Daniel Frenkel

Crucial role of nonspecific interactions in amyloid nucleation

Significance The assembly of normally soluble proteins into large fibrils, known as amyloid aggregation, is associated with a range of pathologies. Prefibrillar protein oligomers but not the grown fibers are believed to be the main toxic agents. It is unresolved if these oligomers are necessary for fibril assembly or just a dangerous byproduct. We show using computer simulations that, at physiological concentrations, amyloid formation must proceed through a two-step process including prefibrillar oligomers. We find that there is an optimal oligomeric size for amyloid nucleation and that classical nucleation theory cannot be applied to this process. Formation of oligomers and hence, fibrils, is controlled by the strength of nonspecific attractions, whose weakening may be crucial in preventing amyloid aggregation. Protein oligomers have been implicated as toxic agents in a wide range of amyloid-related diseases. However, it has remained unsolved whether the oligomers are a necessary step in the formation of amyloid fibrils or just a dangerous byproduct. Analogously, it has not been resolved if the amyloid nucleation process is a classical one-step nucleation process or a two-step process involving prenucleation clusters. We use coarse-grained computer simulations to study the effect of nonspecific attractions between peptides on the primary nucleation process underlying amyloid fibrillization. We find that, for peptides that do not attract, the classical one-step nucleation mechanism is possible but only at nonphysiologically high peptide concentrations. At low peptide concentrations, which mimic the physiologically relevant regime, attractive interpeptide interactions are essential for fibril formation. Nucleation then inevitably takes place through a two-step mechanism involving prefibrillar oligomers. We show that oligomers not only help peptides meet each other but also, create an environment that facilitates the conversion of monomers into the β-sheet–rich form characteristic of fibrils. Nucleation typically does not proceed through the most prevalent oligomers but through an oligomer size that is only observed in rare fluctuations, which is why such aggregates might be hard to capture experimentally. Finally, we find that the nucleation of amyloid fibrils cannot be described by classical nucleation theory: in the two-step mechanism, the critical nucleus size increases with increases in both concentration and interpeptide interactions, which is in direct contrast with predictions from classical nucleation theory.

Rational design of self-assembly pathways for complex multicomponent structures

Significance Recent experiments have demonstrated that complex, three-dimensional nanostructures can be self-assembled out of thousands of short strands of preprogrammed DNA. However, the mechanism by which robust self-assembly occurs is poorly understood, and the same feat has not yet been achieved using any other molecular building block. Using a new theory of “addressable” self-assembly, we explain how the design of the target structure and the choice of interparticle interactions determine the self-assembly pathway, and, to our knowledge, for the first time predict that a time-dependent protocol, rather than merely a carefully tuned set of conditions, may be necessary to optimize the yield. With an understanding of these design principles, it should be possible to engineer addressable nanostructures using a much wider array of materials. The field of complex self-assembly is moving toward the design of multiparticle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such “addressable complexity,” we need to understand the factors that optimize the yield and the kinetics of self-assembly. Here we use a simple theoretical method to explain the key features responsible for the unexpected success of DNA-brick experiments, which are currently the only demonstration of reliable self-assembly with such a large number of components. Simulations confirm that our theory accurately predicts the narrow temperature window in which error-free assembly can occur. Even more strikingly, our theory predicts that correct assembly of the complete structure may require a time-dependent experimental protocol. Furthermore, we predict that low coordination numbers result in nonclassical nucleation behavior, which we find to be essential for achieving optimal nucleation kinetics under mild growth conditions. We also show that, rather surprisingly, the use of heterogeneous bond energies improves the nucleation kinetics and in fact appears to be necessary for assembling certain intricate 3D structures. This observation makes it possible to sculpt nucleation pathways by tuning the distribution of interaction strengths. These insights not only suggest how to improve the design of structures based on DNA bricks, but also point the way toward the creation of a much wider class of chemical or colloidal structures with addressable complexity.

Light-induced actuating nanotransducers.

Significance Scientists have dreamt of nanomachines that can navigate in water, sense their environment, communicate, and respond. Various power sources and propulsion systems have been proposed but they lack speed, strength, and control. We introduce here a previously undefined paradigm for nanoactuation which is incredibly simple, but solves many problems. It is optically powered (although other modes are also possible), and potentially offers unusually large force/mass. This looks to be widely generalizable, because the actuating nanotransducers can be selectively bound to designated active sites. The concept can underpin a plethora of future designs and already we produce a dramatic optical response over large areas at high speed. Nanoactuators and nanomachines have long been sought after, but key bottlenecks remain. Forces at submicrometer scales are weak and slow, control is hard to achieve, and power cannot be reliably supplied. Despite the increasing complexity of nanodevices such as DNA origami and molecular machines, rapid mechanical operations are not yet possible. Here, we bind temperature-responsive polymers to charged Au nanoparticles, storing elastic energy that can be rapidly released under light control for repeatable isotropic nanoactuation. Optically heating above a critical temperature Tc = 32 °C using plasmonic absorption of an incident laser causes the coatings to expel water and collapse within a microsecond to the nanoscale, millions of times faster than the base polymer. This triggers a controllable number of nanoparticles to tightly bind in clusters. Surprisingly, by cooling below Tc their strong van der Waals attraction is overcome as the polymer expands, exerting nanoscale forces of several nN. This large force depends on van der Waals attractions between Au cores being very large in the collapsed polymer state, setting up a tightly compressed polymer spring which can be triggered into the inflated state. Our insights lead toward rational design of diverse colloidal nanomachines.

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.

Self-Assembly of Structures with Addressable Complexity

The self-assembly of structures with addressable complexity, where every component is distinct and is programmed to occupy a specific location within a target structure, is a promising route to engineering materials with precisely defined morphologies. Because systems with many components are inherently complicated, one might assume that the chances of successful self-assembly are extraordinarily small. Yet recent advances suggest otherwise: addressable structures with hundreds of distinct building blocks have been designed and assembled with nanometer precision. Despite this remarkable success, it is often challenging to optimize a self-assembly reaction to ensure that the intended structure is kinetically accessible. In this Perspective, we focus on the prediction of kinetic pathways for self-assembly and implications for the design of robust experimental protocols. The development of general principles to predict these pathways will enable the engineering of complex materials using a much wider range of building blocks than is currently possible.

Numerical calculation of granular entropy.

We present numerical simulations that allow us to compute the number of ways in which N particles can pack into a given volume V. Our technique modifies the method of Xu, Frenkel, and Liu [Phys. Rev. Lett. 106, 245502 (2011)] and outperforms existing direct enumeration methods by more than 200 orders of magnitude. We use our approach to study the system size dependence of the number of distinct packings of a system of up to 128 polydisperse soft disks. We show that, even though granular particles are distinguishable, we have to include a factor 1=N! to ensure that the entropy does not change when exchanging particles between systems in the same macroscopic state. Our simulations provide strong evidence that the packing entropy, when properly defined, is extensive. As different packings are created with unequal probabilities, it is natural to express the packing entropy as S = − Σ(i)p(i) ln pi − lnN!, where pi denotes the probability to generate the ith packing. We can compute this quantity reliably and it is also extensive. The granular entropy thus (re)defined, while distinct from the one proposed by Edwards [J. Phys. Condens. Matter 2, SA63 (1990)], does have all the properties Edwards assumed.

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.

Communication: Theoretical prediction of free-energy landscapes for complex self-assembly

We present a technique for calculating free-energy profiles for the nucleation of multicomponent structures that contain as many species as building blocks. We find that a key factor is the topology of the graph describing the connectivity of the target assembly. By considering the designed interactions separately from weaker, incidental interactions, our approach yields predictions for the equilibrium yield and nucleation barriers. These predictions are in good agreement with corresponding Monte Carlo simulations. We show that a few fundamental properties of the connectivity graph determine the most prominent features of the assembly thermodynamics. Surprisingly, we find that polydispersity in the strengths of the designed interactions stabilizes intermediate structures and can be used to sculpt the free-energy landscape for self-assembly. Finally, we demonstrate that weak incidental interactions can preclude assembly at equilibrium due to the combinatorial possibilities for incorrect association.

Physical determinants of the self-replication of protein fibrils

The ability of biological molecules to replicate themselves, achieved with the aid of a complex cellular machinery, is the foundation of life. However, a range of aberrant processes involve the self-replication of pathological protein structures without any additional factors. A dramatic example is the autocatalytic replication of pathological protein aggregates, including amyloid fibrils and prions, involved in neurodegenerative disorders. Here, we use computer simulations to identify the necessary requirements for the self-replication of fibrillar assemblies of proteins. We establish that a key physical determinant for this process is the affinity of proteins for the surfaces of fibrils. We find that self-replication can only take place in a very narrow regime of inter-protein interactions, implying a high level of sensitivity to system parameters and experimental conditions. We then compare our theoretical predictions with kinetic and biosensor measurements of fibrils formed from the Aβ peptide associated with Alzheimer’s disease. Our results show a quantitative connection between the kinetics of self-replication and the surface coverage of fibrils by monomeric proteins. These findings reveal the fundamental physical requirements for the formation of supra-molecular structures able to replicate themselves, and shed light on mechanisms in play in the proliferation of protein aggregates in nature.

An enhanced version of the heat exchange algorithm with excellent energy conservation properties

We propose a new algorithm for non-equilibrium molecular dynamics simulations of thermal gradients. The algorithm is an extension of the heat exchange algorithm developed by Hafskjold et al. [Mol. Phys. 80, 1389 (1993); 81, 251 (1994)], in which a certain amount of heat is added to one region and removed from another by rescaling velocities appropriately. Since the amount of added and removed heat is the same and the dynamics between velocity rescaling steps is Hamiltonian, the heat exchange algorithm is expected to conserve the energy. However, it has been reported previously that the original version of the heat exchange algorithm exhibits a pronounced drift in the total energy, the exact cause of which remained hitherto unclear. Here, we show that the energy drift is due to the truncation error arising from the operator splitting and suggest an additional coordinate integration step as a remedy. The new algorithm retains all the advantages of the original one whilst exhibiting excellent energy conservation as illustrated for a Lennard-Jones liquid and SPC/E water.