Heuristic energy landscape paving for protein folding problem in the three-dimensional HP lattice model

The protein folding problem, i.e., the prediction of the tertiary structures of protein molecules from their amino acid sequences is one of the most important problems in computational biology and biochemistry. However, the extremely difficult optimization problem arising from energy function is a key challenge in protein folding simulation. The energy landscape paving (ELP) method has already been applied very successfully to off-lattice protein models and other optimization problems with complex energy landscape in continuous space. By improving the ELP method, and subsequently incorporating the neighborhood strategy with the pull-move set into the improved ELP method, a heuristic ELP algorithm is proposed to find low-energy conformations of 3D HP lattice model proteins in the discrete space. The algorithm is tested on three sets of 3D HP benchmark instances consisting 31 sequences. For eleven sequences with 27 monomers, the proposed method explores the conformation surfaces more efficiently than other methods, and finds new lower energies in several cases. For ten 48-monomer sequences, we find the lowest energies so far. With the achieved results, the algorithm converges rapidly and efficiently. For all ten 64-monomer sequences, the algorithm finds lower energies within comparable computation times than previous methods. Numeric results show that the heuristic ELP method is a competitive tool for protein folding simulation in 3D lattice model. To the best of our knowledge, this is the first application of ELP to the 3D discrete space.     

Polymer collapse, protein folding, and the percolation threshold

We study the transition of polymers in the dilute regime from a swollen shape at high temperatures to their low-temperature structures. The polymers are modeled by a single self-avoiding walk (SAW) on a lattice for which l of the monomers (the H monomers) are self-attracting, i.e., if two nonbonded H monomers become nearest neighbors on the lattice they gain energy of interaction (epsilon = -/epsilon/); the second type of monomers, denoted P, are neutral. This HP model was suggested by Lau and Dill (Macromolecules 1989, 22, 3986-3997) to study protein folding, where H and P are the hydrophobic and polar amino acid residues, respectively. The model is simulated on the square and simple cubic (SC) lattices using the scanning method. We show that the ground state and the sharpness of the transition depend on the lattice, the fraction g of the H monomers, as well as on their arrangement along the chain. In particular, if the H monomers are distributed at random and g is larger than the site percolation threshold of the lattice, a collapsed transition is very likely to occur. This conclusion, drawn for the lattice models, is also applicable to proteins where an effective lattice with coordination number between that of the SC lattice and the body centered cubic lattice is defined. Thus, the average fraction of hydrophobic amino acid residues in globular proteins is found to be close to the percolation threshold of the effective lattice.     

The effect of sequence on the conformational stability of a model heteropolymer in explicit water

We investigate the properties of a two-dimensional lattice heteropolymer model for a protein in which water is explicitly represented. The model protein distinguishes between hydrophobic and polar monomers through the effect of the hydrophobic monomers on the entropy and enthalpy of the hydrogen bonding of solvation shell water molecules. As experimentally observed, model heteropolymer sequences fold into stable native states characterized by a hydrophobic core to avoid unfavorable interactions with the solvent. These native states undergo cold, pressure, and thermal denaturation into distinct configurations for each type of unfolding transition. However, the heteropolymer sequence is an important element, since not all sequences will fold into stable native states at positive pressures. Simulation of a large collection of sequences indicates that these fall into two general groups, those exhibiting highly stable native structures and those that do not. Statistical analysis of important patterns in sequences shows a strong tendency for observing long blocks of hydrophobic or polar monomers in the most stable sequences. Statistical analysis also shows that alternation of hydrophobic and polar monomers appears infrequently among the most stable sequences. These observations are not absolute design rules and, in practice, these are not sufficient to rationally design very stable heteropolymers. We also study the effect of mutations on improving the stability of the model proteins, and demonstrate that it is possible to obtain a very stable heteropolymer from directed evolution of an initially unstable heteropolymer.     

Purification of antibody heteropolymers using hydrophobic interaction chromatography

A heteropolymer (HP) is a unique dual antibody conjugate composed of specific, chemically cross-linked monoclonal antibodies (mAbs). In this study we have demonstrated that HPs can be purified using hydrophobic interaction chromatography (HIC). Two propyl HIC resins; [PolyPropyl A and EMD Fractogel Propyl (S)] were evaluated in this study. Phosphate buffers, pH 6.5 containing ammonium sulfate or sodium sulfate were used to bind the HP to the column. A descending sulfate gradient or step gradient was used to elute the bound HP species from the column. The HP reaction mixture typically contains multiple conjugated HP species, as well as unreacted monomer mAbs. Conjugated HP product was successfully separated from unreacted antibody monomers with both propyl resins using buffers with ammonium sulfate. There was no monomer separation from HP using buffers with sodium sulfate. The purification processes, presented in this study allows the non-cross-linked antibodies to pass through the column without being bound to the resin, while the cross-linked antibodies (the HP product) bound to the column were subsequently eluted by decreasing the ammonium sulfate concentration in the running buffer. HP product was efficiently separated from free mAbs using Propyl HIC resins at both analytical and preparative scales.     

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. Wu?st 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.     

Scaling law for the radius of gyration of proteins and its dependence on hydrophobicity

The scaling law between the radius of gyration and the length of a polymer chain has long been an interesting topic since the Flory theory. In this article, we seek to derive a unified formula for the scaling exponent of proteins under different solvent conditions. The formula is obtained by considering the balance between the excluded volume effect and elastic interactions among monomers. Our results show that the scaling exponent is closely related to the fractal dimension of a protein's structure at the equilibrium state. Applying this formula to natural proteins yields a 2/5 law with fractal dimension 2 at the native state, which is in good agreement with other studies based on Protein Data Bank analysis. We also study the dependence of the scaling exponent on the hydrophobicity of a protein chain through a simple two‐letters HP model. The results provides a way to estimate the globular structure of a protein, and could be helpful for the investigation of the mechanisms of protein folding. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 207–214, 2009     

Protein folding simulations of 2D HP model by the genetic algorithm based on optimal secondary structures

In this paper, based on the evolutionary Monte Carlo (EMC) algorithm, we have made four points of ameliorations and propose a so-called genetic algorithm based on optimal secondary structure (GAOSS) method to predict efficiently the protein folding conformations in the two-dimensional hydrophobic–hydrophilic (2D HP) model. Nine benchmarks are tested to verify the effectiveness of the proposed approach and the results show that for the listed benchmarks GAOSS can find the best solutions so far. It means that reasonable, effective and compact secondary structures (SSs) can avoid blind searches and can reduce time consuming significantly. On the other hand, as examples, we discuss the diversity of protein GSC for the 24-mer and 85-mer sequences. Several GSCs have been found by GAOSS and some of the conformations are quite different from each other. It would be useful for the designing of protein molecules. GAOSS would be an efficient tool for the protein structure predictions (PSP).     

In situ AFM study of amelogenin assembly and disassembly dynamics on charged surfaces provides insights on matrix protein self-assembly

Because self-assembly of matrix proteins is a key step in hard tissue mineralization, developing an understanding of the assembly pathways and underlying mechanisms is likely to be important for successful hard tissue engineering. While many studies of matrix protein assembly have been performed on bulk solutions, in vivo these proteins are likely to be in contact with charged biological surfaces composed of lipids, proteins, or minerals. Here we report the results of an in situ atomic force microscopy (AFM) study of self-assembly by amelogenin--the principal protein of the extracellular matrix in developing enamel--in contact with two different charged substrates: hydrophilic negatively charged bare mica and positively charged 3-aminopropyl triethoxysilane (APS) silanized mica. First we demonstrate an AFM-based protocol for determining the size of both amelogenin monomers and oligomers. Using this protocol, we find that, although amelogenin exists primarily as ~26 nm in diameter nanospheres in bulk solution at a pH of 8.0 studied by dynamic light scattering, it behaves dramatically differently upon interacting with charged substrates at the same pH and exhibits complex substrate-dependent assembly pathways and dynamics. On positively charged APS-treated mica surfaces, amelogenin forms a relatively uniform population of decameric oligomers, which then transform into two main populations: higher-order assemblies of oligomers and amelogenin monomers, while on negatively charged bare mica surfaces, it forms a film of monomers that exhibits tip-induced desorption and patterning. The present study represents a successful attempt to identify the size of amelogenin oligomers and to directly monitor assembly and disassembly dynamics on surfaces. The findings have implications for amelogenin-controlled calcium phosphate mineralization in vitro and may offer new insights into in vivo self-assembly of matrix proteins as well as their control over hard tissue formation.     

二维HP格点模型中的紧密高分子链构象及其热力学性质的研究

采用二维HP模型用精确计数法和MonteCarlo方法研究了链长为N(≤ 2 2 )的紧密高分子链的构象和热力学性质 .发现不同HP序列的紧密高分子链的平均自由能和平均配分函数与链长N存在关系 :〈F〉=aN+b ,　ln〈Z〉=a′N +b′ .同时发现对于可折叠成基态且简并度为 1的紧密高分子链 ,其平均自由能和平均配分函数与链长N也存在相似的关系 .在HP模型中对于链长为N的紧密高分子链 ,存在着 2 N + 1 个不同的HP序列 .我们发现可以折叠成基态且简并度为 1的蛋白质分子的HP序列数目NS 为NS =a× 2 N+ 1 　 (a =0 0 2 5 ) ,对应的HP序列中 ,疏水基团 (H)数目的含量为 4 0 %～ 6 0 %的序列出现的几率最大 .同时在这些紧密高分子链中有些具有相同的结构 ,发现结构的‘简并度’为 3 3～ 4 0 (10≤N≤ 16 ) .在紧密高分子链折叠过程中 ,折叠的初期能量下降比较快 ,折叠的中期能量下降比较缓慢 ,折叠的后期能量下降也是比较快     

Classification and functional analyses of putative virulence factors of Mycobacterium tuberculosis: A combined sequence and structure based study

The emergence of the drug-resistant mechanisms in Mycobacterium tuberculosis poses the biggest challenges to the current therapeutic measures, which necessitates the identification of new drug targets. The Hypothetical Proteins (HPs), a class of functionally uncharacterized proteins, may provide a new class of undiscovered therapeutic targets. The genome of M. tuberculosis contains 1000 HPs with their sequences were analyzed using a variety of bioinformatics tools and the functional annotations were performed. The functions of 662 HPs were successfully predicted and further classified 483 HPs as enzymes, 141 HPs were predicted to be involved in the diverse cellular mechanisms and 38 HPs may function as transporters and carriers proteins. Furthermore, 28 HPs were predicted to be virulent in nature. Amongst them, the HP P95201, HP P9WM79, HP I6WZ30, HP I6 × 9T8, HP P9WKP3, and HP P9WK89 showed the highest virulence scores. Therefore, these proteins were subjected to extensive structure analyses and dynamics of their conformations were investigated using the principles of molecular dynamics simulations, each for a 150 ns time scale. This study provides a deeper understanding of the undiscovered drug targets and the generated outputs will facilitate the process of drug design and discovery against the infection of M. tuberculosis.     

Effects of composition and sequential structure on thermal properties for copolymer of 3-hydroxybutyrate and lactate units

Copolymers of (R)-3-hydroxybutyrate (3HB) and (R)-lactate ((R)-2-hydroxypropionate: 2HP) units were synthesized by polycondensation reaction from methyl esters of 3HB and 2HP in the presence of titanium-based catalyst. Mixing of two monomers from the beginning of polymerization yielded random copolymers of 3HB and 2HP units. On the other hand, by controlling the time of mixing of two monomers, copolymers with blocking tendency were obtained. The structure and thermal properties of the obtained copolymers were characterized by ¹H and ¹³C NMR, X-ray diffraction, differential scanning calorimetry, and optical microscopy. Glass-transition temperature of the copolymers was mainly governed by the copolymer composition, and the values varied linearly with the composition. In contrast, the melting temperature was strongly depending on the sequential length of crystallizable monomeric unit, and the values were in inverse proportion to the number-averaged sequential length of crystallizable monomeric unit. The crystallinity of the copolymer samples was affected by both the composition and sequential length of crystallizable monomeric unit. The finding is valuable for design of copolymer molecules with desirable thermal properties by controlling both the copolymer composition and sequential structure.     

Fractionation of basic nuclear proteins of human sperm by zinc chelate affinity chromatography

Immobilized metal affinity chromatography was investigated for the fractionation of basic nuclear proteins of human sperm. Human sperm nuclei essentially contain two classes of protamines: a protamine of type P1 (HPl), rich in cysteine but with only one histidine, and three protamines of type P2 (HP2, HP3, HP4), rich in cysteine and histidine (nine in protamine HP2), potential ligands for transition metal ions. The critical conditions for metal affinity chromatography were defined: choice of metal, protein material and buffer, type of elution and sample loading. Chromatography of nuclear proteins, without histones and with cysteine residues alkylated by iodoacetamide, was optimum on zinc Chelating Sepharose in a Tris-acetate buffer and elution with an increasing concentration gradient of imidazole. Under these conditions, the two classes of protamines were completely separated. The intermediate basic proteins were further purified by reversed-phase high-performance liquid chromatography. Heterogeneity of binding to zinc of protamine HP1 was demonstrated. The proposed method is simple and reproducible and the recovery of proteins is high. It may be applied to study the expression and function of P1 and P2 protamines, e.g., in the case of infertile men.     

Toward beta-amino acid proteins: a cooperatively folded beta-peptide quaternary structure

Folded polymers in nature are assembled from simple monomers and adopt complex folded structures through networks of stabilizing noncovalent interactions. These interactions define secondary and tertiary structure and in most cases specify a unique three-dimensional architecture. Individual secondary or tertiary structures can also associate with one another to form multi-subunit quaternary structures. Nonnatural folded polymers have potential for similar structural versatility. Here we describe a pair of beta3-peptides whose sequences were designed to promote a 14-helix structure in water, favor hetero-oligomer formation, and disfavor nonspecific aggregation. These beta3-peptides assemble noncovalently into a well-defined hetero-oligomer characterized by a defined stoichiometry, a highly stabilized secondary structure, and a cooperative melting transition (TM > 55 degrees C). This work demonstrates that beta3-peptides can assemble into defined, cooperatively folded quaternary structures and constitutes an important step toward designing protein-like assemblies from nonnatural polymers.     

Heteropolymer translocation through nanopores

The authors investigate the translocation dynamics of heteropolymers driven through a nanopore using a constant temperature Langevin thermostat. Specifically, they consider heteropolymers consisting of two types of monomers labeled A and B, which are distinguished by the magnitude of the driving force that they experience inside the pore. From a series of studies on polymers with sequences AmBn the authors identify both universal as well as specific sequence properties of the translocating chains. They find that the scaling of the average translocation time as a function of the chain length N remains unaffected by the heterogeneity, while the residence time of each bead is a strong function of the sequence for short repeat units. They further discover that for a symmetric heteropolymer AnBn of fixed length, the pattern exhibited by the residence times of the individual monomers has striking similarity with a double slit interference pattern where the total number of repeat units N/2n controls the number of interference fringes. These results are relevant for designing nanopore based sequencing techniques.     

Re-examination of structure optimization of off-lattice protein AB models by conformational space annealing

The global structural optimization is carried out for off-lattice protein AB models in two and three dimensions by conformational space annealing. The models consist of hydrophobic and hydrophilic monomers in Fibonacci sequences. To accelerate the convergence, we have introduced a shift operator in the internal coordinate system, and effectively reduced the search space by forming a quotient space. With this, we significantly improve our previous results on AB models, and provide new low energy conformations. This work provides insights on exploring complicated energy landscapes by exploiting the advantages and limitations of CSA.     

Folding a nonbiological polymer into a compact multihelical structure

The only molecules that are currently known to fold into unique three-dimensional conformations and perform sophisticated functions are biological polymers - proteins and some RNA molecules. Our aim is to create a nonbiological sequence-specific polymer that folds in aqueous solution. Toward that end, we synthesized sequence-specific 30mer, 45mer, and 60mer peptoid oligomers (N-substituted glycine polymers) consisting of 15mer units we chained together by disulfide and oxime linkages to mimic the helical bundle structures commonly found in proteins. Because these 15mer sequences were previously shown to form defined helical structures that aggregate together at submillimolar concentrations, we expected that by covalently linking multiple 15mers together, they might fold as helical bundles. To probe whether they folded, we used fluorescence resonance energy transfer (FRET) reporter groups. We found that certain constructs fold up with a hydrophobic core and have cooperative folding transitions. Such molecules may ultimately provide a platform for designing specific functions resembling those of proteins.     

稀土催化极性单体配位均聚及与非极性单体共聚合的研究

将极性基团引入大分子链中可改善非极性聚烯烃材料的表面性能,扩展其应用范围甚至带来不可预见的新功能,是市场需求并由企业驱动.与聚合后功能化改性和物理共混方法相比,极性与非极性单体配位共聚合是最直接和简便的方法,适用范围广,并可保持聚烯烃的立构规整度,一直以来,相关研究备受企业和科研工作者瞩目.然而,极性基团通常具有Lewis碱性,容易与Lewis酸性的聚合催化剂强烈螯合而致其毒化,因此,这又是极具挑战性的课题.目前,该领域的研究取得了很大的进展,已经实现了乙烯与很多极性单体的共聚合.今后,将集中解决如何实现极性单体均聚合,提高共聚合活性,特别是极性单体插入率和分布可调节性,保持立体选择性,以及获得高分子量、具有实际应用意义的共聚产物等问题.本文旨在将课题组近年来在极性功能化苯乙烯和共轭双烯烃单体的均聚合及与苯乙烯、乙烯和共轭双烯烃等非极性单体共聚合方面的最新研究成果以及国内外该领域的相关报道进行综合阐述,为读者提供解决上述关键问题采用的研究路线、实施方法和创新性思维.     

Validation and application of modeling algorithms for the design of molecularly imprinted polymers

In the study, four different semiempirical algorithms, modified neglect of diatomic overlap, a reparameterization of Austin Model 1, complete neglect of differential overlap and typed neglect of differential overlap, have been applied for the energy optimization of template, monomer, and template‐monomer complexes of imprinted polymers. For phosmet‐, estrone‐, and metolcarb‐imprinted polymers, the binding energies of template‐monomer complexes were calculated and the docking configures were assessed in different molar ratio of template/monomer. It was found that two algorithms were not suitable for calculating the binding energy in template‐monomers complex system. For the other algorithms, the obtained optimum molar ratio of template and monomers were consistent with the experimental results. Therefore, two algorithms have been selected and applied for the preparation of enrofloxacin‐imprinted polymers. Meanwhile using a different molar ratio of template and monomer, we prepared imprinted polymers and nonimprinted polymers, and evaluated the adsorption to template. It was verified that the experimental results were in good agreement with the modeling results. As a result, the semiempirical algorithm had certain feasibility in designing the preparation of imprinted polymers.     

RATE OF INTRA-MOLECULAR CONTACT FORMATION IN SHORT TWO-DIMENSIONAL COMPACT POLYMERS CHAINS

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.