Calculating potentials of mean force from steered molecular dynamics simulations

Steered molecular dynamics (SMD) permits efficient investigations of molecular processes by focusing on selected degrees of freedom. We explain how one can, in the framework of SMD, employ Jarzynski's equality (also known as the nonequilibrium work relation) to calculate potentials of mean force (PMF). We outline the theory that serves this purpose and connects nonequilibrium processes (such as SMD simulations) with equilibrium properties (such as the PMF). We review the derivation of Jarzynski's equality, generalize it to isobaric--isothermal processes, and discuss its implications in relation to the second law of thermodynamics and computer simulations. In the relevant regime of steering by means of stiff springs, we demonstrate that the work on the system is Gaussian-distributed regardless of the speed of the process simulated. In this case, the cumulant expansion of Jarzynski's equality can be safely terminated at second order. We illustrate the PMF calculation method for an exemplary simulation and demonstrate the Gaussian nature of the resulting work distribution.     

Potential of mean force calculations of ligand binding to ion channels from Jarzynski's equality and umbrella sampling

Potential of mean force (PMF) calculations provide a reliable method for determination of the absolute binding free energies for protein-ligand systems. The common method used for this purpose -- umbrella sampling with weighted histogram analysis -- is computationally very laborious, which limits its applications. Recently, a much simpler alternative for PMF calculations has become available, namely, using Jarzynski's equality in steered molecular dynamics simulations. So far, there have been a few comparisons of the two methods and mostly in simple systems that do not reflect the complexities of protein-ligand systems. Here, we use both methods to calculate the PMF for ion permeation and ligand binding to ion channels. Comparison of results indicate that Jarzynski's method suffers from relaxation problems in complex systems and would require much longer simulation times to yield reliable PMFs for protein-ligand systems.     

Efficient use of nonequilibrium measurement to estimate free energy differences for molecular systems

A promising method for calculating free energy differences DeltaF is to generate nonequilibrium data via "fast-growth" simulations or by experiments--and then use Jarzynski's equality. However, a difficulty with using Jarzynski's equality is that DeltaF estimates converge very slowly and unreliably due to the nonlinear nature of the calculation--thus requiring large, costly data sets. The purpose of the work presented here is to determine the best estimate for DeltaF given a (finite) set of work values previously generated by simulation or experiment. Exploiting statistical properties of Jarzynski's equality, we present two fully automated analyses of nonequilibrium data from a toy model, and various simulated molecular systems. Both schemes remove at least several k(B)T of bias from DeltaF estimates, compared to direct application of Jarzynski's equality, for modest sized data sets (100 work values), in all tested systems. Results from one of the new methods suggest that good estimates of DeltaF can be obtained using 5-40-fold less data than was previously possible. Extending previous work, the new results exploit the systematic behavior of bias due to finite sample size. A key innovation is better use of the more statistically reliable information available from the raw data.     

Steered molecular dynamics simulations of Na+ permeation across the gramicidin A channel

The potential of mean forces (PMF) governing Na+ permeation through gramicidin A (gA) channels with explicit water and membrane was characterized using steered molecular dynamics (SMD) simulations. Constant-force SMD with a steering force parallel to the channel axis revealed at least seven energy wells in each monomer of the channel dimer. Except at the channel dimer interface, each energy well is associated with at least three and at most four backbone carbonyl oxygens and two water oxygens in a pseudo-hexahedral or pseudo-octahedral coordination with the Na+ ion. Repeated constant-velocity SMD by dragging a Na+ ion from each energy well in opposite directions parallel to the channel axis allowed the computation of the PMF across the gA channel, revealing a global minimum corresponding to Na+ binding sites near the entrance of gA at +/-9.3 A from the geometric center of the channel. The effect of volatile anesthetics on the PMF was also analyzed in the presence of halothane molecules. Although the accuracy of the current PMF calculation from SMD simulations is not yet sufficient to quantify the PMF difference with and without anesthetics, the comparison of the overall PMF profiles nevertheless confirms that the anesthetics cause insignificant changes to the structural makeup of the free energy wells along the channel and the overall permeation barrier. On average, the PMF appears less rugged in the outer part of the channel in the presence of anesthetics, consistent with our earlier finding that halothane interaction with anchoring residues makes the gA channel more dynamic. A causal relationship was observed between the reorientation of the coordinating backbone carbonyl oxygen and Na+ transit from one energy well to another, suggesting the possibility that even minute changes in the conformation of pore-lining residues due to dynamic motion could be sufficient to trigger the ion permeation. Because some of the carbonyl oxygens contribute to Na+ coordination in two adjacent energy wells, our SMD results reveal that the atomic picture of ion "hopping" through a gA channel actually involves a Na+ ion being carried in a relay by the coordinating oxygens from one energy well to the next. Steered molecular dynamics complements other computational approaches as an attractive means for the atomistic interpretation of experimental permeation studies.     

Adaptive steered molecular dynamics: validation of the selection criterion and benchmarking energetics in vacuum

The potential of mean force (PMF) for stretching decaalanine in vacuum was determined earlier by Park and Schulten [J. Chem. Phys. 120, 5946 (2004)] in a landmark article demonstrating the efficacy of combining steered molecular dynamics and Jarzynski's nonequilibrium relation. In this study, the recently developed adaptive steered molecular dynamics (ASMD) algorithm [G. Ozer, E. Valeev, S. Quirk, and R. Hernandez, J. Chem. Theory Comput. 6, 3026 (2010)] is used to reproduce the PMF of the unraveling of decaalanine in vacuum by averaging over fewer nonequilibrium trajectories. The efficiency and accuracy of the method are demonstrated through the agreement with the earlier work by Park and Schulten, a series of convergence checks compared to alternate SMD pulling strategies, and an analytical proof. The nonequilibrium trajectories obtained through ASMD have also been used to analyze the intrapeptide hydrogen bonds along the stretching coordinate. As the decaalanine helix is stretched, the initially stabilized i → i + 4 contacts (α-helix) is replaced by i → i + 3 contacts (3(10)-helix). No significant formation of i → i + 5 hydrogen bonds (π-helix) is observed.     

Steered molecular dynamics studies of the potential of mean force of a Na+ or K+ ion in a cyclic peptide nanotube

Potential of mean force (PMF) profiles of a single Na+ or K+ ion passing through a cyclic peptide nanotube, cyclo[-(D-Ala-Glu-D-Ala-Gln)2-], in water are calculated to provide insight into ion transport and to understand the conductance difference between these two ions. The PMF profiles are obtained by performing steered molecular dynamics (SMD) simulations that are based on the Jarzynski equality. The computed PMF profiles for both ions show barriers of around 2.4 kcal/mol at the channel entrances and exits and energy wells in the middle of the tube. The energy barriers, so-called dielectric energy barriers, arise due to the desolvation of water molecules when ions move across the nanotube, and the energy wells appear as a result of attractive interactions between the cations and negatively charged carbonyl oxygens on the backbone of the tube. We find more and deeper energy wells in the PMF profile for Na+ than for K+, which suggests that Na+ ions have a longer residence time inside the nanotube and that permeation of Na+ ions is reduced compared to K+ ions. Calculations of the radial distribution functions (RDF) between the ions and oxygens in the water molecules and in carbonyl groups on the tube and an investigation of the orientations of the carbonyl groups show that, in contrast with the dynamic carbonyl groups observed in the selectivity filter of the KcsA ion channel, the carbonyl groups in the cyclic peptide nanotube are relatively rigid, with only slight reorientation of the carbonyl groups as the cations pass through. The rigidity of the carbonyl groups in the cyclic peptide nanotube can be attributed to their role in hydrogen bonding, which is responsible for the tube structure. Comparison of the PMF profiles with the electrostatic energy profiles calculated from the Poisson-Boltzmann (PB) equation, a dielectric continuum model, reveals that the dielectric continuum model breaks down in the confined region within the tube that governs ion transport.     

Molecular dynamics simulations of peptide-surface interactions

Proteins, which are bioactive molecules, adsorb on implants placed in the body through complex and poorly understood mechanisms and directly influence biocompatibility. Molecular dynamics modeling using empirical force fields provides one of the most direct methods of theoretically analyzing the behavior of complex molecular systems and is well-suited for the simulation of protein adsorption behavior. To accurately simulate protein adsorption behavior, a force field must correctly represent the thermodynamic driving forces that govern peptide residue-surface interactions. However, since existing force fields were developed without specific consideration of protein-surface interactions, they may not accurately represent this type of molecular behavior. To address this concern, we developed a host-guest peptide adsorption model in the form of a G(4)-X-G(4) peptide (G is glycine, X is a variable residue) to enable determination of the contributions to adsorption free energy of different X residues when adsorbed to functionalized Au-alkanethiol self-assembled monolayers (SAMs). We have previously reported experimental results using surface plasmon resonance (SPR) spectroscopy to measure the free energy of peptide adsorption for this peptide model with X = G and K (lysine) on OH and COOH functionalized SAMs. The objectives of the present research were the development and assessment of methods to calculate adsorption free energy using molecular dynamics simulations with the GROMACS force field for these same peptide adsorption systems, with an oligoethylene oxide (OEG) functionalized SAM surface also being considered. By comparing simulation results to the experimental results, the accuracy of the selected force field to represent the behavior of these molecular systems can be evaluated. From our simulations, the G(4)-G-G(4) and G(4)-K-G(4) peptides showed minimal to no adsorption to the OH SAM surfaces and the G(4)-K-G(4) showed strong adsorption to the COOH SAM surface, which is in agreement with our SPR experiments. Contrary to our experimental results, however, the simulations predicted a relatively strong adsorption of G(4)-G-G(4) peptide to the COOH SAM surface. In addition, both peptides were unexpectedly predicted to adsorb to the OEG surface. These findings demonstrate the need for GROMACS force field parameters to be rebalanced for the simulation of peptide adsorption behavior on SAM surfaces. The developed methods provide a direct means of assessing, modifying, and validating force field performance for the simulation of peptide and protein adsorption to surfaces, without which little confidence can be placed in the simulation results that are generated with these types of systems.     

分子动力学模拟多巴在自组装膜上的黏附性

为了更好地理解贻贝在表面的黏附机理,实现水下胶黏,采用分子动力学方法研究了多巴在自组装膜上的黏附性:采用伞形取样和加权柱状图分析方法计算了多巴在不同自组装膜表面的黏附自由能,使用拉伸分子动力学模拟研究了多巴在不同自组装膜表面上黏附后的脱附力.结果表明,多巴在带负电的羧基自组装膜上的黏附能比在带正电的氨基自组装膜上的大,多巴更容易黏附到带负电表面;多巴在带电表面的黏附能比未带电表面的黏附能更强,表明在带电表面黏附更稳定.进一步分析了多巴在不同表面的取向分布,发现多巴与不同表面相互作用的方式不同:与疏水表面主要通过苯环相互作用;与亲水表面主要通过羟基相互作用;与负电表面主要通过氨基相互作用;与正电表面主要通过羧基相互作用.通过模拟比较了多巴在不同自组装膜上的脱附力,发现多巴在带电表面的脱附力比在未带电表面的大,与黏附能的趋势一致.对比4种非带电表面的脱附力,发现多巴在疏水性甲基自组装膜表面的脱附力最大,黏附更稳定,随着表面疏水性的增加,脱附力增大,黏附稳定性增强.本工作可为研发新型水下胶黏剂提供理论指导.     

Adsorption and desorption processes of self-assembled monolayers studied by surface-sensitive microscopy and spectroscopy

Adsorption and desorption processes of self-assembled monolayers (SAMs) have been studied on an Au(111) surface by scanning tunnelling microscopy (STM), atomic force microscopy (AFM), X-ray photo-electron spectroscopy (XPS) and thermal desorption spectroscopy (TDS). At the initial growth stage, the ordered nucleation of SAM located at the herringbone turns of the Au(111) − (22 × √3) surface reconstruction and diffusion-controlled domain formation have been imaged by STM and AFM. Details of the oxidation process in UV desorption were also investigated by XPS. In addition, the dimerization reaction during desorption was confirmed by TDS for the first time in the alkanethiol SAM system.     

Molecular simulation of interaction between passivated gold nanoparticles in supercritical CO2

Molecular dynamics simulations have been performed to study the potential of mean force (PMF) between passivated gold nanoparticles (NPs) in supercritical CO(2) (scCO(2)). The nanoparticle model consists of a 140 atom gold nanocore and a surface self-assembled monolayer, in which two kinds of fluorinated alkanethiols were considered. The molecular origin of the thermodynamics interaction and the solvation effect has been comprehensively studied. The simulation results demonstrate that increasing the solvent density and ligand length can enhance the repulsive feature of the free energy between the passivated Au nanoparticles in scCO(2), which is in good agreement with previous experimental results. The interaction forces between the two passivated NPs have been decomposed to reveal various contributions to the free energy. It was revealed that the interaction between capping ligands and the interaction between the capping ligands and scCO(2) solvent molecules cooperatively determine the total PMF. A thermodynamic entropy-energy analysis for each PMF contribution was used to explain the density dependence of PMF in scCO(2) fluid. Our simulation study is expected to provide a novel microscopic understanding of the effect of scCO(2) solvent on the interaction between passivated Au nanoparticles, which is helpful to the dispersion and preparation of functional metal nanoparticles in supercritical fluids.     

A comparison of methods to compute the potential of mean force.

Most processes occurring in a system are determined by the relative free energy between two or more states because the free energy is a measure of the probability of finding the system in a given state. When the two states of interest are connected by a pathway, usually called reaction coordinate, along which the free-energy profile is determined, this profile or potential of mean force (PMF) will also yield the relative free energy of the two states. Twelve different methods to compute a PMF are reviewed and compared, with regard to their precision, for a system consisting of a pair of methane molecules in aqueous solution. We analyze all combinations of the type of sampling (unbiased, umbrella-biased or constraint-biased), how to compute free energies (from density of states or force averaging) and the type of coordinate system (internal or Cartesian) used for the PMF degree of freedom. The method of choice is constraint-bias simulation combined with force averaging for either an internal or a Cartesian PMF degree of freedom.     

On the mechanism of surfactant adsorption on solid surfaces: free-energy investigations

The adsorption free-energy of surfactant on solid surfaces has been calculated by molecular dynamics (MD) simulation for a model surfactant/solvent system. The umbrella-sampling with the weight histogram analysis method (WHAM) was applied. The entropic and enthalpic contributions to the full potential of mean force (PMF) were obtained to evaluate the detailed thermodynamics of surfactant adsorption in solid/liquid interfaces. Although we observed that this surfactant adsorption process is driven mainly by a favorable enthalpy change, a highly unfavorable entropic contribution still existed. By decomposing the free energy (including its entropic and enthalpic components) into the solvent-induced contribution and the surfactant-wall term, the effect of surface and solvent on the adsorption free-energy has been distinguished. The contribution to the PMF from the surface effect is thermodynamically favorable, whereas the solvent term displays an obviously unfavorable component with a monotonic increase as the surfactant approaches to the surface. The impact of various interactions from the surfaces (both solvent-philic and solvent-phobic) and the solvent on the adsorption PMF of surfactant has been compared and discussed. Compared to the solvent-philic surface, the solvent-phobic surface generates more stable site for the surfactant adsorption. However, the full PMF profile for the solvent-phobic system shows a clear positive maximum value at the bulk-interface transition region, which leads to a considerable long-range free-energy barrier to the surfactant adsorption. These results have been analyzed in terms of the local interfacial structures. In summary, this comprehensive study is expected to reveal the microscopic interaction mechanisms determining the surfactant adsorption on solid surfaces.     

Fabrication of surface energy/chemical gradients using self-assembled monolayer surfaces

Direct laser patterning of surface energy gradients for alkanethiols on gold has been demonstrated. A homogeneous 1-hexadecanethiol self-assembled monolayer (SAM) on gold (supported by a glass substrate) was selectively desorbed using a focused laser beam. By continually varying the incident laser intensity along a straight line scan, a gradient in desorption was produced. This desorption gradient was then backfilled with the second SAM (16-mercaptohexadecanoic acid), to produce a wettability gradient. The gradient in wettability was characterized by condensation imaging. Secondary ion mass spectroscopy was also used to show variation of the second SAM population from maximum to zero along the length, representative of the chemical gradient. The hexadecanethiol desorption was found to be the most sensitive in a laser intensity range of 29.15-6.5 kW/cm2. By considering the functional behavior of the governing equations, the theoretical trend for desorption as a function of laser intensity (represented by the out-of-focus distance) was determined. It was found to conform to the experimental data. The proposed method is fast, simple, noncontact, and flexible in terms of producing different types of gradients.     

Soft- and reactive-landing of Cr(aniline)2 sandwich complexes onto self-assembled monolayers: separation between functional and binding sites

Soft- and reactive-landing of gas-phase synthesized cationic Cr(aniline)(2) complexes onto self-assembled monolayers of methyl-terminated (CH(3)-SAM) and carboxyl-terminated (COOH-SAM) organothiolates coated on gold were performed at hyperthermal collision energy (5-20 eV). The properties of the Cr(aniline)(2) complexes on the SAM surfaces were characterized using infrared reflection absorption spectroscopy (IRAS) and temperature-programmed desorption (TPD), together with theoretical calculations based on density functional theory (DFT). For the CH(3)-SAM, the Cr(aniline)(2) complexes were embedded inside the SAM matrix in a neutral charge state, keeping a sandwich structure. For the COOH-SAM, the IRAS and TPD study revealed that the amine-containing Cr(aniline)(2) complexes were bound to the SAM surface in two forms of physisorption and chemical linking through an amide bond. In the desorption, the latter form appeared as the reaction product between organothiolates and Cr(aniline)(2) above 400 K, where the organothiolate molecules, forming the SAM, were desorbed from the gold surface. The results show that the hyperthermal depositions onto a COOH-SAM bring about reactive-landing followed by covalent linking of an amide bond between the amine-containing Cr(aniline)(2) complexes to the carboxyl-terminated SAM surface, in which the binding sites can be separated from the functional sites of the d-π interaction.     

Comparative analysis of nucleotide translocation through protein nanopores using steered molecular dynamics and an adaptive biasing force

The translocation of nucleotide molecules across biological and synthetic nanopores has attracted attention as a next generation technique for sequencing DNA. Computer simulations have the ability to provide atomistic‐level insight into important states and processes, delivering a means to develop a fundamental understanding of the translocation event, for example, by extracting the free energy of the process. Even with current supercomputing facilities, the simulation of many‐atom systems in fine detail is limited to shorter timescales than the real events they attempt to recreate. This imposes the need for enhanced simulation techniques that expand the scope of investigation in a given timeframe. There are numerous free energy calculation and translocation methodologies available, and it is by no means clear which method is best applied to a particular problem. This article explores the use of two popular free energy calculation methodologies in a nucleotide‐nanopore translocation system, using the α‐hemolysin nanopore. The first uses constant velocity‐steered molecular dynamics (cv‐SMD) in conjunction with Jarzynski's equality. The second applies an adaptive biasing force (ABF), which has not previously been applied to the nucleotide‐nanpore system. The purpose of this study is to provide a comprehensive comparison of these methodologies, allowing for a detailed comparative assessment of the scientific merits, the computational cost, and the statistical quality of the data obtained from each technique. We find that the ABF method produces results that are closer to experimental measurements than those from cv‐SMD, whereas the net errors are smaller for the same computational cost. © 2014 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Investigation of Binding Affinity Between Prokaryotic Proteins (AHU-IHF) and DNAs: Steered Molecular Dynamics Approach

The aim of this work is to investigate the binding affinity between the prokaryotic proteins—AHU-IHF proteins (AHU (AHU2, TR3, and AHU6) and IHF (IHF-WT and IHF-βE44A))—and DNAs (DNA, H′-DNA, and H′44A-DNA) by using the steered molecular dynamics (SMD) simulation and the molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method. The gained results show that although the fluctuation of the pulling force yielded the change of the pulling work, the higher pulling work of the AHU/DNA complexes in comparison to those of the IHF/DNA complexes is not only dependent on the pulling force but also controlled by the change of the trajectory in SMD simulation process. In this study, the pulling work profile not only described the pulling pathway of the complexes but also reflected the hindered process of DNAs when AHU-IHF proteins come out from the binding pocket of DNAs. Additionally, the binding free energy (estimated by the MM-PBSA method) is more confident in giving a true effect to the experimental results in comparison to the pulling force and the pulling work values. These results have also shown a fact that the AHU/DNA complexes were more stable than the IHF/DNA complexes.     

Calculating potentials of mean force and diffusion coefficients from nonequilibrium processes without Jarzynski's equality

In general, the direct application of the Jarzynski equality (JE) to reconstruct potentials of mean force (PMFs) from a small number of nonequilibrium unidirectional steered molecular-dynamics (SMD) paths is hindered by the lack of sampling of extremely rare paths with negative dissipative work. Such trajectories that transiently violate the second law of thermodynamics are crucial for the validity of JE. As a solution to this daunting problem, we propose a simple and efficient method, referred to as the FR method, for calculating simultaneously both the PMF U(z) and the corresponding diffusion coefficient D(z) along a reaction coordinate z for a classical many-particle system by employing a small number of fast SMD pullings in both forward (F) and time reverse (R) directions, without invoking JE. By employing Crooks [Phys. Rev. E 61, 2361 (2000)] transient fluctuation theorem (that is more general than JE) and the stiff-spring approximation, we show that (i) the mean dissipative work W(d) in the F and R pullings is the same, (ii) both U(z) and W(d) can be expressed in terms of the easily calculable mean work of the F and R processes, and (iii) D(z) can be expressed in terms of the slope of W(d). To test its viability, the FR method is applied to determine U(z) and D(z) of single-file water molecules in single-walled carbon nanotubes (SWNTs). The obtained U(z) is found to be in very good agreement with the results from other PMF calculation methods, e.g., umbrella sampling. Finally, U(z) and D(z) are used as input in a stochastic model, based on the Fokker-Planck equation, for describing water transport through SWNTs on a mesoscopic time scale that in general is inaccessible to MD simulations.     

Self-assembling cyclic peptides: molecular dynamics studies of dimers in polar and nonpolar solvents

The self-assembly of cyclic D,L-alpha-peptides into hollow nanotubes is a crucial mechanistic step in their application as antibacterial and drug-delivery agents. To understand this process, molecular dynamics (MD) simulations were performed on dimers of cyclic peptides formed from cyclo [(-L-Trp-D-N-MeLeu-)4-]2 and cyclo [(-L-Trp-D-Leu-)4-]2 subunits in nonpolar (nonane) and polar (water) solvent. The dimers were observed to be stable only in nonpolar solvent over the full 10 ns length of the MD trajectory. The behavior of the dimers in different solvents is rationalized in terms of the intersubunit hydrogen bonding, hydrogen bonding with the solvent, and planarity of the rings. It is shown that the phi and psi dihedral angles of a single uncapped ring in nonane lie in the beta-sheet region of the Ramachandran plot, and the ring stays in a flat conformation. Steered MD (SMD) simulations based on Jarzynski's equality were performed to obtain the potential of mean force as a function of the distance between the two rings of the capped dimer in nonane. It is also shown that a single peptide subunit prefers to reside close to the nonane/water interface rather than in bulk solvent because of the amphiphilic character of the peptide ring. The present MD results build the foundation for using MD simulations to study the mechanism of the formation of cyclic peptide nanotubes in lipid bilayers.     

Playing with peptides: how to build a supramolecular peptide nanostructure by exploiting helix···helix macrodipole interactions

A novel method to build bicomponent peptide self-assembled monolayers (SAMs) has been developed, by exploiting helix···helix macrodipole interactions. In this work, a peptide-based self-assembled monolayer composed of two helical peptides was immobilized on a gold surface. Specifically, a pyrene-containing octapeptide, devoid of any sulfur atom (A8Pyr), and a hexapeptide, functionalized at the N-terminus with (S,R) lipoic acid, for binding to gold substrates (SSA4WA) via a Au-S linkage, have been employed. Both peptides investigated attain a helical structure, because they are almost exclusively formed by strongly folding inducer C(α)-tetrasubstituted α-amino acids. We demonstrate that the two peptides generate a stable supramolecular nanostructure (a densely packed bicomponent peptide monolayer), where A8Pyr is incorporated into the SSA4WA palisade by exploiting helix···helix macrodipole interactions. The presence of both peptides on the gold surface was investigated by spectroscopic and electrochemical techniques, while the morphology of the monolayer was analyzed by ultra high-vacuum scanning tunnelling microscopy. The composition of the bicomponent SAM on the surface was studied by a combination of electrochemical and spectroscopic techniques. In particular, the amount of Au-S linkages from the sulfur-containing peptides was quantified from reductive desorption of the peptide-based SAM, while the amount of A8Pyr was estimated by fluorescence spectroscopy. The antiparallel orientation of the A8Pyr and SSA4WA peptide chains minimizes the interaction energy between the helix dipoles, suggesting that this kind of electrostatic phenomenon is the driving force that stabilizes the bicomponent SAM.