Structure and thermodynamics of protein-polymer solutions: effects of spatially distributed hydrophobic surface residues

Protein-polymer association in solution driven by a short-range attraction has been investigated using a simple coarse-grain model solved by Monte Carlo simulations. The effect of the spatial distribution of the hydrophobic surface residues of the protein on the adsorption of weakly hydrophobic polymers at variable polymer concentration, polymer length, and polymer stiffness has been considered. Structural data on the adsorbed polymer layer and thermodynamic properties, such as the free energy, energy, and entropy, related to the protein-polymer interaction were calculated. It was found that a more heterogeneous distribution of the surface residues promotes adsorption and that this also applies for different polymer concentrations, polymer chain lengths, and polymer flexibilities. Furthermore, the polymer adsorption onto proteins with more homogeneous surface distributions displayed larger sensitivity to polymer properties such as chain length and flexibility. Finally, a simple relation between the adsorption probability and the change in the free energy was found and rationalized by a simple two-state adsorption model.     

Macroscopic simulations of microtubule dynamics predict two steady-state processes governing array morphology

Microtubule polymers typically function through their collective organization into a patterned array. The formation of the pattern, whether it is a relatively simple astral array or a highly complex mitotic spindle, relies on controlled microtubule nucleation and the basal dynamics parameters governing polymer growth and shortening. We have investigated the interaction between the microtubule nucleation and dynamics parameters, using macroscopic Monte Carlo simulations, to determine how these parameters contribute to the underlying microtubule array morphology (i.e. polymer density and length distribution). In addition to the well-characterized steady state achieved between free tubulin subunits and microtubule polymer, we propose that microtubule nucleation and extinction constitute a second, interdependent steady state process. Our simulation studies show that the magnitude of both nucleation and extinction additively impacts the final steady state free subunit concentration. We systematically varied individual microtubule dynamics parameters to survey the effects on array morphology and find specific sensitivity to perturbations of catastrophe frequency. Altering the cellular context for the microtubule array, we find that nucleation template number plays a defining role in shaping the microtubule length distribution and polymer density.     

Unexpected relaxation dynamics of a self-avoiding polymer in cylindrical confinement

We report extensive simulations of the relaxation dynamics of a self-avoiding polymer confined inside a cylindrical pore. In particular, we concentrate on examining how confinement influences the scaling behavior of the global relaxation time of the chain, tau, with the chain length N and pore diameter D. An earlier scaling analysis based on the de Gennes blob picture led to tau approximately N(2)D(13). Our numerical effort that combines molecular dynamics and Monte Carlo simulations, however, consistently produces different tau results for N up to 2000. We argue that the previous scaling prediction is only asymptotically valid in the limit N"D(53)"1, which is currently inaccessible to computer simulations and, more interestingly, is also difficult to reach in experiments. Our results are thus relevant for the interpretation of recent experiments with DNA in nano- and microchannels.     

Confinement of transmembrane cell receptors in tunable stripe micropatterns

We report a simple method to confine transmembrane cell receptors in stripe micropatterns of a lipid/lipopolymer monolayer, which are formed as result of the transfer onto a solid substrate. The stripes are aligned perpendicular to the meniscus, whose periodicity can systematically be tuned by the transfer velocity. This strongly suggests the dominant role of the cooperative interaction between the film and substrate. Selective fluorescence labeling of lipids and lipopolymers confirms that the observed patterns coincide with the demixing of two species. Covalent coupling of polymer headgroups enables us to use the stripe patterns as a support for a lipid bilayer membrane. Spreading of lipid vesicles with platelet integrin alphaIIbbeta3 on a self-assembled membrane micropattern demonstrates that cell adhesion receptors are selectively incorporated into the lipopolymer-rich region. The method established here provides us with a tunable template for the confinement of receptor proteins to geometrically control the cell adhesion.     

Influence of surface chemical heterogeneities on adsorption/desorption hysteresis and coexistence diagram of metastable states within cylindrical pores

Grand canonical Monte Carlo simulations are performed to determine the adsorption/desorption isotherms at different temperatures of a Lennard-Jones fluid confined within a simple model of cylindrical pores presenting chemical heterogeneities. A complex hysteresis loop is observed, showing hysteresis subloops (scanning curves). This is shown to be consistent with the existence of several metastable states (local minima in the system free energy). A recent extension to the Gibbs ensemble technique is then used to calculate the complete coexistence diagram of these local minima.     

Monte Carlo Calculations of Polymer Adsorption at the Entrance of Cylindrical Pores in Flat Adsorbing Surfaces

The influence of surface interactions on the conformation of flexible polymers partially confined inside narrow cylindrical pores in a flat surface is studied above the critical adsorption energy in a good solvent. We use a static configurational bias computational sampling method to calculate the adsorption free energy and the radius of gyration components parallel and perpendicular to the pore axis as a function of the polymer center of mass position at different degrees of confinement. We find strong free‐energy minima just in front of the pore entry for all degrees of confinement studied. At the location of the free‐energy minimum, polymers are partially adsorbed inside the pore and on the outer solid surface and adopt “drawing pin”‐like conformations. A distinct maximum in the average loop length at the pore entry indicates that the polymer bridges the pore entry of small pores.     

Controlling drop size and polydispersity using chemically patterned surfaces

We explore numerically the feasibility of using chemical patterning to control the size and polydispersity of micrometer-scale drops. The simulations suggest that it is possible to sort drops by size or wetting properties by using an array of hydrophilic stripes of different widths. We also demonstrate that monodisperse drops can be generated by exploiting the pinning of a drop on a hydrophilic stripe. Our results follow from using a lattice Boltzmann algorithm to solve the hydrodynamic equations of motion of the drops and demonstrate the applicability of this approach as a design tool for micofluidic devices with chemically patterned surfaces.     

Polymer brushes on periodically nanopatterned surfaces

Structural properties of polymer brushes tethered on a periodically nanopatterned substrate are investigated by computer simulations. The substrate consists of an alternating succession of two different types of equal-width parallel stripes, and the polymers are end-tethered selectively on every second stripe. Three distinct morphologies of the nanopatterned brush have been identified, and their range of stability has been determined in terms of a single universal parameter that combines the grafting density, the polymer length, and the stripe width. We propose scaling relations for the average brush height and for the architectural properties of the outer surface of the nanopatterned brush under good solvent conditions. Our analysis provides guidelines for fabricating well-defined and tunable nanopatterned polymeric films.     

Adsorption of diblock copolymers on stripe-patterned surfaces

We present the results of extensive Monte Carlo simulations of diblock copolymers adsorbed on stripe-patterned surfaces of various widths. We have found that the width of the stripe pattern is an important parameter which dictates favorable recognition on the surface. For certain stripe widths, the adsorption of diblock copolymers to striped surfaces exhibits two transitions. The process involves recognition of the surface pattern by the diblock copolymer which follows a two step process in which the first block getting adsorbed to the appropriate pattern on the surface, without any recognition of the surface pattern, followed by the adsorption of the second block, where a reorganization process happens. For small widths and also for higher widths, the chain behaves just like a homopolymer where the twofold adsorbing process changes to the typical homopolymer adsorption. We have also found that there exists an optimal width of the stripes, independent of the chain length, where the recognition on the surface pattern is most favored. The characteristic temperature of the adsorption of the second block with weaker interactions is found to be independent of the chain length at this optimal width, proving that only local rearrangements take place after the first step. Some of our results describing the thermodynamics compare very well with the recent semianalytical approach of Kriksin et al. [J. Chem. Phys. 122, 114703 (2005)] on multiblock copolymers on heterogeneous surfaces. We also present some interesting conformational properties of the copolymer chain near the stripe-patterned surface.     

Curvature effects upon interactions of polymer-grafted nanoparticles in chemically identical polymer matrices

We study the interactions between polymer-grafted nanoparticles immersed in a chemically identical polymer melt using a numerical implementation of polymer mean-field theory. We focus on the interpenetration width between the grafted and free chains and its relationship to the polymer-mediated interparticle interactions. To this end, we quantify the interpenetration width as a function of particle curvature, grafting density, and the relative molecular weights of the grafted and free chains. We show the onset of wetting and dewetting as a function of these quantities and explain our results through simple scaling arguments to include the effects of curvature. Subsequently, we show that the interparticle potentials correlate quantitatively with the trends displayed by the interpenetration widths.     

Modeling contact angle hysteresis on chemically patterned and superhydrophobic surfaces

We investigate contact angle hysteresis on chemically patterned and superhydrophobic surfaces, as the drop volume is quasistatically increased and decreased. We consider both two (cylindrical drops) and three (spherical drops) dimensions using analytical and numerical approaches to minimize the free energy of the drop. In two dimensions, we find, in agreement with other authors, a slip, jump, stick motion of the contact line. In three dimensions, this behavior persists, but the position and magnitude of the contact line jumps are sensitive to the details of the surface patterning. In two dimensions, we identify analytically the advancing and receding contact angles on the different surfaces, and we use numerical insights to argue that these provide bounds for the three-dimensional cases. We present explicit simulations to show that a simple average over the disorder is not sufficient to predict the details of the contact angle hysteresis and to support an explanation for the low contact angle hysteresis of suspended drops on superhydrophobic surfaces.     

Simulation study on the translocation of a partially charged polymer through a nanopore

The translocation of a partially charged polymer through a neutral nanopore under external electrical field is studied by using dynamic Monte Carlo method on a simple cubic lattice. One monomer in the polymer is charged and it suffers a driving force when it locates inside the pore. Two time scales, mean first passage time τ(FP) with the first monomer restricted to never draw back into cis side and translocation time τ for polymer continuously threading through nanopore, are calculated. The first passage time τ(FP) decreases with the increase in the driving force f, and the dependence of τ(FP) on the position of charged monomer M is in agreement with the theoretical results using Fokker-Planck equation [A. Mohan, A. B. Kolomeisky, and M. Pasquali, J. Chem. Phys. 128, 125104 (2008)]. But the dependence of τ on M shows a different behavior: It increases with f for M < N/2 with N the polymer length. The novel behavior of τ is explained qualitatively from dynamics of polymer during the translocation process and from the free energy landscape.     

Folding kinetics of a polymer

We present the results of computer simulations giving a kinetic insight into the liquid-to-solid transition of a homopolymer chain with short-range interactions. By calculating the absolute rates in each direction of the transition, using molecular dynamics employing the forward flux sampling scheme, we provide the phase diagram based on purely kinetic data, and compare it with the results from Monte Carlo simulations. Additionally, we present and discuss a remarkably simple and general relation between the polymer topology and the folding pathway, and show that the eigenvalue spectrum of a matrix defined by non-bonded contacts (the Laplacian matrix) provides an insight into the nonequilibrium ensembles of these trajectories. In particular, the Laplacian matrix seems to identify a large fraction of configurations on the folding pathway at the free energy maximum that have a very low probability of reaching the crystallized state. This implies that the eigenvalues of this matrix may be suitable additional reaction coordinates to describe the folding transition of chain molecules.     

Optimization of functionalized polymer layers for specific targeting of mobile receptors on cell surfaces

The reversible binding between a planar polymer layer functionalized by ligands and a planar cell surface containing different densities of mobile receptors has been studied by Monte Carlo simulations. Using the acceptance-ratio method, the distance-dependent profiles for the average number of ligands bound to receptors, the total free energy for the polymer layer-cell surface interaction and the interaction force were obtained. Four main design parameters for the polymer layer were considered: the degree of functionalization, chain degree of polymerization, polymer grafting density and the binding energy for the ligand-receptor interaction. We found that an increase in the degree of functionalization or in the absolute energy of ligand-receptor binding results in a larger number of ligands bound to the receptors, lower free energy, and stronger attractive force. Polymer layers composed of shorter chains were found to exhibit a deeper and narrower free energy profile and a larger attractive force, while longer tethers can interact with the cell surface at a larger and broader range of separation distances, in agreement with experimental observations. Our simulation results show that the increase in polymer grafting density from the mushroom to brush regime enhances the ligand availability and results in a stronger attractive force, increases the maximum binding distance, but exhibits a shallower free energy minimum due to the smaller tolerance to compression for polymer layers with high grafting density. We used two measures of the polymer layer binding affinity to the cell surface: the free energy minimum, related to the equilibrium binding constant and the fraction of bound ligands. We found that the polymer layers with a smaller chain length and grafting density, larger degree of functionalization, and larger absolute binding energy exhibit both a larger equilibrium binding constant to the cell surface and a larger average number of bound ligands, except for high binding energies when the maximum level of binding is reached independently of polymer length and grafting density. We showed that high binding specificity can be achieved by the polymer layers with intermediate ligand-receptor binding energies or an intermediate number of ligands, as a larger binding energy or number of ligands ensures a high binding affinity but lacks specificity while a smaller binding energy or number of ligands provides inadequate affinity. We found that the results for polymer layers with different properties follow a similar pattern when both high binding affinity to cells with high receptor density and high binding specificity are considered. As a result, the optimal design of the polymer layers can be achieved by using several different strategies, which are discussed.     

Polymer chains in a soft nanotube: a Monte Carlo study

We study the equilibrium properties of flexible polymer chains confined in a soft tube by means of extensive Monte Carlo simulations. The tube wall is that of a single sheet six-coordinated self-avoiding tethered membrane. Our study assumes that there is no adsorption of the chain on the wall. By varying the length N of the polymer and the tube diameter D we examine the variation of the polymer gyration radius Rg and diffusion coefficient Ddiff in soft and rigid tubes of identical diameter and compare them to scaling theory predictions. We find that the swollen region of the soft tube surrounding the chain exhibits a cigarlike cylindrical shape for sufficiently narrow tubes with D相似文献   

Towards a modellisation of the solvation energy in multi-component solvents. The interesting case of a charged solute imbedded in a polymer-containing electrolyte solution

In this paper we propose a mean-field theory to calculate the solvation free energy of a charged solute imbedded in a complex multi-component solvent. We considered a solvent made up of a mixture of small (electrolyte solution) and large (polymer) components. The presence of macromolecules ensures reduced mixing entropy among the different solvent components, an effect due to polymer connectivity. The reduced entropy favours strong preferential distribution of a particular solvent even in the presence of weak preferential solute–solvent interactions. In addition, two energy terms must be considered: (a) the interaction between the solute electrostatic potential and the electrolyte solution and (b) the formation of a polymer–solute interface. Because of the different dielectric permittivity of the solvent components, the electrolyte and polymer distribution functions are strongly coupled: ions, indeed, are more solvated in regions of higher local dielectric permittivity arising from the inhomogeneous mixing of solvent and polymer. We combined together the different energy terms in the framework of the de Gennes free energy functional for polymer solutions along with a generalised Poisson–Boltzmann equation developed for inhomogeneous dielectric media. Moreover, the preferential electrolyte solvation in regions of greater polarity was considered by an extension of the Born equation. Setting the polymer dielectric permittivity smaller than the solvent one and making null the specific polymer–solute interactions, we calculated enhanced electrolyte concentration and reduced polymer concentration near the solute surface on raising the solute surface charge density. The theory shows also the breakdown of the widely used separation between electrostatic and surface tension-dependent contributions to solvation energy when non-ideal mixed solvents are considered. In fact, according to the model, the surface tension of such mixed solvents strongly depends on the solute surface charge density: at high potentials the interfacial tension may increase rather than decrease on raising the polymer volume fraction. The theoretical results have been compared with experimental data on polymer+electrolyte solution surface tension and with solubility data of colloidal particles. The comparison evidences the complex behaviour of multi-component solvents going well beyond the trivial weighted average of the dielectric permittivity and surface tension of the isolated chemical components. Deviations from the simple behaviour predicted by an average picture of multi-component solvents could be understood by developing more sophisticated, but still simple, approaches like that proposed in this paper.Contribution to the Jacopo Tomasi Honorary Issue. This paper is dedicated to Jacopo Tomasi. I learned much of the difficult art of transforming complex problems into simple models after reading his early works on solvation energy.     

Boundary effects on the electrophoretic motion of cylindrical particles: concentrically and eccentrically-positioned particles in a capillary

The bounded electrophoretic motion of a cylindrical particle in a circular cylindrical microchannel is explored for two cases: (1) the particle is located on the centerline of a channel (concentrically), with a symmetric wall boundary condition since gap width is constant throughout; and (2) the particle is at an eccentric location in the channel, with an asymmetric boundary condition set by the walls. The objective is to determine the effect of different boundary conditions, geometries, and physical properties on the velocity and orientation of the cylinder with respect to the boundary. A theoretical model for the motion of the cylinder is presented and the problem is solved numerically. The steady-state simulations show that the velocity of the cylinder is reduced at small gap widths for the concentric case, but the velocity is increased at small gap widths for the eccentric case. When the cylinder is angled with respect to the horizontal in the symmetric case or is near the boundary in the asymmetric case, vertical and rotational components of velocity are predicted. In such cases, transient simulations are appropriate for most accurately representing particle motion. Two such simulations are included herein and show both horizontal and vertical translation plus rotation of the particle as a function of time.     

Shear viscosity of simple fluids in porous media: molecular dynamic simulations and correlation models

Equilibrium molecular dynamic simulations have been used to calculate the shear viscosity of liquid argon in macrovolume system and in porous media at different temperatures, densities and pore widths. On the other hand, based on the Chapman–Enskog theory and Heyes relationships, two correlation models which can describe the viscosity of simple liquids in porous media are proposed as a function of the reduced temperature, density and pore width. The validity of the models is evaluated by comparing the calculated viscosity to simulation data.     

Tuning the orientation of an antigen by adsorption onto nanostriped templates

We investigate the adsorption of a globular protein (P.69 pertactin, also known as antigen 69k) on protein-repellent hydrophilic substrates bearing regularly spaced hydrophobic nanostripes, for stripe widths comprised between 20 and 160 nm. Protein adsorption is shown to be remarkably well-controlled by the templating substrates, with a near-to-perfect reproduction of stripes by the protein monolayer down to 20 nm width, except for a 5-10 nm broadening. However, whereas the ellipsoidal protein forms a dense monolayer with random orientation of its long axis for large stripe widths, it adsorbs in a predominantly side-on (flat-on) orientation for stripe widths below 50 nm, due to the easier reorientation (interfacial relaxation) of the proteins adsorbed at the edges of the stripes, which experience a decreased lateral interaction. These results show that protein confinement in regions of a size similar to their dimensions can be used to tune their orientation, which may be of interest for applications in high-density sensor devices.     

Fluorescence and visual detection of single nucleotide polymorphism using cationic conjugated polyelectrolyte

We report a simple assay for visual detection of single nucleotide polymorphisms (SNPs) with good sensitivity and selectivity. The selectivity is determined by Escherichia coli (E. coli) DNA ligase mediated circular formation upon recognition of the point mutation on DNA targets. Rolling cycle amplification (RCA) of the perfect-matched DNA target is then initiated using the in situ formed circular template in the presence of Phi29 enzyme. Due to amplification of the DNA target, the RCA product has a tandem-repeated sequence, which is significantly longer than that for the SNP strand. Direct addition of a cationic conjugated polymer of poly[9,9'-bis(6'-(N,N,N-trimethylammonium)hexyl)fluorene-co-9,9'-bis(2-(2-(2-(N,N,N-trimethylammonium)ethoxyl)-ethoxy)-ethyl)fluorene tetrabromide] containing 20 mol% 2,1,3-benzothiadiazole (PFBT(20)) into the RCA solution leads to blue-whitish fluorescent color for SNP strand and yellowish fluorescent color for amplified DNA, due to PFBT(20)/DNA complexation induced intrachain/interchain energy transfer. To further improve the contrast for visual detection, FAM-labeled peptide nucleic acid (PNA) was hybridized to each amplified sequence, which is followed by the addition of poly{2,7-[9,9-bis(6'-N,N,N-trimethylammoniumhexyl)]fluorene-co-2,5-difluoro-1,4-phenylene dibromide} (PFP). The PNA/DNA hybridization brings PFP and FAM-PNA into close proximity for energy transfer, and the solution fluorescent color appears green in the presence of target DNA with a detection limit of 1 nM, which is significantly improved as compared to that for most reported visual SNP assay.