₀) while under an ethylene pressure of 1 atm and at 15 °C. At higher [NB]₀ values between 0.42 and 0.64 M, E–NB copolymerization with 1 renders nearly perfect alternating copolymers. At lower [NB]₀ values (0.11–0.22 M), gradient copolymers yield due to gradual reduction in NB concentration, with the starting chain end containing primarily alternating segments and the finishing end being hyperbranched polyethylene segments. Through two‐stage or three‐stage “living” copolymerization with sequential NB feeding, diblock or triblock copolymers containing gradient block(s) have been designed. This work thus greatly expands the family of E–NB copolymers. All the copolymers have controllable molecular weight and relatively low polydispersity (with polydispersity index below 1.20). Most notably, some of the gradient and block–gradient copolymers have been found to exhibit the characteristic broad glass transitions as a result of their possession of broad composition distribution. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

The effect of copolymer composition on the dynamics of random copolymers in a homopolymer matrix

The effect of copolymer composition on the dynamics of random copolymers in a homopolymer matrix is studied using computer simulations within the framework of the bond-fluctuation model on blends containing low concentrations (10%) of A-B copolymers, where A and B are two different types of monomers, dispersed in a homopolymer matrix of chains with only A-type monomers. Four copolymer compositions were studied, phi(A)=0.33, phi(A)=0.5, phi(A)=0.66, and phi(A)=0.82, while maintaining a statistically random sequence distribution. For this study, we have only included intermolecular interactions between A and B monomers. Our results indicate, in agreement with experimental data, that copolymer composition has an impact on system dynamics. Analysis of the structure reveals that copolymers with majority A content are expanded in the homopolymer matrix, have fewer interchain copolymer-copolymer contacts, and are well dispersed in the homopolymer matrix. On the other hand, copolymers with lower A content form a more compact structure, have more interchain contacts, and form aggregates that are short lived. This in turn leads to slower system dynamics. Both the radius of gyration (Rg) and copolymer end-to-end vectors (Re) increase with increasing A content until phi(A)=0.66 and then decrease. Copolymers with lower A content form more compact structures as the repulsive interactions between unlike species are minimized by the copolymers folding back on themselves and forming aggregates of copolymer chains. Thus, these results provide insight into the variation of copolymer dynamics with composition in the system by documenting the correlation between the thermodynamics of this mixture, the conformation of a copolymer chain in a homopolymer matrix, and the dynamics of both components in this blend.     

Comparing three stochastic search algorithms for computational protein design: Monte Carlo,replica exchange Monte Carlo,and a multistart,steepest‐descent heuristic

Computational protein design depends on an energy function and an algorithm to search the sequence/conformation space. We compare three stochastic search algorithms: a heuristic, Monte Carlo (MC), and a Replica Exchange Monte Carlo method (REMC). The heuristic performs a steepest‐descent minimization starting from thousands of random starting points. The methods are applied to nine test proteins from three structural families, with a fixed backbone structure, a molecular mechanics energy function, and with 1, 5, 10, 20, 30, or all amino acids allowed to mutate. Results are compared to an exact, “Cost Function Network” method that identifies the global minimum energy conformation (GMEC) in favorable cases. The designed sequences accurately reproduce experimental sequences in the hydrophobic core. The heuristic and REMC agree closely and reproduce the GMEC when it is known, with a few exceptions. Plain MC performs well for most cases, occasionally departing from the GMEC by 3–4 kcal/mol. With REMC, the diversity of the sequences sampled agrees with exact enumeration where the latter is possible: up to 2 kcal/mol above the GMEC. Beyond, room temperature replicas sample sequences up to 10 kcal/mol above the GMEC, providing thermal averages and a solution to the inverse protein folding problem. © 2016 Wiley Periodicals, Inc.     

Protein-like copolymers: Computer simulation

The model ofAB copolymers with a “protein-like” primary sequence was developed. This type of copolymers was obtained in a computer experiment. First, the conformation of a collapsed dense homopolymer globule was generated and then, based on this conformation, the primaryAB sequence was determied by denoting the monomeric units located near the surface of the globule as unitsA and those constituting the core of the globule as unitsB. After that, the primary structure of the chain was fixed, and different interaction potentials for theA andB units were introduced. Drawing an analogy of this model to aqueous solutions of globular proteins,A units were interpreted as hydrophilic, andB units were regarded as hydrophobic. By means of Monte Carlo simulation using the bond fluctuation model, the coli—globule transition in “protein-like”AB copolymer, induced by an increase in the attraction between the hydrophobicB units, was studied. The coil—globule transition in a copolymer with the “protein-like” primary sequence occurs at a higher temperature and has higher rate and is sharper than that in a random copolymer with the sameA/B composition and in a random block copolymer with the sameA/B composition and the same “degree of blockiness”. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 884–889, May, 1998.     

Using Monte Carlo simulations and self-consistent field theory to design interfacially active copolymers

We use both Monte Carlo computer simulations and numerical self-consistent field lattice calculations to determine the behavior of copolymers at penetrable and impenetrable interfaces. These computational techniques are useful as “design tools”: they allow us to systemically vary the copolymer architecture, determine optimal structures for specific applications, and establish guidelines for fabricating copolymers that yield the desired interfacial properties. We illustrate this principle with three different examples. In the first study, we combine the techniques to design copolymer compatibilizers that enhance the strength of immiscible polymer blends. These copolymers contain teeth that associate across the penetrable interface between the phase-separated regions and form a “molecular velcro” that effectively binds the regions together. In the case of impenetrable interfaces, we determine how the copolymer sequence distribution affects the structure of a layer of copolymers grafted onto a solid surface. The results indicate how to control the morphology of the layer and the surface properties of the substrate, by varying the microstructure of the grafted copolymers. Finally, we design a polymer channel that “opens” and “closes” in response to changes in the pH and quality of the surrounding solvent. The channel is formed from polyacid chains that are anchored onto a solid surface. Due to these properties, the system can be used for controlled release or sensor devices.     

Evolutionary Approach in Copolymer Sequence Design

Summary : In this work, we discuss a simple evolutionary algorithm that introduces a “selection pressure” under which two-letter (AB) copolymer sequences can mutate and transform into the sequences tuned to microphase separation transition (MIST). In particular, we are interested in determining how a sequence of A and B units should be organized in order to reach maximum length scale for MIST at a given AB composition. It is found that such sequences are similar to those known for tapered or gradient copolymers exhibiting strong composition inhomogeneity along their chain. The problems of the evolution of copolymer sequences are considered from the viewpoint of emerging of information complexity in the sequences in the course of this evolution.     

Liquid-crystal Assembly of Semiflexible-coil/Homopolymer Blends: a Dissipative Particle Dynamics Study

The liquid-crystal assembly of semiflexible-coil diblock copolymers with coil or semiflexible homopolymers is studied by dissipative particle dynamics simulation. Phase diagrams of the blends and orientation ordering parameters among semiflexible blocks are constructed as a function of chain stiffness and homopolymer volume fraction. For semiflexible-coil/coil blends with varying stiffness of semiflexible blocks, we display the rich phase behaviors of the system transited from coil-coil/coil to rod-coil/coil blends. The disorder-lamellae or lamellae-liquid crystalline transition and “dry brush” phenomenon induced by coil homopolymers are observed. For semiflexible-coil/semiflexible blends, adding semiflexible homopolymers also leads to a disorder-order transition and even a transition between monolayer and bilayer smectic-A phase. The results demonstrate that blending homopolymers into semiflexible copolymers can induce liquid-crystal assembly and even improve the orientation ordering of semiflexible blocks effectively.     

Design of random copolymers with statistically controlled monomer sequence distributions via Monte Carlo simulations

We use Monte Carlo simulations to model the formation of random copolymers with tunable monomer sequence distributions. Our scheme is based on the original idea proposed a few years ago by Khokhlov and Khalatur [Physica A 249, 253 (1998); Phys. Rev. Lett. 82, 3456 (1999)], who showed that the distribution of species B in A-B random copolymers can be regulated by (a) adjusting the coil size of a homopolymer A and (b) chemically modifying ("coloring") monomers that reside at (or close to) the periphery of the coil with species B. In contrast to Khokhlov and Khalatur's work, who modeled the polymer modification by performing the coloring instantaneously, we let the chemical coloring reaction progress over time using computer simulations. We show that similar to Khokhlov and Khalatur's work, the blockiness (i.e., number of consecutive monomers) of the B species along the A-B copolymer increases with increasing degree of collapse of the parent homopolymer A. A simple analysis of the A-B monomer sequences in the copolymers reveals that monomer sequence distributions in homopolymers "colored" under collapsed conformations possess certain degrees of self-similarity, while there is no correlation found among the monomer sequence distributions formed by coloring homopolymers with expanded conformations.     

DFT study of polymorphism of the DNA double helix at the level of dinucleoside monophosphates

We apply DFT calculations to deoxydinucleoside monophosphates (dDMPs) which represent minimal fragments of the DNA chain to study the molecular basis of stability of the DNA duplex, the origin of its polymorphism and conformational heterogeneity. In this work, we continue our previous studies of dDMPs where we detected internal energy minima corresponding to the “classical” B conformation (BI‐form), which is the dominant form in the crystals of oligonucleotide duplexes. We obtained BI local energy minima for all existing base sequences of dDMPs. In the present study, we extend our analysis to other families of DNA conformations, successfully identifying A, BI, and BII energy minima for all dDMP sequences. These conformations demonstrate distinct differences in sugar ring puckering, but similar sequence‐dependent base arrangements. Internal energies of BI and BII conformers are close to each other for nearly all the base sequences. The dGpdG, dTpdG, and dCpdA dDMPs slightly favor the BII conformation, which agrees with these sequences being more frequently experimentally encountered in the BII form. We have found BII‐like structures of dDMPs for the base sequences both existing in crystals in BII conformation and those not yet encountered in crystals till now. On the other hand, we failed to obtain dDMP energy minima corresponding to the Z family of DNA conformations, thus giving us the ground to conclude that these conformations are stabilized in both crystals and solutions by external factors, presumably by interactions with various components of the media. Overall the accumulated computational data demonstrate that the A, BI, and BII families of DNA conformations originate from the corresponding local energy minimum conformations of dDMPs, thus determining structural stability of a single DNA strand during the processes of unwinding and rewinding of DNA. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2548–2559, 2010