Simulations of morphology control of self-assembled amphiphilic surfactants

One of the grand challenges of amphiphilic self-assembly is the design of ordered structures whose morphology or shape can be explicitly and dynamically controlled by adjusting the properties of the amphiphiles or their surroundings. Such a capacity would enable researchers to create synthetic systems with functionality that meets or exceeds biological cells, and provide a robust platform for a broad range of engineering applications such as artificial tissues, drug delivery, and separation membranes. Despite significant progress, important fundamental questions remain unanswered, due in part to the limited resolution and the restricted parameter spaces that are readily accessible in experiments. Computational studies thus provide an important complement to experiments, enabling in-depth insight into underlying mechanisms and an exploration of the parameter spaces for behavior that has not yet been achieved in experiments. In this review, we briefly introduce fundamental concepts and pertinent experiments related to dynamic shape modulation in self-assembled amphiphiles. Then, in the bulk of the review, we survey the most influential simulation studies that investigate and identify approaches to control the self-assembled shape of amphiphiles, with an emphasis on kinetic and mechanical effects. Finally, we conclude with a perspective on future research directions in this exciting field

Using Reactive Dissipative Particle Dynamics to Understand Local Shape Manipulation of Polymer Vesicles

Biological cells have long been of interest to researchers due to their capacity to actively control their shape. Accordingly, there is significant interest in generating simplified synthetic protocells that can alter their shape based on an externally or internally generated stimulus. To date, most progress has been made towards controlling the global shape of a protocell, whereas less is known about generating a local shape change. Here, we seek to better understand the possible mechanisms for producing local morphological changes in a popular protocell system, the block copolymer vesicle. Accordingly, we have combined Dissipative Particle Dynamics (DPD) and the Split Reactive Brownian Dynamics algorithm (SRBD) to produce a simulation tool that is capable of modeling the dynamics of self-assembled polymer structures as they undergo chemical reactions. Using this Reactive DPD or RDPD method, we investigate local morphological change driven by either the microinjection of a stimulus or an enzymatically-produced stimulus. We find that sub-vesicle-scale morphological change can be induced by either a solvent stimulus that swells the vesicle membrane, or by a reactant stimulus that alters the chemistry of the block polymer in the membrane corona. Notably, the latter method results in a more persistent local deformation than the former, which we attribute to the slower diffusion of polymer chains relative to the solvent. We quantify this deformation and show that it can be modulated by altering the interaction parameter of the parts of the polymer chain that are affected by the stimulus

Extension of DNA in a Nanochannel as a Rod-to-Coil Transition

DNA confinement in nanochannels is emerging as an important tool for genomics and an excellent platform for testing the theories of confined wormlike polymers. Using cutting-edge, large scale Monte Carlo simulations of asymptotically long wormlike chains, we show that, in analogy to the rod-to-coil transition for free wormlike polymers, there exists a universal, Gauss–de Gennes regime that connects the classic Odijk and de Gennes regimes of channel-confined chains. For DNA in a nanochannel, this Gauss–de Gennes regime spans practically the entire experimentally relevant range of channel sizes, including the nanochannels used in an incipient genome mapping technology

Simulation of DNA Extension in Nanochannels

We have used a realistic model for double-stranded DNA and Monte Carlo simulations to compute the extension (mean span) of a DNA molecule confined in a nanochannel over the full range of confinement in a high ionic strength buffer. The simulation data for square nanochannels resolve the apparent contradiction between prior simulation studies and the predictions from Flory theory, demonstrating the existence of two transition regimes between weak confinement (the de Gennes regime) and strong confinement (the Odijk regime). The simulation data for rectangular nanochannels support the use of the geometric mean for mapping data obtained in rectangular channels onto models developed for cylinders. The comparison of our results with experimental data illuminates the challenges in applying models for confined, neutral polymers to polyelectrolytes. Using a Flory-type approach, we also provide an improved scaling result for the relaxation time in the transition regime close to that found in experiments

Modeling the relaxation time of DNA confined in a nanochannel

Using a mapping between a Rouse dumbbell model and fine-grained Monte Carlo simulations, we have computed the relaxation time of λ-DNA in a high ionic strength buffer confined in a nanochannel. The relaxation time thus obtained agrees quantitatively with experimental data [Reisner et al., Phys. Rev. Lett. 94, 196101 (2005)] using only a single O(1) fitting parameter to account for the uncertainty in model parameters. In addition to validating our mapping, this agreement supports our previous estimates of the friction coefficient of DNA confined in a nanochannel [Tree et al., Phys. Rev. Lett. 108, 228105 (2012)], which have been difficult to validate due to the lack of direct experimental data. Furthermore, the model calculation shows that as the channel size passes below approximately 100 nm (or roughly the Kuhn length of DNA) there is a dramatic drop in the relaxation time. Inasmuch as the chain friction rises with decreasing channel size, the reduction in the relaxation time can be solely attributed to the sharp decline in the fluctuations of the chain extension. Practically, the low variance in the observed DNA extension in such small channels has important implications for genome mapping

Mobility of a Semiflexible Chain Confined in a Nanochannel

The classic results of de Gennes and Odijk describe the mobility of a semiflexible chain confined in a nanochannel only in the limits of very weak and very strong confinement, respectively. Using Monte Carlo sampling of the Kirkwood diffusivity with full hydrodynamic interactions, we show that the mobility of a semiflexible chain exhibits a broad plateau as a function of extension before transitioning to an Odijk regime, and that the width of the plateau depends on the anisotropy of the monomers. For the particular case of DNA in a high ionic strength buffer, which has highly anisotropic monomers, we predict that this Rouse-like behavior will be observed over most of the measurable chain extensions seen in experiments

Steering particles via micro-actuation of chemical gradients using model predictive control

Biological systems rely on chemical gradients to direct motion through both chemotaxis and signaling, but synthetic approaches for doing the same are still relatively naïve. Consequently, we present a novel method for using chemical gradients to manipulate the position and velocity of colloidal particles in a microfluidic device. Specifically, we show that a set of spatially localized chemical reactions that are sufficiently controllable can be used to steer colloidal particles via diffusiophoresis along an arbitrary trajectory. To accomplish this, we develop a control method for steering colloidal particles with chemical gradients using nonlinear model predictive control with a model based on the unsteady Green’s function solution of the diffusion equation. We illustrate the effectiveness of our approach using Brownian dynamics simulations that steer single particles along paths, such as circle, square, and figure-eight. We subsequently compare our results with published techniques for steering colloids using electric fields, and we provide an analysis of the physical parameter space where our approach is useful. Based on these findings, we conclude that it is theoretically possible to explicitly steer particles via chemical gradients in a microfluidics paradigm

The Odijk Regime in Slits

De Gennes’ blob theory has been remarkably successful at describing weakly confined polymers in both slits and channels, and comparable results surround Odijk’s theory of deflection segments for strongly confined wormlike polymers in nanochannels. However, given the success of Odijk’s theory in channels, it is remarkable that there is no comprehensive theory for the simple case of a wormlike polymer strongly confined between two parallel plates. We propose such a theory by drawing inspiration from the existing literature on ideal wormlike chains in slits and Daoud and de Gennes’ idea of mapping a slit-confined chain to a two-dimensional chain. We postulate that the chain can be quantitatively described as a two-dimensional wormlike chain with a weak perturbation in the confining dimension due to deflection segments. By incorporating the effects of real chains, where the variable slit depth adds subtlety due to concomitant changes in the strength of excluded volume interactions, our theory predicts the existence of three distinct subregimes. We investigate the validity of our claims by performing Monte Carlo simulations of a slit-confined wormlike chain using an off-lattice implementation of the pruned–enriched Rosenbluth method. From these simulations, we find strong numerical evidence supporting our predictions, including the existence of subregimes within the Odijk regime

Is DNA a Good Model Polymer?

The details surrounding the crossover from wormlike-specific to universal polymeric behavior has been the subject of debate and confusion even for the simple case of a dilute, unconfined wormlike chain. We have directly computed the polymer size, form factor, free energy, and Kirkwood diffusivity for unconfined wormlike chains as a function of molecular weight, focusing on persistence lengths and effective widths that represent single-stranded and double-stranded DNA in a high ionic strength buffer. To do so, we use a chain-growth Monte Carlo algorithm, the pruned-enriched Rosenbluth method (PERM), which allows us to estimate equilibrium and near-equilibrium dynamic properties of wormlike chains over an extremely large range of contour lengths. From our calculations, we find that very large DNA chains (≈1 000 000, base pairs depending on the choice of size metric) are required to reach flexible, swollen nondraining coils. Furthermore, our results indicate that the commonly used model polymer λ-DNA (48 500, base pairs) does not exhibit “ideal” scaling but exists in the middle of the transition to long-chain behavior. We subsequently conclude that typical DNA used in experiments are too short to serve as an accurate model of long-chain, universal polymer behavior

Resolution limit for DNA barcodes in the Odijk regime

We develop an approximation for the probability of optically resolving two fluorescent labels on the backbone of a DNA molecule confined in a nanochannel in the Odijk regime as a function of the fluorescence wavelength, channel size, and the properties of the DNA (persistence length and effective width). The theoretical predictions agree well with equivalent data produced by Monte Carlo simulations of a touching wormlike bead model of DNA in a high ionic strength buffer. Although the theory is only strictly valid in the limit where the effective width of the nanochannel is small compared with the persistence length of the DNA, simulations indicate that the theoretical predictions are reasonably accurate for channel widths up to two-thirds of the persistence length. Our results quantify the conjecture that DNA barcoding has kilobase pair resolution—provided the nanochannel lies in the Odijk regime