Phase separation and ripening in a viscoelastic gel.

The process of phase separation in elastic solids and viscous fluids is of fundamental importance to the stability and function of soft materials. We explore the dynamics of phase separation and domain growth in a viscoelastic material such as a polymer gel. Using analytical theory and Monte Carlo simulations, we report a domain growth regime in which the domain size increases algebraically with a ripening exponent [Formula: see text] that depends on the viscoelastic properties of the material. For a prototypical Maxwell material, we obtain [Formula: see text], which is markedly different from the well-known Ostwald ripening process with [Formula: see text]. We generalize our theory to systems with arbitrary power-law relaxation behavior and discuss our findings in the context of the long-term stability of materials as well as recent experimental results on phase separation in cross-linked networks and cytoskeleton.

Determinants of Superselectivity─Practical Concepts for Application in Biology and Medicine.

Multivalent interactions are common in biological systems and are also widely deployed for targeting applications in biomedicine. A unique feature of multivalent binding is "superselectivity". Superselectivity refers to the sharp discrimination of surfaces (e.g., on cells or cell compartments) by their comparative surface densities of a given receptor. This feature is different from the conventional "type" selectivity, which discriminates surfaces by their distinct receptor types. In a broader definition, a probe is superselective if it converts a gradual change in any one interaction parameter into a sharp on/off dependency in probe binding.This Account describes our systematic experimental and theoretical efforts over the past decade to analyze the determinants of superselective binding. It aims to offer chemical biologists, biophysicists, biologists, and biomedical scientists a set of guidelines for the interpretation of multivalent binding data, and design rules for tuning superselective targeting. We first provide a basic introduction that identifies multiple low-affinity interactions and combinatorial entropy as the minimal set of conditions required for superselective recognition. We then introduce the main experimental and theoretical tools and analyze how salient features of the multivalent probes (i.e., their concentration, size, ligand valency, and scaffold type), of the surface receptors (i.e., their affinity for ligands, surface density, and mobility), and of competitors and cofactors (i.e., their concentration and affinity for the ligands and/or receptors) influence the sharpness and the position of the threshold for superselective recognition.Emerging from this work are a set of relatively simple yet quantitative data analysis guidelines and superselectivity design rules that apply to a broad range of probe types and interaction systems. The key finding is the scaling variable xS which faithfully predicts the influence of the surface receptor density, probe ligand valency, receptor-ligand affinity, and competitor/cofactor concentrations and affinities on superselective recognition. The scaling variable is a simple yet versatile tool to quantitatively tune the on/off threshold of superselective probes. We exemplify its application by reviewing and reinterpreting literature data for selected biological and biomedical interaction systems where superselectivity clearly is important.Our guidelines can be deployed to generate a new mechanistic understanding of multivalent recognition events inside and outside cells and the downstream physiological/pathological implications. Moreover, the design rules can be harnessed to develop novel superselective probes for analytical purposes in the life sciences and for diagnostic/therapeutic intervention in biomedicine.

Erratum: Spontaneous Domain Formation in Spherically Confined Elastic Filaments [Phys. Rev. Lett. 123, 047801 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.123.047801.

Dissipative particle dynamics for coarse-grained models.

We develop a computational method based on Dissipative Particle Dynamics (DPD) that introduces solvent hydrodynamic interactions to coarse-grained models of solutes, such as ions, molecules, or polymers. DPD-solvent (DPDS) is a fully off-lattice method that allows straightforward incorporation of hydrodynamics at desired solvent viscosity, compressibility, and solute diffusivity with any particle-based solute model. Solutes interact with the solvent only through the DPD thermostat, which ensures that the equilibrium properties of the solute system are not affected by the introduction of the DPD solvent, while the thermostat coupling strength sets the desired solute diffusivity. Thus, DPDS can be used as a replacement for traditional molecular dynamics thermostats such as Nosé-Hoover and Langevin. We demonstrate the applicability of DPDS in the case of polymer dynamics and electroosmotic flow through a nanopore. The method should be broadly useful as a means to introduce hydrodynamic interactions to existing coarse-grained models of solutes and soft materials.

Collapse and expansion kinetics of a single polyelectrolyte chain with hydrodynamic interactions.

We investigate the collapse and expansion dynamics of a linear polyelectrolyte (PE) with hydrodynamic interactions. Using dissipative particle dynamics with a bead-spring PE model, long-range electrostatics, and explicit ions, we examine how the timescales of collapse tcol and expansion texp depend on the chain length N and obtain scaling relationships tcol ∼ Nα and texp ∼ Nß. For neutral polymers, we derive values of α = 0.94 ± 0.01 and ß = 1.97 ± 0.10. Interestingly, the introduction of electrostatic interaction markedly shifts α to α ≈ 1.4 ± 0.1 for salt concentrations within c = 10-4 to 10-2 M. A reduction in the ion-to-monomer size ratio noticeably reduces α. On the other hand, the expansion scaling remains approximately constant, ß ≈ 2, regardless of the salt concentration or ion size considered. We find ß > α for all conditions considered, implying that expansion is always slower than collapse in the limit of long polymers. This asymmetry is explained by distinct kinetic pathways of collapse and expansion processes.

A Study of the Drift Phenomena of Gate-Functionalized Biosensors and Dual-Gate-Functionalized Biosensors in Human Serum.

In this paper, we study the drift behavior of organic electrochemical transistor (OECT) biosensors in a phosphate-buffered saline (PBS) buffer solution and human serum. Theoretical and experimental methods are illustrated in this paper to understand the origin of the drift phenomenon and the mechanism of ion diffusion in the sensing layer. The drift phenomenon is explained using a first-order kinetic model of ion adsorption into the gate material and shows very good agreement with experimental data on drift in OECTs. We show that the temporal current drift can be largely mitigated using a dual-gate OECT architecture and that dual-gate-based biosensors can increase the accuracy and sensitivity of immuno-biosensors compared to a standard single-gate design. Specific binding can be detected at a relatively low limit of detection, even in human serum.

Computational design of probes to detect bacterial genomes by multivalent binding.

Rapid methods for diagnosis of bacterial infections are urgently needed to reduce inappropriate use of antibiotics, which contributes to antimicrobial resistance. In many rapid diagnostic methods, DNA oligonucleotide probes, attached to a surface, bind to specific nucleotide sequences in the DNA of a target pathogen. Typically, each probe binds to a single target sequence; i.e., target-probe binding is monovalent. Here we show using computer simulations that the detection sensitivity and specificity can be improved by designing probes that bind multivalently to the entire length of the pathogen genomic DNA, such that a given probe binds to multiple sites along the target DNA. Our results suggest that multivalent targeting of long pieces of genomic DNA can allow highly sensitive and selective binding of the target DNA, even if competing DNA in the sample also contains binding sites for the same probe sequences. Our results are robust to mild fragmentation of the bacterial genome. Our conclusions may also be relevant for DNA detection in other fields, such as disease diagnostics more broadly, environmental management, and food safety.

Controlling Superselectivity of Multivalent Interactions with Cofactors and Competitors.

Moieties that compete with multivalent interactions or act as cofactors are common in living systems, but their effect on multivalent binding remains poorly understood. We derive a theoretical model that shows how the superselectivity of multivalent interactions is modulated by the presence of cofactors or competitors. We find that the role of these participating moieties can be fully captured by a simple rescaling of the affinity constant of the individual ligand-receptor bonds. Theoretical predictions are supported by experimental data of the membrane repair protein annexin A5 binding to anionic lipid membranes in the presence of Ca2+ cofactors and of the extracellular matrix polysaccharide hyaluronan (HA) binding to CD44 cell surface receptors in the presence of HA oligosaccharide competitors. The obtained findings should facilitate understanding of multivalent recognition in biological systems and open new routes for fine-tuning the selectivity of multivalent nanoprobes in medicinal chemistry.

Accelerated simulation method for charge regulation effects.

The net charge of solvated entities, ranging from polyelectrolytes and biomolecules to charged nanoparticles and membranes, depends on the local dissociation equilibrium of individual ionizable groups. Incorporation of this phenomenon, charge regulation (CR), in theoretical and computational models requires dynamic, configuration-dependent recalculation of surface charges and is therefore typically approximated by assuming constant net charge on particles. Various computational methods exist that address this. We present an alternative, particularly efficient CR Monte Carlo method (CR-MC), which explicitly models the redistribution of individual charges and accurately samples the correct grand-canonical charge distribution. In addition, we provide an open-source implementation in the large-scale Atomic/Molecular Massively Parallel Simulator molecular dynamics (MD) simulation package, resulting in a hybrid MD/CR-MC simulation method. This implementation is designed to handle a wide range of implicit-solvent systems that model discreet ionizable groups or surface sites. The computational cost of the method scales linearly with the number of ionizable groups, thereby allowing accurate simulations of systems containing thousands of individual ionizable sites. By matter of illustration, we use the CR-MC method to quantify the effects of CR on the nature of the polyelectrolyte coil-globule transition and on the effective interaction between oppositely charged nanoparticles.

Charge Regulation Effects in Nanoparticle Self-Assembly.

Nanoparticles in solution acquire charge through the dissociation or association of surface groups. Thus, a proper description of their electrostatic interactions requires the use of charge-regulating boundary conditions rather than the commonly employed constant-charge approximation. We implement a hybrid Monte Carlo/molecular dynamics scheme that dynamically adjusts the charges of individual surface groups of objects while evolving their trajectories. Charge regulation effects are shown to qualitatively change self-assembled structures due to global charge redistribution, stabilizing asymmetric constructs. We delineate under which conditions the conventional constant-charge approximation may be employed and clarify the interplay between charge regulation and dielectric polarization.

Optimal multivalent targeting of membranes with many distinct receptors.

Cells can often be recognized by the concentrations of receptors expressed on their surface. For better (targeted drug treatment) or worse (targeted infection by pathogens), it is clearly important to be able to target cells selectively. A good targeting strategy would result in strong binding to cells with the desired receptor profile and barely binding to other cells. Using a simple model, we formulate optimal design rules for multivalent particles that allow them to distinguish target cells based on their receptor profile. We find the following: (i) It is not a good idea to aim for very strong binding between the individual ligands on the guest (delivery vehicle) and the receptors on the host (cell). Rather, one should exploit multivalency: High sensitivity to the receptor density on the host can be achieved by coating the guest with many ligands that bind only weakly to the receptors on the cell surface. (ii) The concentration profile of the ligands on the guest should closely match the composition of the cognate membrane receptors on the target surface. And (iii) irrespective of all details, the effective strength of the ligand-receptor interaction should be of the order of the thermal energy [Formula: see text], where [Formula: see text] is the absolute temperature and [Formula: see text] is Boltzmann's constant. We present simulations that support the theoretical predictions. We speculate that, using the above design rules, it should be possible to achieve targeted drug delivery with a greatly reduced incidence of side effects.

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.

Spontaneous Domain Formation in Spherically Confined Elastic Filaments.

Although the free energy of a genome packing into a virus is dominated by DNA-DNA interactions, ordering of the DNA inside the capsid is elasticity driven, suggesting general solutions with DNA organized into spool-like domains. Using analytical calculations and computer simulations of a long elastic filament confined to a spherical container, we show that the ground state is not a single spool as assumed hitherto, but an ordering mosaic of multiple homogeneously ordered domains. At low densities, we observe concentric spools, while at higher densities, other morphologies emerge, which resemble topological links. We discuss our results in the context of metallic wires, viral DNA, and flexible polymers.

Controlling Cargo Trafficking in Multicomponent Membranes.

Biological membranes typically contain a large number of different components dispersed in small concentrations in the main membrane phase, including proteins, sugars, and lipids of varying geometrical properties. Most of these components do not bind the cargo. Here, we show that such "inert" components can be crucial for the precise control of cross-membrane trafficking. Using a statistical mechanics model and molecular dynamics simulations, we demonstrate that the presence of inert membrane components of small isotropic curvatures dramatically influences cargo endocytosis, even if the total spontaneous curvature of such a membrane remains unchanged. Curved lipids, such as cholesterol, as well as asymmetrically included proteins and tethered sugars can, therefore, actively participate in the control of the membrane trafficking of nanoscopic cargo. We find that even a low-level expression of curved inert membrane components can determine the membrane selectivity toward the cargo size and can be used to selectively target membranes of certain compositions. Our results suggest a robust and general method of controlling cargo trafficking by adjusting the membrane composition without needing to alter the concentration of receptors or the average membrane curvature. This study indicates that cells can prepare for any trafficking event by incorporating curved inert components in either of the membrane leaflets.

Coarse-grained simulation of DNA using LAMMPS : An implementation of the oxDNA model and its applications.

During the last decade coarse-grained nucleotide models have emerged that allow us to study DNA and RNA on unprecedented time and length scales. Among them is oxDNA, a coarse-grained, sequence-specific model that captures the hybridisation transition of DNA and many structural properties of single- and double-stranded DNA. oxDNA was previously only available as standalone software, but has now been implemented into the popular LAMMPS molecular dynamics code. This article describes the new implementation and analyses its parallel performance. Practical applications are presented that focus on single-stranded DNA, an area of research which has been so far under-investigated. The LAMMPS implementation of oxDNA lowers the entry barrier for using the oxDNA model significantly, facilitates future code development and interfacing with existing LAMMPS functionality as well as other coarse-grained and atomistic DNA models.

Designing multivalent probes for tunable superselective targeting.

Specific targeting is common in biology and is a key challenge in nanomedicine. It was recently demonstrated that multivalent probes can selectively target surfaces with a defined density of surface binding sites. Here we show, using a combination of experiments and simulations on multivalent polymers, that such "superselective" binding can be tuned through the design of the multivalent probe, to target a desired density of binding sites. We develop an analytical model that provides simple yet quantitative predictions to tune the polymer's superselective binding properties by its molecular characteristics such as size, valency, and affinity. This work opens up a route toward the rational design of multivalent probes with defined superselective targeting properties for practical applications, and provides mechanistic insight into the regulation of multivalent interactions in biology. To illustrate this, we show how the superselective targeting of the extracellular matrix polysaccharide hyaluronan to its main cell surface receptor CD44 is controlled by the affinity of individual CD44-hyaluronan interactions.

Liquid-crystalline ordering of antimicrobial peptide-DNA complexes controls TLR9 activation.

Double-stranded DNA (dsDNA) can trigger the production of type I interferon (IFN) in plasmacytoid dendritic cells (pDCs) by binding to endosomal Toll-like receptor-9 (TLR9; refs 1-5). It is also known that the formation of DNA-antimicrobial peptide complexes can lead to autoimmune diseases via amplification of pDC activation. Here, by combining X-ray scattering, computer simulations, microscopy and measurements of pDC IFN production, we demonstrate that a broad range of antimicrobial peptides and other cationic molecules cause similar effects, and elucidate the criteria for amplification. TLR9 activation depends on both the inter-DNA spacing and the multiplicity of parallel DNA ligands in the self-assembled liquid-crystalline complex. Complexes with a grill-like arrangement of DNA at the optimum spacing can interlock with multiple TLR9 like a zipper, leading to multivalent electrostatic interactions that drastically amplify binding and thereby the immune response. Our results suggest that TLR9 activation and thus TLR9-mediated immune responses can be modulated deterministically.

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.

Nanoparticle organization in sandwiched polymer brushes.

The organization of nanoparticles 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 nanoparticles in between. We show that the pattern formation can be efficiently controlled by the applied pressure, while the characteristic length-scale, that is, 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 nanosandwiches.

Superselective targeting using multivalent polymers.

Despite their importance for material and life sciences, multivalent interactions between polymers and surfaces remain poorly understood. Combining recent achievements of synthetic chemistry and surface characterization, we have developed a well-defined and highly specific model system based on host/guest interactions. We use this model to study the binding of hyaluronic acid functionalized with host molecules to tunable surfaces displaying different densities of guest molecules. Remarkably, we find that the surface density of bound polymer increases faster than linearly with the surface density of binding sites. Based on predictions from a simple analytical model, we propose that this superselective behavior arises from a combination of enthalpic and entropic effects upon binding of nanoobjects to surfaces, accentuated by the ability of polymer chains to interpenetrate.