Multivalent dendrimers at molecular printboards: influence of dendrimer structure on binding strength and stoichiometry and their electrochemically induced desorption

A fundamental understanding of multivalency can have a profound influence on bottom-up nanofabrication. For this purpose, three different types of ferrocenyl (Fc) functionalized dendrimers of generations 1-5 with various spacer groups were adsorbed at self-assembled monolayers (SAMs) of heptathioether-functionalized beta-cyclodextrin (betaCD) on gold. The dendrimers formed kinetically stable supramolecular assemblies at the betaCD host surface having up to eight multivalent supramolecular interactions, but could be efficiently removed from the host surface by electrochemical oxidation of the Fc end groups. Dendrimer desorption and re-adsorption could be repeated a number of times without significant decomposition of the system. The stoichiometries of the dendrimers at the surface were determined using cyclic voltammetry (CV). These were quantitatively confirmed for the lower generations by surface plasmon resonance (SPR) titrations of the dendrimers to the betaCD SAM. Measuring CV and SPR simultaneously gave crucial mechanistic information on the electrochemically induced desorption of the dendrimers from the host surface. The redox-active dendrimers effectively blocked the host surface for binding other molecules, e.g. adamantyl-functionalized dendrimers, but electrochemically induced release of the blocking layer revealed the host surface to which the adamantyl dendrimers could then bind.     

Modeling competitive guest binding to beta-cyclodextrin molecular printboards

Anchoring of functionalized guest molecules to self-assembled monolayers (SAMs) is key to the development of molecular printboards for nanopatterning. One very promising system involves guest binding to immobilized beta-cyclodextrin (beta-CD) hosts, with guest:host recognition facilitated by a hydrophobic interaction between uncharged anchor groups on the guest molecule and beta-CD hosts self-assembled at gold surfaces. We use molecular dynamics free energy (MDFE) simulations to describe the specificity of guest:beta-CD association. We find good agreement with experimental thermodynamic measurements for binding enthalpy differences between three commonly used phenyl guests: benzene, toluene, and t-butylbenzene. van der Waals interaction with the inside of the host cavity accounts for almost all of the net stabilization of the larger phenyl guests in beta-CD. Partial and full methylation of the secondary rim of beta-CD decreases host rigidity and significantly impairs binding of both phenyl and larger adamantane guest molecules. The beta-CD cavity is also very intolerant of guest charging, penalizing the oxidized state of ferrocene by at least 7 kcal/mol. beta-CD hence expresses moderate specificity toward uncharged organic guest molecules by van der Waals recognition, with a much higher specificity calculated for electrostatic recognition of organometallic guests.     

Multivalent binding of small guest molecules and proteins to molecular printboards inside microchannels

Beta-Cyclodextrin (beta-CD) monolayers have been immobilized in microchannels. The host-guest interactions on the beta-CD monolayers inside the channels were comparable to the interactions on beta-CD monolayers on planar surfaces, and a divalent fluorescent guest attached with a comparable binding strength. Proteins were attached to these monolayers inside microchannels in a selective manner by employing a strategy that uses streptavidin and orthogonal linker molecules. The design of the chip, which involved a large channel that splits into four smaller channels, allowed the channels to be addressed separately and led to the selective immobilization of antibodies. Experiments with labeled antibodies showed the selective immobilization of these antibodies in the separate channels.     

In silico engineering of tailored ink-binding ability at molecular printboards.

Molecular recognition between guest ink molecules and beta-cyclodextrin (beta-CD) cavities at self-assembled monolayers provides a molecular printboard for nanopatterning applications. We recently used molecular dynamics (MD) simulations to describe the specificity of ink-printboard binding and here extend the simulations to include charged cyclodextrin hosts, necessary to broaden the chemistry of molecular printboards and bind charged inks such as the ferrocenium cation. Shifting to high pH, or alternatively grafting a charged sidearm onto beta-CD, created three distinct types of anionic beta-CD cavity and we used electronic structure calculations and MD simulations to measure host-guest charge transfer and binding strengths. We find that steric recognition of uncharged organic molecules is retained at the charged printboards, and that improved guest-host electrostatic contacts can strengthen binding of larger inks while penalising small inks, enhancing the level of discrimination. A prudent choice of complementary host-guest shape and charge states thus provides a means of tuning both ink binding strength and specificity at molecular printboards.     

Free energy perturbation and molecular dynamics calculations of copper binding to azurin

Free energy perturbation/molecular dynamics simulations have been carried out on copper/azurin systems calculating the binding affinities of copper (II) ion to azurin either in the native or in the unfolded state. In order to test the validity of the strategy adopted for the calculations and to establish what force field is suitable for these kinds of calculations, three different force fields, AMBER, CVFF, and CFF, have been alternatively used for the calculations and the results have been compared with experimental data obtained by spectroscopic titrations of copper (II)/azurin solutions and denaturation experiments. Our findings have pointed out that only CFF gives satisfactory results, thus providing a reliable tool for copper binding simulations in copper protein.     

Controlling the supramolecular assembly of redox-active dendrimers at molecular printboards by scanning electrochemical microscopy

Redox-active ferrocenyl (Fc)-functionalized poly(propylenimine) (PPI) dendrimers solubilized in aqueous media by complexation of the Fc end groups with beta-cyclodextrin (betaCD) were immobilized at monolayers of betaCD on glass ("molecular printboards") via multiple host-guest interactions. The directed immobilization of the third-generation dendrimer-betaCD assembly G3-PPI-(Fc)16-(betaCD)16 at the printboard was achieved by supramolecular microcontact printing. The redox activity of the patterned dendrimers was mapped by scanning electrochemical microscopy (SECM) in the positive feedback mode using [IrCl(6)](3-) as a mediator. Local oxidation of the Fc-dendrimers by the microelectrode-generated [IrCl(6)](2-) resulted in an effective removal of the Fc-dendrimers from the host surface since the oxidation of Fc to the oxidized form (Fc+) leads to a concomitant loss of affinity for betaCD. Thus, SECM provided a way not only to image the surface, but also to control the binding of the Fc-terminated dendrimers at the molecular printboard. Additionally, the electrochemical desorption process could be monitored in time as the dendrimer patterns were gradually erased upon multiple scans.     

Free energy perturbation simulations of cation binding to valinomycin

Experimental values of the free energies of cation binding to the cyclic depsipeptide molecule, valinomycin, obtained from Pedersen-type salt extraction measurements, provide data against which it is possible to test the adequacy of the procedures and force fields of the molecular dynamics algorithms, MOLARIS and GROMOS. These data are then used to assess appropriate values for the partial charges of the ester carbonyl oxygen and carbon. Valinomycin was chosen because it has only one kind of ion-binding ligand and because the cation is sufficiently enfolded by the molecule in the ion-complexes that the overall size and shape of the complex is virtually the same regardless of the species of cation bound. For such an isosteric complex, the experimentally measured selectivities are sufficiently similar in a wide variety of solvent environments that thedifferences in free energies measured between the different ion-valinomycin complexes by two-phase salt extraction experiments into dichloromethane can be taken as equivalent to the differences in free energies in vacuo. Thesedifferences were therefore compared with those computed for ion-valinomycin complexationin vacuo by Free Energy Perturbation/Molecular Dynamics (FEP/MD) simulations using the MOLARIS and GROMOS programs. Starting with a set of Lennard-Jones 6–12 parameters for the monovalent cations assessed for aqueous solution we explored the effect of varying the partial charges of the ester carbonyl ligands on binding free energy differences (i.e. the selectivity) among Na, K, Rb, and Cs. The computed selectivity was found to depend strongly on the value of partial charge, following a typical Eisenman Selectivity Pattern in which the correct selectivity sequence and magnitude occurred only over a very narrow range of partial charge (around 0.33 and 0.6 for the standard carbonyls of MOLARIS and GROMOS, respectively). Using MOLARIS we explored the effect of varying the size of the ester carbonyl ligands by comparing the standard carbonyl of MOLARIS with the somewhat smaller carbonyls of GROMOS and found an equally satisfactory ability to reproduce the experimental data with a partial charge value of 0.41. These results validate the use of both the MOLARIS and GROMOS force fields as starting points for quantitative calculations of ion-binding in more complex molecules (e.g., ion-binding sites and channels in proteins).This paper is dedicated to the memory of the late Dr C. J. Pedersen.     

Free energy of a trans-membrane pore calculated from atomistic molecular dynamics simulations

Atomistic molecular dynamics simulations of a lipid bilayer were performed to calculate the free energy of a trans-membrane pore as a function of its radius. The free energy was calculated as a function of a reaction coordinate using a potential of mean constraint force. The pore radius was then calculated from the reaction coordinate using Monte Carlo particle insertions. The main characteristics of the free energy that comes out of the simulations are a quadratic shape for a radius less than about 0.3 nm, a linear shape for larger radii than this, and a rather abrupt change without local minima or maxima between the two regions. In the outer region, a line tension can be calculated, which is consistent with the experimentally measured values. Further, this line tension can be rationalized and understood in terms of the energetic cost for deforming a part of the lipid bilayer into a hydrophilic pore. The region with small radii can be described and understood in terms of statistical mechanics of density fluctuations. In the region of crossover between a quadratic and linear free energy there was some hysteresis associated with filling and evacuation of the pore with water. The metastable prepore state hypothesized to interpret the experiments was not observed in this region.     

Free energy calculations using flexible-constrained, hard-constrained and non-constrained molecular dynamics simulations.

A comparison of different treatments of bond-stretching interactions in molecular dynamics simulation is presented. Relative free energies from simulations using rigid bonds maintained with the SHAKE algorithm, using partially rigid bonds maintained with a recently introduced flexible constraints algorithm, and using fully flexible bonds are compared in a multi-configurational thermodynamic integration calculation of changing liquid water into liquid methanol. The formula for the free energy change due to a changing flexible constraint in a flexible constraint simulation is derived. To allow for a more direct comparison between these three methods, three different pairs of models for water and methanol were used: a flexible model (simulated without constraints and with flexible constraints), a rigid model (simulated with standard hard constraints), and an alternative flexible model (simulated with flexible constraints and standard hard constraints) in which the ideal or constrained bond lengths correspond to the average bond lengths obtained from a short simulation of the unconstrained flexible model. The particular treatment of the bonds induces differences of up to 2 % in the liquid densities, whereas (excess) free energy differences of up to 5.7 (4.3) kJ mol(-1) are observed. These values are smaller than the differences observed between the three different pairs of methanol/water models: up to 5 % in density and up to 8.5 kJ mol(-1) in (excess) free energy.     

Parallelized-over-parts computation of absolute binding free energy with docking and molecular dynamics

We present a technique for biomolecular free energy calculations that exploits highly parallelized sampling to significantly reduce the time to results. The technique combines free energies for multiple, nonoverlapping configurational macrostates and is naturally suited to distributed computing. We describe a methodology that uses this technique with docking, molecular dynamics, and free energy perturbation to compute absolute free energies of binding quickly compared to previous methods. The method does not require a priori knowledge of the binding pose as long as the docking technique used can generate reasonable binding modes. We demonstrate the method on the protein FKBP12 and eight of its inhibitors.     

Free volume hypothetical scanning molecular dynamics method for the absolute free energy of liquids

The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy, S, and free energy, F, by analyzing Boltzmann samples obtained by Monte Carlo (MC) or molecular dynamics (MD) techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by gradually placing the molecules in their positions at i using transition probabilities (TPs). With our recent version of HS, called HSMC-EV, each TP is calculated from MC simulations, where the simulated particles are excluded from the volume reconstructed in previous steps. In this paper we remove the excluded volume (EV) restriction, replacing it by a "free volume" (FV) approach. For liquid argon, HSMC-FV leads to an improvement in efficiency over HSMC-EV by a factor of 2-3. Importantly, the FV treatment greatly simplifies the HS implementation for liquids, allowing a much more natural application of the method for MD simulations. Given the success and popularity of MD, the present development of the HSMD method for liquids is an important advancement for HS methodology. Results for the HSMD-FV approach presented here agree well with our HSMC and thermodynamic integration results. The efficiency of HSMD-FV is equivalent to HSMC-EV. The potential use of HSMC(MD)-FV in protein systems with explicit water is discussed.     

Free energy of transfer ofn-nitroalkanes fromn-octane to water at 25°C

Calorimetric determinations of the thermodynamics of transfer of nitromethane, nitroethane, 1-nitrobutane, 1-nitropentane, and 1-nitrohexane from n-octane to water at 25°C have been made. Transfer free energies calculated by four different models agree reasonably well with observations. Calculations indicate that the dipolar part of the transfer free energy depends only on the dipole moment and size of the-C?NO₂ group and is independent of the length of the alkyl chain in nitroalkanes.     

Free energy calculations on the two drug binding sites in the M2 proton channel

Two alternative binding sites of adamantane-type drugs in the influenza A M2 channel have been suggested, one with the drug binding inside the channel pore and the other with four drug molecule S-binding to the C-terminal surface of the transmembrane domain. Recent computational and experimental studies have suggested that the pore binding site is more energetically favorable but the external surface binding site may also exist. Nonetheless, which drug binding site leads to channel inhibition in vivo and how drug-resistant mutations affect these sites are not completely understood. We applied molecular dynamics simulations and potential of mean force calculations to examine the structures and the free energies associated with these putative drug binding sites in an M2-lipid bilayer system. We found that, at biological pH (~7.4), the pore binding site is more thermodynamically favorable than the surface binding site by ~7 kcal/mol and, hence, would lead to more stable drug binding and channel inhibition. This result is in excellent agreement with several recent studies. More importantly, a novel finding of ours is that binding to the channel pore requires overcoming a much higher energy barrier of ~10 kcal/mol than binding to the C-terminal channel surface, indicating that the latter site is more kinetically favorable. Our study is the first computational work that provides both kinetic and thermodynamic energy information on these drug binding sites. Our results provide a theoretical framework to interpret and reconcile existing and often conflicting results regarding these two binding sites, thus helping to expand our understanding of M2-drug binding, and may help guide the design and screening of novel drugs to combat the virus.     

Free energy of binding of a small molecule to an amorphous polymer in a solvent

Crystallization is a commonly used purification process in industrial practice. It usually begins with heterogeneous nucleation on a foreign surface. The complicated mechanism of heterogeneous nucleation is not well understood, but we hypothesize that a possible correlation between binding affinity to a surface and nucleation enhancement might exist. Amorphous polymers have been used in controlling crystallization. However, to our knowledge, no attempt has been made to calculate the free energy of binding of a small molecule to an amorphous polymer in a solvent, and to characterize the binding sites/conformations of this system at a molecular level. We developed a two-step approach, first using Adsorption Locator to identify probable binding sites and molecular dynamics to screen for the best binding sites and then using the Blue-Moon Ensemble method to compute the free energy of binding. A system of ethylene glycol, polyvinyl alcohol (PVA), and heavy water (D(2)O) was used for validation, since experimental data exists on a related system. Looking at four independently constructed surfaces, we found that ethylene glycol binds to an indentation on the surface or in a hole beneath the surface. We focused on the indentation binding sites because they are easily accessible and do not have large free energy barriers. The closest system for which experimental data on binding energetics exists is ethylene glycol on PVA in aqueous solutions/gels, and the magnitudes of the free energy of binding to the three best indentation binding sites are close to the experimental value, 0.4-3.7 kcal/mol higher. Our approach offers a way to compute the free energy of binding and characterize the binding sites/conformations, and is general enough to apply to other small molecule/amorphous polymer/solvent systems.     

Free energy of solvation from molecular dynamics simulation applying Voronoi-Delaunay triangulation to the cavity creation

The free energy of solvation for a large number of representative solutes in various solvents has been calculated from the polarizable continuum model coupled to molecular dynamics computer simulation. A new algorithm based on the Voronoi-Delaunay triangulation of atom-atom contact points between the solute and the solvent molecules is presented for the estimation of the solvent-accessible surface surrounding the solute. The volume of the inscribed cavity is used to rescale the cavitational contribution to the solvation free energy for each atom of the solute atom within scaled particle theory. The computation of the electrostatic free energy of solvation is performed using the Voronoi-Delaunay surface around the solute as the boundary for the polarizable continuum model. Additional short-range contributions to the solvation free energy are included directly from the solute-solvent force field for the van der Waals-type interactions. Calculated solvation free energies for neutral molecules dissolved in benzene, water, CCl4, and octanol are compared with experimental data. We found an excellent correlation between the experimental and computed free energies of solvation for all the solvents. In addition, the employed algorithm for the cavity creation by Voronoi-Delaunay triangulation is compared with the GEPOL algorithm and is shown to predict more accurate free energies of solvation, especially in solvents composed by molecules with nonspherical molecular shapes.     

Poly(amidoamine) dendrimers on lipid bilayers I: Free energy and conformation of binding

Third-generation (G3) poly(amidoamine) (PAMAM) dendrimers are simulated approaching 1,2-dimyristoyl- sn-glycero-3-phosphocholine (DMPC) bilayers with fully atomistic molecular dynamics, which enables the calculation of a free energy profile along the approach coordinate. Three different dendrimer terminations are examined: protonated primary amine, uncharged acetamide, and deprotonated carboxylic acid. As the dendrimer and lipids become closer, their attractive force increases (up to 240 pN) and the dendrimer becomes deformed as it interacts with the lipids. The total energy release upon binding of a G3-NH3+, G3-Ac, or G3-COO- dendrimer to a DMPC bilayer is, respectively, 36, 26, or 47 kcal/mol or, equivalently, 5.2, 3.2, or 4.7x10(-3) kcal/g. These results are analyzed in terms of the dendrimers' size, shape, and atomic distributions as well as proximity of individual lipid molecules and particular lipid atoms to the dendrimer. For example, an area of 9.6, 8.2, or 7.9 nm2 is covered on the bilayer for the G3-NH3+, G3-Ac, or G3-COO- dendrimers, respectively, while interacting strongly with 18-13 individual lipid molecules.     

Computation of binding free energy with molecular dynamics and grand canonical Monte Carlo simulations

The binding of a ligand to a receptor is often associated with the displacement of a number of bound water molecules. When the binding site is exposed to the bulk region, this process may be sampled adequately by standard unbiased molecular dynamics trajectories. However, when the binding site is deeply buried and the exchange of water molecules with the bulk region may be difficult to sample, the convergence and accuracy in free energy perturbation (FEP) calculations can be severely compromised. These problems are further compounded when a reduced system including only the region surrounding the binding site is simulated. To address these issues, we couple molecular dynamics (MD) with grand canonical Monte Carlo (GCMC) simulations to allow the number of water to fluctuate during an alchemical FEP calculation. The atoms in a spherical inner region around the binding pocket are treated explicitly while the influence of the outer region is approximated using the generalized solvent boundary potential (GSBP). At each step during thermodynamic integration, the number of water in the inner region is equilibrated with GCMC and energy data generated with MD is collected. Free energy calculations on camphor binding to a deeply buried pocket in cytochrome P450cam, which causes about seven water molecules to be expelled, are used to test the method. It concluded that solvation free energy calculations with the GCMC/MD method can greatly improve the accuracy of the computed binding free energy compared to simulations with fixed number of water.     

Free energy calculations on the binding of colchicine and its derivatives with the alpha/beta-tubulin isoforms

Tubulin is the target for numerous small molecule ligands which alter microtubule dynamics leading to cell cycle arrest and apoptosis. Many of these ligands are currently used clinically for the treatment of several types of cancer, and they bind to one of three distinct binding sites within beta-tubulin (paclitaxel, vinca, and colchicine), all of which have been identified crystallographically. Unfortunately, serious side effects always accompany chemotherapy since these drugs bind to tubulin indiscriminately, leading to the death of both cancerous and healthy cells. However, the existence and distribution of divergent tubulin isoforms provide a platform upon which we may build novel chemotherapeutic drugs that can differentiate between different cell types and therefore reduce undesirable side effects. We report results of computational analysis that aims at predicting differences between the binding energies of a family of colchicine derivatives against 10 human alpha/beta-tubulin isoforms. Free energy perturbation method has been used in our calculations and the results provide a proof of principle by indicating significant differences both among the derivatives and between tubulin isoforms.     

Determination of binding energy and solubility parameters for functionalized gold nanoparticles by molecular dynamics simulation

The binding energy, density, and solubility of functionalized gold nanoparticles in a vacuum are computed using molecular dynamics simulations. Numerous parameters including surface coverage fraction, functional group (-CH(3), -OH, -NH(2)), and nanoparticle orientation are considered. The analysis includes computation of minimum interparticle binding distances and energies and an analysis of mechanisms that may contribute to changes in system potential energy. A number of interesting trends and results are observed, such as increasing binding distance with higher terminal group electronegativity and a minimum particle-particle binding energy (solubility parameter) based upon surface coverage. These results provide a fundamental understanding of ligand-coated nanoparticle interactions required for the design and processing of high-density polymer composites. The computational model and results are presented as support for these conclusions.