Sequential programmable self-assembly: Role of cooperative interactions

Density-tunable pathway complexity in a minimalistic self-assembly model

An open challenge in self-assembly is learning how to design systems that can be conditionally guided towards different target structures depending on externally-controlled conditions. Using a theoretical and numerical approach, here we discuss a minimalistic self-assembly model that can be steered towards different types of ordered constructs at the equilibrium by solely tuning a facile selection parameter, namely the density of building blocks. Metadynamics and Langevin dynamics simulations allow us to explore the behavior of the system in and out of equilibrium conditions. We show that the density-driven tunability is encoded in the pathway complexity of the system, and specifically in the competition between two different main self-assembly routes. A comprehensive set of simulations provides insight into key factors allowing to make one self-assembling pathway prevailing on the other (or vice versa), determining the selection of the final self-assembled products. We formulate and validate a practical criterion for checking whether a specific molecular design is predisposed for such density-driven tunability of the products, thus offering a new, broader perspective to realize and harness this facile extrinsic control of conditional self-assembly.

Programming Directed Motion with DNA-Grafted Particles

Colloidal particles can be programmed to interact in complex ways by functionalizing them with DNA oligonucleotides. Adding DNA strand-displacement reactions to the system allows these interparticle interactions to respond to specific changes in temperature. We present the requirements for thermally driven directed motion of colloidal particles, and we explore how these conditions can be realized experimentally using strand-displacement reactions. To evaluate the concept, we build and test a colloidal "dancer": a single particle that can be driven to move through a programmed sequence of steps along a one-dimensional track composed of other particles. The results of these tests reveal the capabilities and limitations of using DNA-mediated interactions for applications in dynamic systems. Specifically, we discuss how to design the substrate to limit complexity while permitting full control of the motile component, how to ratchet the interactions to move over many substrate positions with a limited regime of control parameters, and how to use technological developments to reduce the probability of detachment without sacrificing speed.

Nonequilibrium self-assembly of multiple stored targets in a dimer-based system

Nonequilibrium self-assembly can be found in various biological processes where chemical potential gradients are exploited to steer the system to a desired organized structure with a particular function. Microtubules, for example, are composed of two globular protein subunits, α-tubulin and β-tubulin, which bind together to form polar dimers that self-assemble a hollow cylinder structure in a process driven by GTPase activity. Inspired by this process, we define a generic self-assembly lattice model containing particles of two subunits, which is driven out-of-equilibrium by a dimer-favoring local driving force. Using Monte Carlo simulations, we characterize the ability of this system to restore pre-encoded target structures as a function of the initial seed size, interaction energy, chemical potential, number of target structures, and strength of the nonequilibrium drive. We demonstrate some intriguing consequences of the drive, such as a smaller critical seed and an improved target assembly stability, compared to the equilibrium scenario. Our results can expand the theoretical basis of nonequilibrium self-assembly and provide deeper understanding of how nonequilibrium driving can overcome equilibrium constraints.

Adaptable DNA interactions regulate surface triggered self assembly

DNA-mediated multivalent interactions between colloidal particles have been extensively applied for their ability to program bulk phase behaviour and dynamic processes. Exploiting the competition between different types of DNA-DNA bonds, here we experimentally demonstrate the selective triggering of colloidal self-assembly in the presence of a functionalised surface, which induces changes in particle-particle interactions. Besides its relevance to the manufacturing of layered materials with controlled thickness, the intrinsic signal-amplification features of the proposed interaction scheme make it valuable for biosensing applications.

Self-assembly of finite-sized colloidal aggregates

One of the challenges of self-assembling finite-sized colloidal aggregates with a sought morphology is the necessity of precisely sorting the position of the colloids at the microscopic scale to avoid the formation of off-target structures. Microfluidic platforms address this problem by loading into single droplets the exact amount of colloids entering the targeted aggregate. Using theory and simulations, in this paper, we validate a more versatile design allowing us to fabricate different types of finite-sized aggregates, including colloidal molecules or core-shell clusters, starting from finite density suspensions of isotropic colloids in bulk. In our model, interactions between particles are mediated by DNA linkers with mobile tethering points, as found in experiments using DNA oligomers tagged with hydrophobic complexes immersed into supported bilayers. By fine-tuning the strength and number of the different types of linkers, we prove the possibility of controlling the morphology of the aggregates, in particular, the valency of the molecules and the size of the core-shell clusters. In general, our design shows how multivalent interactions can lead to microphase separation under equilibrium conditions.

First-order 'hyper-selective' binding transition of multivalent particles under force

Multivalent particles bind to targets via many independent ligand-receptor bonding interactions. This microscopic design spans length scales in both synthetic and biological systems. Classic examples include interactions between cells, virus binding, synthetic ligand-coated micrometer-scale vesicles or smaller nano-particles, functionalised polymers, and toxins. Equilibrium multivalent binding is a continuous yet super-selective transition with respect to the number of ligands and receptors involved in the interaction. Increasing the ligand or receptor density on the two particles leads to sharp growth in the number of bound particles at equilibrium. Here we present a theory and Monte Carlo simulations to show that applying mechanical force to multivalent particles causes their adsorption/desorption isotherm on a surface to become sharper and more selective, with respect to variation in the number of ligands and receptors on the two objects. When the force is only applied to particles bound to the surface by one or more ligands, then the transition can become infinitely sharp and first-order-a new binding regime which we term 'hyper-selective'. Force may be imposed by, e.g. flow of solvent around the particles, a magnetic field, chemical gradients, or triggered uncoiling of inert oligomers/polymers tethered to the particles to provide a steric repulsion to the surface. This physical principle is a step towards 'all or nothing' binding selectivity in the design of multivalent constructs.

Programmable interactions with biomimetic DNA linkers at fluid membranes and interfaces

At the heart of the structured architecture and complex dynamics of biological systems are specific and timely interactions operated by biomolecules. In many instances, biomolecular agents are spatially confined to flexible lipid membranes where, among other functions, they control cell adhesion, motility and tissue formation. Besides being central to several biological processes, multivalent interactions mediated by reactive linkers confined to deformable substrates underpin the design of synthetic-biological platforms and advanced biomimetic materials. Here we review recent advances on the experimental study and theoretical modelling of a heterogeneous class of biomimetic systems in which synthetic linkers mediate multivalent interactions between fluid and deformable colloidal units, including lipid vesicles and emulsion droplets. Linkers are often prepared from synthetic DNA nanostructures, enabling full programmability of the thermodynamic and kinetic properties of their mutual interactions. The coupling of the statistical effects of multivalent interactions with substrate fluidity and deformability gives rise to a rich emerging phenomenology that, in the context of self-assembled soft materials, has been shown to produce exotic phase behaviour, stimuli-responsiveness, and kinetic programmability of the self-assembly process. Applications to (synthetic) biology will also be reviewed.

Computational protein design: a review

Proteins are one of the most versatile modular assembling systems in nature. Experimentally, more than 110 000 protein structures have been identified and more are deposited every day in the Protein Data Bank. Such an enormous structural variety is to a first approximation controlled by the sequence of amino acids along the peptide chain of each protein. Understanding how the structural and functional properties of the target can be encoded in this sequence is the main objective of protein design. Unfortunately, rational protein design remains one of the major challenges across the disciplines of biology, physics and chemistry. The implications of solving this problem are enormous and branch into materials science, drug design, evolution and even cryptography. For instance, in the field of drug design an effective computational method to design protein-based ligands for biological targets such as viruses, bacteria or tumour cells, could give a significant boost to the development of new therapies with reduced side effects. In materials science, self-assembly is a highly desired property and soon artificial proteins could represent a new class of designable self-assembling materials. The scope of this review is to describe the state of the art in computational protein design methods and give the reader an outline of what developments could be expected in the near future.

Spontaneous emergence of catalytic cycles with colloidal spheres

Colloidal particles endowed with specific time-dependent interactions are a promising route for realizing artificial materials that have the properties of living ones. Previous work has demonstrated how this system can give rise to self-replication. Here, we introduce the process of colloidal catalysis, in which clusters of particles catalyze the creation of other clusters through templating reactions. Surprisingly, we find that simple templating rules generically lead to the production of huge numbers of clusters. The templating reactions among this sea of clusters give rise to an exponentially growing catalytic cycle, a specific realization of Dyson's notion of an exponentially growing metabolism. We demonstrate this behavior with a fixed set of interactions between particles chosen to allow a catalysis of a specific six-particle cluster from a specific seven-particle cluster, yet giving rise to the catalytic production of a sea of clusters of sizes between 2 and 11 particles. The fact that an exponentially growing cycle emerges naturally from such a simple scheme demonstrates that the emergence of exponentially growing metabolisms could be simpler than previously imagined.

Communication: Free energy of ligand-receptor systems forming multimeric complexes

Ligand-receptor interactions are ubiquitous in biology and have become popular in materials in view of their applications to programmable self-assembly. Although complex functionalities often emerge from the simultaneous interaction of more than just two linker molecules, state of the art theoretical frameworks enable the calculation of the free energy only in systems featuring one-to-one ligand/receptor binding. In this Communication, we derive a general formula to calculate the free energy of systems featuring simultaneous direct interaction between an arbitrary number of linkers. To exemplify the potential and generality of our approach, we apply it to the systems recently introduced by Parolini et al. [ACS Nano 10, 2392 (2016)] and Halverson and Tkachenko [J. Chem. Phys. 144, 094903 (2016)], both featuring functionalized Brownian particles interacting via three-linker complexes.

Melting transition in lipid vesicles functionalised by mobile DNA linkers

We study phase behaviour of lipid-bilayer vesicles functionalised by ligand-receptor complexes made of synthetic DNA by introducing a modelling framework and a dedicated experimental platform. In particular, we perform Monte Carlo simulations that combine a coarse grained description of the lipid bilayer with state of art analytical models for multivalent ligand-receptor interactions. Using density of state calculations, we derive the partition function in pairs of vesicles and compute the number of ligand-receptor bonds as a function of temperature. Numerical results are compared to microscopy and fluorimetry experiments on large unilamellar vesicles decorated by DNA linkers carrying complementary overhangs. We find that vesicle aggregation is suppressed when the total number of linkers falls below a threshold value. Within the model proposed here, this is due to the higher configurational costs required to form inter-vesicle bridges as compared to intra-vesicle loops, which are in turn related to membrane deformability. Our findings and our numerical/experimental methodologies are applicable to the rational design of liposomes used as functional materials and drug delivery applications, as well as to study inter-membrane interactions in living systems, such as cell adhesion.