Random Heteropolymers Research Articles

Controlling the Chain Folding for the Synthesis of Single-Chain Polymer Nanoparticles Using Thermoresponsive Polymers

Synthetic polymer single-chain nanoparticles (SCNPs) are an emerging new class of nanomaterials that possess similar folded structures as natural proteins. However, most SCNPs reported so far are p...

Automation of Controlled/Living Radical Polymerization.

Controlled/living radical polymerization (CLRP) techniques are widely utilized to synthesize advanced and controlled synthetic polymers for chemical and biological applications. While automation has long stood as a high-throughput (HTP) research tool to increase productivity as well as synthetic/analytical reliability and precision, oxygen intolerance of CLRP has limited the widespread adoption of these systems. Recently, however, oxygen-tolerant CLRP techniques, such as oxygen-tolerant photoinduced electron/energy transfer–reversible addition–fragmentation chain transfer (PET–RAFT), enzyme degassing of RAFT (Enz-RAFT), and atom-transfer radical polymerization (ATRP), have emerged. Herein, the use of a Hamilton MLSTARlet liquid handling robot for automating CLRP reactions is demonstrated. Synthesis processes are developed using Python and used to automate reagent handling, dispensing sequences, and synthesis steps required to create homopolymers, random heteropolymers, and block copolymers in 96-well plates, as well as postpolymerization modifications. Using this approach, the synergy between highly customizable liquid handling robotics and oxygen-tolerant CLRP to automate advanced polymer synthesis for HTP and combinatorial polymer research is demonstrated.

Solution structure and oligomeric state of the E. coliglycerol facilitator

Protein dynamics at atomic resolution can provide deep insights into the biological activities of proteins and enzymes but they can also make structure and dynamics studies challenging. Despite their well-known biological and pharmaceutical importance, integral membrane protein structure and dynamics studies lag behind those of water-soluble proteins mainly owing to solubility problems that result upon their removal from the membrane. Escherichia coli glycerol facilitator (GF) is a member of the aquaglyceroporin family that allows for the highly selective passive diffusion of its substrate glycerol across the inner membrane of the bacterium. Previous molecular dynamics simulations and hydrogen-deuterium exchange studies suggested that protein dynamics play an important role in the passage of glycerol through the protein pore. With the aim of studying GF dynamics by solution and solid-state nuclear magnetic resonance (NMR) spectroscopy we optimized the expression of isotope-labelled GF and explored various solubilizing agents including detergents, osmolytes, amphipols, random heteropolymers, lipid nanodiscs, bicelles and other buffer additives to optimize the solubility and polydispersity of the protein. The GF protein is most stable and soluble in lauryl maltose neopentyl glycol (LMNG), where it exists in a tetramer-octamer equilibrium. The solution structures of the GF tetramer and octamer were determined by negative-stain transmission electron microscopy (TEM), size-exclusion chromatography small-angle X-ray scattering (SEC-SAXS) and solid-state magic-angle spinning NMR spectroscopy. Although NMR sample preparation still needs optimization for full structure and dynamics studies, negative stain TEM and SEC-SAXS revealed low-resolution structures of the detergent-solubilized tetramer and octamer particles. The non-native octamer appears to form from the association of the cytoplasmic faces of two tetramers, the interaction apparently mediated by their disordered N- and C-termini. This information may be useful in future studies directed at reducing the heterogeneity and self-association of the protein.

Single-chain heteropolymers transport protons selectively and rapidly.

Precise protein sequencing and folding are believed to generate the structure and chemical diversity of natural channels1,2, both of which are essential to synthetically achieve proton transport performance comparable to that seen in natural systems. Geometrically defined channels have been fabricated using peptides, DNAs, carbon nanotubes, sequence-defined polymers and organic frameworks3-13. However, none of these channels rivals the performance observed in their natural counterparts. Here we show that without forming an atomically structured channel, four-monomer-based random heteropolymers (RHPs)14 can mimic membrane proteins and exhibit selective proton transport across lipid bilayers at a rate similar to those of natural proton channels. Statistical control over the monomer distribution in an RHP leads to segmental heterogeneity in hydrophobicity, which facilitates the insertion of single RHPs into the lipid bilayers. It also results in bilayer-spanning segments containing polar monomers that promote the formation of hydrogen-bonded chains15,16 for proton transport. Our study demonstrates the importance of the adaptability that is enabled by statistical similarity among RHP chains and of the modularity provided by the chemical diversity of monomers, to achieve uniform behaviour in heterogeneous systems. Our results also validate statistical randomness as an unexplored approach to realize protein-like behaviour at the single-polymer-chain level in a predictable manner.

Observation of Continuous Contraction and a Metastable Misfolded State during the Collapse and Folding of a Small Protein

To obtain proper insight into how structure develops during a protein folding reaction, it is necessary to understand the nature and mechanism of the polypeptide chain collapse reaction, which marks the initiation of folding. Here, the time-resolved fluorescence resonance energy transfer technique, in which the decay of the fluorescence light intensity with time is used to determine the time evolution of the distribution of intra-molecular distances, has been utilized to study the folding of the small protein, monellin. It is seen that when folding begins, about one-third of the protein molecules collapse into a molten globule state (IMG), from which they relax by continuous further contraction to transit to the native state. The larger fraction gets trapped into a metastable misfolded state. Exit from this metastable state occurs via collapse to the lower free energy IMG state. This exit is slow, on a time scale of seconds, because of activation energy barriers. The trapped misfolded molecules as well as the IMG molecules contract continuously and slowly as structure develops. A phenomenological model of Markovian evolution of the polymer chain undergoing folding, incorporating these features, has been developed, which fits well the experimentally observed time evolution of distance distributions. The observation that the “wrong turn” to the misfolded state has not been eliminated by evolution belies the common belief that the folding of functional protein sequences is very different from that of a random heteropolymer, and the former have been selected by evolution to fold quickly.

Reusable Enzymatic Fiber Mats for Neurotoxin Remediation in Water.

Highly effective and reusable organophosphorus hydrolase (OPH)-loaded fiber mats have been fabricated that are capable of degrading toxic organophosphates (OPs) over a broad range of relevant concentrations (from 8 to 8250 ppm). The inherent fragility of enzymes, a major impediment in their incorporation into technologically relevant materials, was overcome while retaining their high catalytic efficiency, selectivity, and sensitivity via a random heteropolymers (RHP) approach. Kinetic analysis guides the design of polycaprolactone matrix morphology from films to fibers, facilitating substrate diffusion in the material. The RHP-OPH fiber mats demonstrate excellent stability and reusability with minimal requirements for storage, retaining over 40% of their initial activity after repeated daily use for three months. Practically, present studies provide valuable guidance toward fabrication of enzyme-based functional materials.

Theoretical Study of Adsorption of Random and Regular Heteropolymers Using the Generating Functions Approach

Adsorption of single macromolecules of random and regular heterpolymers was studied by the generating functions approach (or the method of grand canonical ensemble). Adsorption of random copolymers characterized by a sequence of monomer units set as a first order Markov chain was considered using the approximation of annealed disorder and constrained annealed disorder (the Morita approximation). It was shown that use of the Morita approximation makes it possible to describe accurately the adsorption of random copolymer with a fixed (quenched) sequence of units. Adsorption of periodic heteropolymers can be described by representing the periodic sequence as a first order Markov chain with circulant transition probability matrix.

Polymer chain protects proteins

A new random heteropolymer with mixed hydrophilic and hydrophobic groups coats proteins to help them remain folded and active in environments that would normally unfold and inactivate them (Science 2018, DOI: 10.1126/science.aao0335). Random heteropolymers have been designed before to enhance the properties of small molecules, but not proteins. And researchers have previously enhanced protein stability by incorporating proteins in micelles or sol-gel networks or by combining proteins with polyelectrolytes and other polymers. But the new heteropolymer preserves native protein function and structure more faithfully in both aqueous and organic media, say Ting Xu of the University of California, Berkeley, and coworkers, who developed it. The heteropolymer could have bioremediation applications and allow researchers to make proteins without the help of cells. “This is outstanding work showing the ability of functionally diverse, random copolymers to act as chaperones and protein stabilizers for diverse applica...

Random heteropolymers preserve protein function in foreign environments.

The successful incorporation of active proteins into synthetic polymers could lead to a new class of materials with functions found only in living systems. However, proteins rarely function under the conditions suitable for polymer processing. On the basis of an analysis of trends in protein sequences and characteristic chemical patterns on protein surfaces, we designed four-monomer random heteropolymers to mimic intrinsically disordered proteins for protein solubilization and stabilization in non-native environments. The heteropolymers, with optimized composition and statistical monomer distribution, enable cell-free synthesis of membrane proteins with proper protein folding for transport and enzyme-containing plastics for toxin bioremediation. Controlling the statistical monomer distribution in a heteropolymer, rather than the specific monomer sequence, affords a new strategy to interface with biological systems for protein-based biomaterials.

Looping probability of random heteropolymers helps to understand the scaling properties of biopolymers.

Random heteropolymers are a minimal description of biopolymers and can provide a theoretical framework to the investigate the formation of loops in biophysical experiments. The looping probability as a function of polymer length was observed to display in some biopolymers, like chromosomes in cell nuclei or long RNA chains, anomalous scaling exponents. Combining a two-state model with self-adjusting simulated-tempering calculations, we calculate numerically the looping properties of several realizations of the random interactions within the chain. We find a continuous set of exponents upon varying the temperature, which arises from finite-size effects and is amplified by the disorder of the interactions. We suggest that this could provide a simple explanation for the anomalous scaling exponents found in experiments. In addition, our results have important implications notably for the study of chromosome folding as they show that scaling exponents cannot be the sole criteria for testing hypothesis-driven models of chromosome architecture.

Folding and Stabilization of Native-Sequence-Reversed Proteins.

Though the problem of sequence-reversed protein folding is largely unexplored, one might speculate that reversed native protein sequences should be significantly more foldable than purely random heteropolymer sequences. In this article, we investigate how the reverse-sequences of native proteins might fold by examining a series of small proteins of increasing structural complexity (α-helix, β-hairpin, α-helix bundle, and α/β-protein). Employing a tandem protein structure prediction algorithmic and molecular dynamics simulation approach, we find that the ability of reverse sequences to adopt native-like folds is strongly influenced by protein size and the flexibility of the native hydrophobic core. For β-hairpins with reverse-sequences that fail to fold, we employ a simple mutational strategy for guiding stable hairpin formation that involves the insertion of amino acids into the β-turn region. This systematic look at reverse sequence duality sheds new light on the problem of protein sequence-structure mapping and may serve to inspire new protein design and protein structure prediction protocols.

Role of single-point mutations and deletions on transition temperatures in ideal proteinogenic heteropolymer chains in the gas phase.

A coarse-grained statistical mechanics-based model for ideal heteropolymer proteinogenic chains of non-interacting residues is presented in terms of the size K of the chain and the set of helical propensities [Formula: see text] associated with each residue j along the chain. For this model, we provide an algorithm to compute the degeneracy tensor [Formula: see text] associated with energy level [Formula: see text] where [Formula: see text] is the number of residues with a native contact in a given conformation. From these results, we calculate the equilibrium partition function [Formula: see text] and characteristic temperature [Formula: see text] at which a transition from a low to a high entropy states is observed. The formalism is applied to analyze the effect on characteristic temperatures [Formula: see text] of single-point mutations and deletions of specific amino acids [Formula: see text] along the chain. Two probe systems are considered. First, we address the case of a random heteropolymer of size K and given helical propensities [Formula: see text] on a conformational phase space. Second, we focus our attention to a particular set of neuropentapeptides, [Met-5] and [Leu-5] enkephalins whose thermodynamic stability is a key feature on their coupling to [Formula: see text] and [Formula: see text] receptors and the triggering of biochemical responses.

Effect of disorder on the contact probability of elongated conformations of biopolymers.

Biopolymers are characterized by heterogeneous interactions, and usually perform their biological tasks forming contacts within domains of limited size. Combining polymer theory with a replica approach, we study the scaling properties of the probability of contact formation in random heteropolymers as a function of their linear distance. It is found that, close to or above the θ point, it is possible to define a contact probability which is typical (i.e., "self-averaging") for different realizations of the heterogeneous interactions, and which displays an exponential cutoff, dependent on temperature and on the interaction range. In many cases this cutoff is comparable with the typical sizes of domains in biopolymers. While it is well known that disorder causes interesting effects at low temperature, the behavior elucidated in the present study is an example of a nontrivial effect at high temperature.

Quantifying protein sequences with reference to the genetic code.

Although the analysis of protein molecules is extensive, their primary sequences have yet to be quantified like their mass or size. The composition and particular arrangement of amino acids in proteins confers the distinct biochemical functionality, but it remains unclear why only a tiny proportion of possible character combinations are potentially functional. Here, I offer a simple but effective technique, utilizing the assignment of codons in the genetic code, that permits the quantification of polypeptide sequences and establishes statistical parameters through which they can now be numerically compared. Two main tests were conducted, one analyzing the composition and the other the specific order of the amino acids within the primary sequence. The results confirm that natural proteins are significantly different to random heteropolymers of equivalent size, although this is much more marginal in the case of the arrangement than it is for the composition. Moreover, they reveal that there are key patterns that have hitherto not been identified, relevant to the the study of the evolution of proteins, and which raise doubts about the plausibility of some purported cases of the de novo origination of protein-coding genes from intergenic DNA. Despite the fact that the applicability of quantification to the design of novel proteins is probably limited, it nonetheless provides a useful guideline that could complement much more precise methods.

Helix-coil transition in biopolymers with multicomponent heterogeneity of energy and number of conformations

We consider the theory of helix-coil transition in heteropolymeric biopolymers with an arbitrary number of components in cases of heterogeneity with respect to both energy and number of conformations. The theory is based on the Generalized Model of Polypeptide Chain (GMPC) with employing the constrained annealing method. Expression for the free energy of heteropolymer is derived using averaged transfer-matrix of homopolymer GMPC with redefined energy and conformation parameters. We obtain an algorithm of calculation of the melting curve of a heteropolymeric system and compare that with the homopolymeric curve. We show that bimodal heterogeneity determines qualitatively the basic properties of melting of a random heteropolymer. We also show that heterogeneity with respect to energy and heterogeneity with respect to number of conformations provide essentially the same characteristics of melting curves.

Conformational transitions in random heteropolymer models.

We study the conformational properties of heteropolymers containing two types of monomers A and B, modeled as self-attracting self-avoiding random walks on a regular lattice. Such a model can describe in particular the sequences of hydrophobic and hydrophilic residues in proteins [K. F. Lau and K. A. Dill, Macromolecules 22, 3986 (1989)] and polyampholytes with oppositely charged groups [Y. Kantor and M. Kardar, Europhys. Lett. 28, 169 (1994)]. Treating the sequences of the two types of monomers as quenched random variables, we provide a systematic analysis of possible generalizations of this model. To this end we apply the pruned-enriched Rosenbluth chain-growth algorithm, which allows us to obtain the phase diagrams of extended and compact states coexistence as function of both the temperature and fraction of A and B monomers along the heteropolymer chain.

Glassy Dynamics of Random Heteropolymers

The dynamics of random heteropolymers and their rugged free energy landscape are studied using a replica approach. Metastable states, barriers between lowest minima, entropic droplets are calculated between the static and dynamic glass transition temperatures.

Principles for designing ideal protein structures

Unlike random heteropolymers, natural proteins fold into unique ordered structures. Understanding how these are encoded in amino-acid sequences is complicated by energetically unfavourable non-ideal features--for example kinked α-helices, bulged β-strands, strained loops and buried polar groups--that arise in proteins from evolutionary selection for biological function or from neutral drift. Here we describe an approach to designing ideal protein structures stabilized by completely consistent local and non-local interactions. The approach is based on a set of rules relating secondary structure patterns to protein tertiary motifs, which make possible the design of funnel-shaped protein folding energy landscapes leading into the target folded state. Guided by these rules, we designed sequences predicted to fold into ideal protein structures consisting of α-helices, β-strands and minimal loops. Designs for five different topologies were found to be monomeric and very stable and to adopt structures in solution nearly identical to the computational models. These results illuminate how the folding funnels of natural proteins arise and provide the foundation for engineering a new generation of functional proteins free from natural evolution.

Optimized Wang-Landau sampling of lattice polymers: Ground state search and folding thermodynamics of HP model proteins

Coarse-grained (lattice-) models have a long tradition in aiding efforts to decipher the physical or biological complexity of proteins. Despite the simplicity of these models, however, numerical simulations are often computationally very demanding and the quest for efficient algorithms is as old as the models themselves. Expanding on our previous work [T. Wüst and D. P. Landau, Phys. Rev. Lett. 102, 178101 (2009)], we present a complete picture of a Monte Carlo method based on Wang-Landau sampling in combination with efficient trial moves (pull, bond-rebridging, and pivot moves) which is particularly suited to the study of models such as the hydrophobic-polar (HP) lattice model of protein folding. With this generic and fully blind Monte Carlo procedure, all currently known putative ground states for the most difficult benchmark HP sequences could be found. For most sequences we could also determine the entire energy density of states and, together with suitably designed structural observables, explore the thermodynamics and intricate folding behavior in the virtually inaccessible low-temperature regime. We analyze the differences between random and protein-like heteropolymers for sequence lengths up to 500 residues. Our approach is powerful both in terms of robustness and speed, yet flexible and simple enough for the study of many related problems in protein folding.

New Alphabet-Dependent Morphological Transition in Random RNA Alignment

We study the fraction f of nucleotides involved in the formation of a cactuslike secondary structure of random heteropolymer RNA-like molecules. In the low-temperature limit, we study this fraction as a function of the number c of different nucleotide species. We show, that with changing c, the secondary structures of random RNAs undergo a morphological transition: f(c)→1 for c≤c(cr) as the chain length n goes to infinity, signaling the formation of a virtually perfect gapless secondary structure; while f(c)<1 for c>c(cr), which means that a nonperfect structure with gaps is formed. The strict upper and lower bounds 2≤c(cr)≤4 are proven, and the numerical evidence for c(cr) is presented. The relevance of the transition from the evolutional point of view is discussed.