Modelling multivalent interactons

A Multivalent entity, which could represent a protein, nanoparticle, polymer, virus or a lipid bilayer, has the ability to form multiple bonds to a substrate. Hence, a multivalent interaction can be strong, even if the individual bonds are weak. However, much more interestingly, multivalency enables the design of highly specific interactions using non-specific individual bonds. We attempt to rationalise multivalent effects using simple physical models complemented with numerical simulations. Based on physiochemical characteristics of multivalent binders, we aim to predict the overall strength of interaction and its sensitivity to variation in parameters. We start with a simple model of homo-multivalency, where all bonds are equivalent. Such systems can exhibit a super-selective response, which denotes the high sensitivity of the strength of multivalent binding to the number of accessible binding sites on the target surface. We present a theoretical analysis of systems of multivalent particles and show that a certain degree of disorder is necessary for super-selective behaviour. Moreover, we formulate a set of simple design rules for multivalent interactions that yield optimal selectivity. In the second stage, we expand the model to hetero-multivalency, accounting for multiple distinct types of binding partners. We consider targeting of cells based on a density profile of different membrane receptors types and demonstrate, that speci city towards a desired receptor density profile can be obtained. Hence, cells can be reliably targeted in the absence of specific markers. Crucially, we show that for optimal selectivity, individual bonds must be weak. Finally, we add information about specific geometry and positions of binding sites on the multivalent entity. We focus on molecular imprinting; the process whereby a polymer matrix is cross-linked in the presence of template molecules. The cross-linking process endows the polymer matrix with a chemical ‘memory’, such that the target molecules can subsequently be recognised by the matrix. We show how the binding multivalency and the polymer material properties affect the efficiency and selectivity of molecular imprinting.Herchel Smith fun

Nanoparticle ordering in sandwiched polymer brushes

The organization of nano-particles inside grafted polymer layers is governed by the interplay of polymer-induced entropic interactions and the action of externally applied fields. Earlier work had shown that strong external forces can drive the formation of colloidal structures in polymer brushes. Here we show that external fields are not essential to obtain such colloidal patterns: we report Monte Carlo and Molecular dynamics simulations that demonstrate that ordered structures can be achieved by compressing a `sandwich' of two grafted polymer layers, or by squeezing a coated nanotube, with nano-particles in between. We show that the pattern formation can be efficiently controlled by the applied pressure, while the characteristic length--scale, i.e. the typical width of the patterns, is sensitive to the length of the polymers. Based on the results of the simulations, we derive an approximate equation of state for nano-sandwiches.Comment: 18 pages, 4 figure

Rational design of molecularly imprinted polymers.

Molecular imprinting is the process whereby a polymer matrix is cross-linked in the presence of molecules with surface sites that can bind selectively to certain ligands on the polymer. The cross-linking process endows the polymer matrix with a chemical 'memory', such that the target molecules can subsequently be recognized by the matrix. We present a simple model that accounts for the key features of this molecular recognition. Using a combination of analytical calculations and Monte Carlo simulations, we show that the model can account for the binding of rigid particles to an imprinted polymer matrix with valence-limited interactions. We show how the binding multivalency and the polymer material properties affect the efficiency and selectivity of molecular imprinting. Our calculations allow us to formulate design criteria for optimal molecular imprinting.This work was supported by the Fundamental Research Funds for the Central Universities of P. R. China, ERC Advanced Grant 227758 (COLSTRUCTION), ITN grant 234810 (COMPPLOIDS) and by EPSRC Programme Grant EP/I001352/1. TC acknowledges support from the Herchel Smith fund.This is the final version of the article. It first appeared from RSC via http://dx.doi.org/10.1039/C5SM02144

The Effect of Attractive Interactions and Macromolecular Crowding on Crystallins Association.

In living systems proteins are typically found in crowded environments where their effective interactions strongly depend on the surrounding medium. Yet, their association and dissociation needs to be robustly controlled in order to enable biological function. Uncontrolled protein aggregation often causes disease. For instance, cataract is caused by the clustering of lens proteins, i.e., crystallins, resulting in enhanced light scattering and impaired vision or blindness. To investigate the molecular origins of cataract formation and to design efficient treatments, a better understanding of crystallin association in macromolecular crowded environment is needed. Here we present a theoretical study of simple coarse grained colloidal models to characterize the general features of how the association equilibrium of proteins depends on the magnitude of intermolecular attraction. By comparing the analytic results to the available experimental data on the osmotic pressure in crystallin solutions, we identify the effective parameters regimes applicable to crystallins. Moreover, the combination of two models allows us to predict that the number of binding sites on crystallin is small, i.e. one to three per protein, which is different from previous estimates. We further observe that the crowding factor is sensitive to the size asymmetry between the reactants and crowding agents, the shape of the protein clusters, and to small variations of intermolecular attraction. Our work may provide general guidelines on how to steer the protein interactions in order to control their association

Multivalent Recognition at Fluid Surfaces: The Interplay of Receptor Clustering and Superselectivity.

The interaction between a biological membrane and its environment is a complex process, as it involves multivalent binding between ligand/receptor pairs, which can self-organize in patches. Any description of the specific binding of biomolecules to membranes must account for the key characteristics of multivalent binding, namely, its unique ability to discriminate sharply between high and low receptor densities (superselectivity), but also for the effect of the lateral mobility of membrane-bound receptors to cluster upon binding. Here we present an experimental model system that allows us to compare systematically the effects of multivalent interactions on fluid and immobile surfaces. A crucial feature of our model system is that it allows us to control the membrane surface chemistry, the properties of the multivalent binder, and the binding affinity. We find that multivalent probes retain their superselective binding behavior at fluid interfaces. Supported by numerical simulations, we demonstrate that, as a consequence of receptor clustering, superselective binding is enhanced and shifted to lower receptor densities at fluid interfaces. To translate our findings into a simple, predictive tool, we propose an analytical model that enables rapid predictions of how the superselective binding behavior is affected by the lateral receptor mobility as a function of the physicochemical characteristics of the multivalent probe. We believe that our model, which captures the key physical mechanisms underpinning multivalent binding to biological membranes, will greatly facilitate the rational design of nanoprobes for the superselective targeting of cells.EU ETN grant 674979-NANOTRAN

Layering, freezing and re-entrant melting of hard spheres in soft confinement

Confinement can have a dramatic effect on the behavior of all sorts of particulate systems and it therefore is an important phenomenon in many different areas of physics and technology. Here, we investigate the role played by the softness of the confining potential. Using grand canonical Monte Carlo simulations, we determine the phase diagram of three-dimensional hard spheres that in one dimension are constrained to a plane by a harmonic potential. The phase behavior depends strongly on the density and on the stiffness of the harmonic confinement. Whilst we find the familiar sequence of confined hexagonal and square-symmetric packings, we do not observe any of the usual intervening ordered phases. Instead, the system phase separates under strong confinement, or forms a layered re-entrant liquid phase under weaker confinement. It is plausible that this behavior is due to the larger positional freedom in a soft confining potential and to the contribution that the confinement energy makes to the total free energy. The fact that specific structures can be induced or suppressed by simply changing the confinement conditions (e.g. in a dielectrophoretic trap) is important for applications that involve self-assembled structures of colloidal particles.Comment: 5 pages, 5 figure