Hydrogen bonding in nucleosides and nucleotides

An analysis of the hydrogen bonding in 76 nucleoside and 11 nucleotide crystal structures shows that the hydrogen bond lengths fall into well-defined categories according to the nature of the donor or acceptor groups. The shortest bonds are those involving P---OH or O=P groups. For donor groups, the sequence in bond lengths is

P—OH<C—OH< N−H<O_w(H)—H<N(H)—H<C−H

There are ten examples of two centre

H—H…O

bonds, which are comparable in length with P---OH …O bonds. The acceptor seqeunce is

O=P<OH₂<OH₂<O=CO(H)C<N N(H₂)C<Cl^…<O<S=C

The number of three-centre bonds, about 24%, is comparable to that observed in the carbohydrates and the amino acids. Most hydrogen bonds are involved in short finite chains. Only in the nucleotides are cyclic hydrogen bonding schemes observed.     

Effects of base polymer hydrophobicity and end-group modification on polymeric gene delivery

A new 320-member polymer library of end-modified poly(β-amino ester)s was synthesized. This library was chosen such that small differences to the structures of component backbone, side-chain, and end-group monomers could be systematically and simultaneously evaluated. The in vitro transfection efficacy and cytotoxicity of DNA nanoparticles formed from this library were assessed. This library approach not only enabled us to synthesize and test a large variety of structures rapidly but also provided us with a robust data set to analyze for the effect of small structural permutations to polymer chain structure. Small changes to the side chains, backbones, and end groups within this polymer library produced dramatic results, with transfection efficacy of CMV-Luc varying over 4 orders in a 96-well plate format. Increasing hydrophobicity of the base polymer backbone and side chain tended to increase transfection efficacy, but the most hydrophobic side chains and backbones showed the least requirement for a hydrophobic pair. Optimal PBAE formulations were superior to commercially available nonviral alternatives FuGENE HD and Lipofectamine 2000, enabling ~3-fold increased luminescence (2.2 × 10(6) RLU/well vs 8.1 × 10(5) RLU/well) and 2-fold increased transfection percentage (76.7% vs 42.9%) as measured by flow cytometry with comparable or reduced toxicity.     

Cooperative effects in hydrogen-bonding of protein secondary structure elements: a systematic analysis of crystal data using Secbase

A systematic analysis of the hydrogen-bonding geometry in helices and beta sheets has been performed. The distances and angles between the backbone carbonyl O and amide N atoms were correlated considering more than 1500 protein chains in crystal structures determined to a resolution better than 1.5 A. They reveal statistically significant trends in the H-bond geometry across the different secondary structural elements. The analysis has been performed using Secbase, a modular extension of Relibase (Receptor Ligand Database) which integrates information about secondary structural elements assigned to individual protein structures with the various search facilities implemented into Relibase. A comparison of the mean hydrogen-bond distances in alpha helices and 3(10) helices of increasing length shows opposing trends. Whereas in alpha helices the mean H-bond distance shrinks with increasing helix length and turn number, the corresponding mean dimension in 3(10) helices expands in a comparable series. Comparing similarly the hydrogen-bond lengths in beta sheets there is no difference to be found between the mean H-bond length in antiparallel and parallel beta sheets along the strand direction. In contrast, an interesting systematic trend appears to be given for the hydrogen bonds perpendicular to the strands bridging across an extended sheet. With increasing number of accumulated strands, which results in a growing number of back-to-back piling hydrogen bonds across the strands, a slight decrease of the mean H-bond distance is apparent in parallel beta sheets whereas such trends are obviously not given in antiparallel beta sheets. This observation suggests that cooperative effects mutually polarizing spatially well-aligned hydrogen bonds are present either in alpha helices and parallel beta sheets whereas such influences seem to be lacking in 3(10) helices and antiparallel beta sheets.     

Evaluation of short-range interactions as secondary structure energies for protein fold and sequence recognition.

Short-range interactions for secondary structures of proteins are evaluated as potentials of mean force from the observed frequencies of secondary structures in known protein structures which are assumed to have an equilibrium distribution with the Boltzmann factor of secondary structure energies. A secondary conformation at each residue position in a protein is described by a tripeptide, including one nearest neighbor on each side. The secondary structure potentials are approximated as additive contributions from neighboring residues along the sequence. These are part of an empirical potential to provide a crude estimate of protein conformational energy at a residue level. Unlike previous works, interactions are decoupled into intrinsic potentials of residues, potentials of backbone-backbone interactions, and of side chain-backbone interactions. Also interactions are decoupled into one-body, two-body, and higher order interactions between peptide backbone and side chain and between backbones. These decouplings are essential to correctly evaluate the total secondary structure energy of a protein structure without overcounting interactions. Each interaction potential is evaluated separately by taking account of the correlation in the amino acid order of protein sequences. Interactions among side chains are neglected, because of the relatively limited number of protein structures. Proteins 1999;36:347-356. Published 1999 Wiley-Liss, Inc.     

Docking of calcium ions in proteins with flexible side chains and deformable backbones

A method of docking Ca²⁺ ions in proteins with flexible side chains and deformable backbones is proposed. The energy was calculated with the AMBER force field, implicit solvent, and solvent exposure-dependent and distance-dependent dielectric function. Starting structures were generated with Ca²⁺ coordinates and side-chain torsions sampled in 1000 Å³ cubes centered at the experimental Ca²⁺ positions. The energy was Monte Carlo-minimized. The method was tested on fourteen Ca²⁺-binding sites. For twelve Ca²⁺-binding sites the root mean square (RMS) deviation of the apparent global minimum from the experimental structure was below 1.3 and 1.7 Å for Ca²⁺ ions and side-chain heavy atoms, respectively. Energies of multiple local minima correlate with the RMS deviations from the X-ray structures. Two Ca²⁺-binding sites at the surface of proteinase K were not predicted, because of underestimation of Ca²⁺ hydration energy by the implicit-solvent method.     

Dynamic simulations of the molecular conformations of wild type and mutant xanthan polymers suggest that conformational differences may contribute to observed differences in viscosity

Xanthan gum is an exopolysaccharide secreted by the bacterium Xanthamonas campestris whose ability to make solutions viscous at low concentrations and over a pH and temperature range have generated much interest in both academic and industrial environments. Mutant Xanthamonas strains have been derived that produce xanthan gums with an altered or variant subunit chemical structure and different measured viscosities when compared with the wild type (wt) form of the polymer. Two variant gums were targeted as potentially interesting in this study, these being the nonacetylated tetramer (natct; and the acetylated tetramer (atet), which both lack a side-chain terminal mannose residue and in one case (natet) lacks an acetate group on an internal mannose residue. Solutions of these tetrameric gums possess viscosities higher (natet) and lower (atet) than the wt gum, and therefore we have attempted to determine whether these molecules possess unique conformational preferences when compared with the wt and with each other. In this manner we can initiate an understanding of how a polysaccharide's conformation contributes to its solution properties. The GEGOP software permits a sampling of the static and dynamic equilibrium states of carbohydrate molecules, and this software was employed to calculate equilibrium states of representative oligosaccharides with chemical structures representative of xanthan-like molecules. Energy minimization techniques revealed similar local minima for all three molecules. Some of these minima are comprised of elongate backbone conformations (A type) in which side chains fold onto backbone surfaces. Other minima with A backbones possessed side chains in less intimate backbone contact especially when calculations were performed with a low dielectric constant. This phenomenon was particularly pronounced in the wt molecule where an increased number of negatively charged side-chain residues experience charge repulsion resulting in reduced side-chain-backbone contact. Metropolis Monte Carlo (MMC) dynamic simulations performed with an elevated temperature factor (1000 K) allowed a better qualitative representation of conformational space than 300 K simulations. Employing a nonhierarchical cluster analysis method (population density profile: PDP) coupled with a classification scheme, it was possible to partition resulting MMC data sets into conformational families. This analysis revealed that in simulations performed with different dielectric constant values (10, 25, and ∞) all molecules possessed primarily A-type backbones. Less elongate, more open helical backbone forms (B, C, D, J, and Flat-a) did occur during the simulations but were populated to a lesser extent. In the natet molecule significantly open helical backbones existed (E, F, G, H, and I) that did not occur in the lower viscosity wt and atet molecules. PDP clustering methods and subsequent conformational classification applied to the first residue (mannose) of the side chain permitted a determination of side-chain orientation. Comparison of all three molecules indicated a larger population of side-chain conformational families in less direct backbone contact for the wt molecule than either of the variant molecules (natet/atet) suggesting that the side chains in the wt are more flexible. Thus, a major conformational difference between the high viscosity natet. In addition, the significant difference between the higher viscosity wt and the lower viscosity atet is the increase side-chain flexibility in the wt. We hypothesize that conformational differences of this kind could form a partial explanation of the observed differences in viscosity between these xanthan-like polymers. © 1996 John Wiley & Sons, Inc.     

Local sequence of protein β‐strands influences twist and bend angles

β‐Sheet twisting is thought to be mainly determined by interstrand hydrogen bonds with little contribution from side chains, but some proteins have large, flat β‐sheets, suggesting that side chains influence β‐structures. We therefore investigated the relationship between amino acid composition and twists or bends of β‐strands. We calculated and statistically analyzed the twist and bend angles of short frames of β‐strands in known protein structures. The most frequent twist angles were strongly negatively correlated with the proportion of hydrophilic amino acid residues. The majority of hydrophilic residues (except serine and threonine) were found in the edge regions of β‐strands, suggesting that the side chains of these residues likely do not affect β‐strand structure. In contrast, the majority of serine, threonine, and asparagine side‐chains in β‐strands made contacts with a nitrogen atom of the main chain, suggesting that these residues suppress β‐strand twisting. Proteins 2014; 82:1484–1493. © 2014 Wiley Periodicals, Inc.     

Peculiarities and applications of galactanolytic enzymes that act on type I and II arabinogalactans

Arabinogalactans (AGs) are branched galactans to which arabinose residues are bound as side chains and are widely distributed in plant cell walls. They can be grouped into two types based on the structures of their backbones. Type I AGs have β-1,4-galactan backbones and are often covalently linked to the rhamnogalacturonan-I region of pectins. Type II AGs have β-1,3-galactan backbones and are often covalently linked to proteins. The main enzymes involved in the degradation of AGs are endo-β-galactanases, exo-β-galactanases, and β-galactosidases, although other enzymes such as α-l-arabinofuranosidases, β-l-arabinopyranosidases, and β-d-glucuronidases are required to remove the side chains for efficient degradation of the polysaccharides. Galactanolytic enzymes have a wide variety of potential uses, including the bioconversion of AGs to fermentable sugars for production of commodity chemicals like ethanol, biobleaching of cellulose pulp, modulation of pectin properties, improving animal feed, and determining the chemical structure of AGs. This review summarizes our current knowledge about the biochemical properties and potential applications of AG-degrading enzymes.     

Criteria that discriminate between native proteins and incorrectly folded models

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.     

Structural transitions and oligomerization along polyalanine fibril formation pathways from computer simulations

The results of a computer simulation study of the aggregation kinetics of a large system of model peptides with particular focus on the formation of intermediates are presented. Discontinuous molecular dynamic simulations were used in combination with our intermediate-resolution protein model, PRIME, to simulate the aggregation of a system of 192 polyalanine (KA(14) K) peptides at a concentration of 5 mM and a reduced temperature of T* = 0.13 starting from a random configuration and ending in the assembly of a fibrillar structure. The population of various structures, including free monomers, beta sheets, amorphous aggregates, hybrid aggregates, and fibrils, and the transitions between the structures were tracked over the course of 30 independent simulations and averaged together. The aggregation pathway for this system starts with the association of free monomers into small amorphous aggregates that then grow to moderate size by incorporating other free monomers or merging with other small amorphous aggregates. These then rearrange into either small beta sheets or hybrid aggregates formed by association between unstructured chains and beta sheets, both of which grow in size by adding free monomer chains or other small aggregates, one at a time. Fibrillar structures are formed initially either by the stacking of beta sheets, rearrangement of hybrid aggregates or association between beta sheets and hybrid aggregates. They grow by the addition of beta sheets, hybrid aggregates, and other small fibrillar structures. The rearrangement of amorphous aggregates into beta sheets is a critical and necessary step in the fibril formation pathway.     

Self-assembly and dynamics of poly(gamma-benzyl-l-glutamate) peptides

The structure and the associated dynamics have been investigated in a series of oligopeptides of gamma-benzyl-l-glutamate using DSC, WAXS, FTIR, NMR and dielectric spectroscopy, and rheology, respectively. The peptides with degrees of polymerization below 18 are mixtures of a lamellar assembly of beta sheets and of columnar hexagonal arrangement of alpha helices, whereas for longer chains, the intramolecular hydrogen bonds stabilize only the alpha-helical conformations. Multiple dielectrically active processes were found. Starting from low temperatures, the two Arrhenius processes (gamma and beta), with apparent activation energies of 20.6 and 50.2 kJ/mol, respectively, associate with the local relaxation of the side-chain methylene units (gamma process) and with more cooperative motions of the side chain dipoles sensitive to the 7/2 helical packing (beta process). The glass transition is manifested in the thermal properties with a step in the heat capacity and with an intense dielectric process bearing characteristics (molecular weight dependence, temperature dependence of relaxation times) known from amorphous polymers. Based on these findings, the alpha process is attributed to the relaxation of amorphous segments located between and at the end of helically ordered segments. Two slower processes were identified with opposite molecular weight dependence. The weak intermediate mode with an M2 molecular weight dependence of the characteristic relaxation times suggests amorphous-like chains, whereas the strong slower process originates from the loss of dipole orientational capacity caused by structural defects and reflects the migration of helical sequences along the chains. This identifies the helices as structures extending over rather short fragments of chains (i.e., of low persistence length). The viscoelastic response indicated that the structural defects arise from locally aggregated chains that inhibit the flow of oligopeptides.     

Three-dimensional solution structure of apo-neocarzinostatin from Streptomyces carzinostaticus determined by NMR spectroscopy.

The three-dimensional solution structure of apo-neocarzinostatin has been resolved from nuclear magnetic resonance spectroscopy data. Up to 1034 constraints were used to generate an initial set of 45 structures using a distance geometry algorithm (DSPACE). From this set, ten structures were subjected to refinement by restrained energy minimization and molecular dynamics. The average atomic root mean square deviations between the final ten structures and the mean structure obtained by averaging their coordinates run from 0.085 nm for the best defined beta-sheet regions of the protein to 0.227 nm for the side chains of the most flexible loops. The solution structure of apo-neocarzinostatin is closely similar to that of the related proteins, macromomycin and actinoxanthin. It contains a seven-stranded antiparallel beta-barrel which forms, together with two external loops, a deep cavity that is the chromophore binding site. It is noteworthy that aromatic side chains extend into the binding cleft. They may be responsible for the stabilization of the holo-protein complex and for the chromophore specificity within the antitumoral family.     

Exploiting diverse stereochemistry of β-amino acids: toward a rational design of sheet-forming β-peptide systems

Due to the two methylene groups in their backbone, β-amino acids can adopt numerous secondary structures, including helices, sheets and nanotubes. Chirality introduced by the additional side chains can significantly influence the folding preference of β-peptides composed of chiral β-amino acids. However, only conceptual suggestions are present in the literature about the effect of chirality on folding preferences. Summarizing both the experimental and computational results, Seebach (Chem Biodivers 1:1111-1240, 2004) has proposed the first selection rule on the effect of side chain chirality, on the folding preference of β-peptides. In order to extend and fine-tune the aforementioned predictions of Seebach, we have investigated its validity to the novel type of apolar sheet proposed recently (Pohl et al. in J Phys Chem B 114:9338-9348, 2010). In order to facilitate the rational design of sheet-like structures, a systematic study on the effect of chirality on "apolar" sheet stability is presented on disubstituted [HCO-β-Ala-β(2,3)-hAla-β-Ala-NH(2)](2) model peptides calculated at the M05-2X/6-311++G(d,p)//M05-2X/6-31G(d) and B3LYP/6-311++G(d,p)//B3LYP/6-31G(d) levels of theory both in vacuum and in polar and apolar solvents. In addition, both types of "apolar" sheets were investigated; the one with two strands of identical (AA) and enantiomeric (AB) backbone structure. Our results show that heterochirally disubstituted sheets have the greatest preference for sheet formation (ΔG ~ -11 kcal mol(-1)). However, in contrast to Seebach's predictions, "homochiral disubstitution" itself does not necessarily disrupt the sheet structure, rather it could result stable fold (ΔG ~ -5 kcal mol(-1)). Results indicate that both the methyl group orientation and the local conformational effect of substitution affects sheet stability, as point chirality was found to have influence only on the backbone torsional angles. These results enabled us to extend and generalize Seebach's predictions and to propose a more general and accurate "rule of thumb" describing the effect of chirality on sheet stability. This offers an easy-to-use summary on how to design β-peptide sheet structures. We conclude that heterochirally disubstituted models are the best candidates for sheet formation, if the two strands are substituted in a way to create identical torsional angle sets on the two backbones for ideal hydrogen-bonding pattern. With adequately selected side chains, homochirally disubtituted derivatives may also form sheet structures, and the position of methyl groups would prevent assembly of more than two strands making it ideal to create hairpins.     

DNA recognition by β-sheets

The modes of DNA recognition by β-sheets are analyzed by using the known crystal and solution three-dimensional structures of DNA-protein complexes. Close fitting of the protein surface and the DNA surface determines the binding geometry. Interaction takes place so that essentially the N-to-C direction of the β-strands either follows or crosses the DNA groove. Upon following the major groove a two-stranded antiparallel β-sheet dives into the groove and contacts DNA bases with its convex side facing the DNA, while upon following the minor groove, it binds around the sugar-phosphate backbones, with its opposite concave side shielding the DNA. In order for the β-strands crossing the minor groove to interact with the DNA, the dinucleotide steps need to almost totally helically untwist and roll around major groove. The β-sheet, on the other hand, needs to adopt a concave curvature on the binding surface in the direction that follows the DNA minor groove, and a convex surface in the direction that bridges the sugar-phosphate backbones across the groove. The result is to produce a hyperbolic paraboloidal DNA-binding surface. © 1998 John Wiley & Sons, Inc. Biopoly 44: 335–359, 1997     

Cyclo-hexa-peptides at the water/cyclohexane interface: a molecular dynamics simulation

Molecular dynamic (MD) simulations have been performed to study the behaviors of ten kinds of cyclo-hexa-peptides (CHPs) composed of amino acids with the diverse hydrophilic/hydrophobic side chains at the water/cyclohexane interface. All the CHPs take the “horse-saddle” conformations at the interface and the hydrophilicity/hydrophobicity of the side chains influences the backbones’ structural deformations. The orientations and distributions of the CHPs at the interface and the differences of interaction energies (ΔΔE) between the CHPs and the two liquid phases have been determined. RDF analysis shows that the H-bonds were formed between the O_C atoms of the CHPs’ backbones and H_w atoms of water molecules. N atoms of the CHPs’ backbones formed the H-bonds or van der Waals interactions with the water solvent. It was found that there is a parallel relationship between ΔΔE and the lateral diffusion coefficients (D _xy ) of the CHPs at the interface. The movements of water molecules close to the interface are confined to some extent, indicating that the dynamics of the CHPs and interfacial water molecules are strongly coupled.

Design and synthesis of self-degradable antibacterial polymers by simultaneous chain- and step-growth radical copolymerization

Self-degradable antimicrobial copolymers bearing cationic side chains and main-chain ester linkages were synthesized using the simultaneous chain- and step-growth radical polymerization of t-butyl acrylate and 3-butenyl 2-chloropropionate, followed by the transformation of t-butyl groups into primary ammonium salts. We prepared a series of copolymers with different structural features in terms of molecular weight, monomer composition, amine functionality, and side chain structures to examine the effect of polymer properties on their antimicrobial and hemolytic activities. The acrylate copolymers containing primary amine side chains displayed moderate antimicrobial activity against E. coli but were relatively hemolytic. The acrylate copolymer with quaternary ammonium groups and the acrylamide copolymers showed low or no antimicrobial and hemolytic activities. An acrylate copolymer with primary amine side chains degraded to lower molecular weight oligomers with lower antimicrobial activity in aqueous solution. This degradation was due to amidation of the ester groups of the polymer chains by the nucleophilic addition of primary amine groups in the side chains resulting in cleavage of the polymer main chain. The degradation mechanism was studied in detail by model reactions between amine compounds and precursor copolymers.     

Towards a pharmacophore for amyloid

Diagnosing and treating Alzheimer's and other diseases associated with amyloid fibers remains a great challenge despite intensive research. To aid in this effort, we present atomic structures of fiber-forming segments of proteins involved in Alzheimer's disease in complex with small molecule binders, determined by X-ray microcrystallography. The fiber-like complexes consist of pairs of β-sheets, with small molecules binding between the sheets, roughly parallel to the fiber axis. The structures suggest that apolar molecules drift along the fiber, consistent with the observation of nonspecific binding to a variety of amyloid proteins. In contrast, negatively charged orange-G binds specifically to lysine side chains of adjacent sheets. These structures provide molecular frameworks for the design of diagnostics and drugs for protein aggregation diseases.     

毛乌素沙地油蒿叶建成成本及相关叶性状沿降水梯度的变化

干旱区植物在如何提高水分利用效率与降低叶建成成本之间可能存在一种权衡。我们假设: 与湿润区植物相比, 干旱区植物能通过调节叶功能性状之间的关系(如通过提高单位面积叶氮含量(N_area)), 实现在相同的叶建成成本下具有更高的水分利用效率。为了验证这一假设, 该研究以毛乌素沙地的广布物种油蒿(Artemisia ordosica)为研究对象, 分析了油蒿叶建成成本沿降水梯度的变化规律及其与比叶面积(SLA)、单位质量叶氮含量(N_mass)、N_area和叶碳稳定同位素比率(δ ¹³C)的关系。结果表明: 油蒿单位质量叶建成成本(CC_m)在不同降水条件下差异不显著, 而单位面积叶建成成本(CC_a)在不同降水条件下虽有显著差异, 但并未随降水减少而明显增加。油蒿CC_m与SLA无显著相关性, 与叶δ ¹³C值呈显著正相关关系。油蒿叶建成成本与N_area呈显著正相关关系, 但这种关系格局在低降水量(264 mm)区与高降水量(310-370 mm)区之间存在策略位移现象——即在相同叶建成成本下, 低降水量区植物比高降水量区植物具有更高的N_area。以上结果表明, 尽管高水分利用效率与高叶建成成本相关, 但与高降水量区植物相比, 低降水量区植物具有较高的N_area并没有导致其叶建成成本增加。     

Molecular dynamics simulation on structural conformation of conjugated polymer-functionalised films for optimal fluorescent performance

The sensitive structure-related fluorescent properties of p-phenyleneethynylene (PPE)-functionalised fluorescent films with side chains and without side chains in different chemical environments are studied by molecular dynamics simulations. The calculations demonstrate that the structural change plays a crucial role in the fluorescent performance of PPE films, in which a major contribution is from the conformation of side chains. The PPE molecules with sides chains immobilised on SiO₂ substrate prefer to aggregate together in a dry state, but are more likely to stay in a monomolecular state in THF solvent. To an optimal concentration of the solvent molecules, the side chains are even perpendicular to the backbones of the molecules. The aggregation and separation of the PPE molecules with side chains are found to be controlled by the contraction and extension of the side chains connected to PPE. The van der Waals' force between the side chains is mainly responsible for these changes, which leads to a spreading out of the side chains in the presence of THF. All the results from the simulation studies can successfully explain the experimental observations.