Brownian Dynamics is the designated technique to simulate the collective dynamics of colloidal particles suspended in a solution, e.g., the self-assembly of patchy particles. Simulating the rotational dynamics of anisotropic particles by a first-order Langevin equation, however, gives rise to a number of complications, ranging from singularities when using a set of three rotational coordinates to subtle metric and drift corrections. Here, we derive and numerically validate a quaternion-based Rotational Brownian Dynamics algorithm that handles these complications in a simple and elegant way. The extension to hydrodynamic interactions is also discussed.

Water is known to play an important role in collagen self-assembly, but it is still largely unclear how water–collagen interactions influence the assembly process and determine the fibril network properties. Here, we use the H 2 O/D 2 O isotope effect on the hydrogen-bond strength in water to investigate the role of hydration in collagen self-assembly. We dissolve collagen in H 2 O and D 2 O and compare the growth kinetics and the structure of the collagen assemblies formed in these water isotopomers. Surprisingly, collagen assembly occurs ten times faster in D 2 O than in H 2 O, and collagen in D 2 O self-assembles into much thinner fibrils, that form a more inhomogeneous and softer network, with a fourfold reduction in elastic modulus when compared to H 2 O. Combining spectroscopic measurements with atomistic simulations, we show that collagen in D 2 O is less hydrated than in H 2 O. This partial dehydration lowers the enthalpic penalty for water removal and reorganization at the collagen–water interface, increasing the self-assembly rate and the number of nucleation centers, leading to thinner fibrils and a softer network. Coarse-grained simulations show that the acceleration in the initial nucleation rate can be reproduced by the enhancement of electrostatic interactions. These results show that water acts as a mediator between collagen monomers, by modulating their interactions so as to optimize the assembly process and, thus, the final network properties. We believe that isotopically modulating the hydration of proteins can be a valuable method to investigate the role of water in protein structural dynamics and protein self-assembly.

Collagen is the most abundant protein in the human body and plays an essential role in determining the mechanical properties of the tissues. Both as a monomeric protein and in fibrous assemblies, collagen interacts with its surrounding molecules, in particular with water. Interestingly, while it is well established that the interaction with water strongly influences the molecular and mechanical properties of collagen and its assemblies, the underlying mechanisms remain largely unknown. Here, we review the research conducted over the past 30 years on the interplay between water and collagen and its relevance for tissue properties. We discuss the water-collagen interaction on relevant time- and length scales, ranging from the vital role of water in stabilizing the characteristic triple helix structure to the negative impact of dehydration on the mechanical properties of tissues. A better understanding of the water-collagen interaction will help to unravel the effect of mutations and defective collagen production in collagen-related diseases and to pinpoint the key design features required to synthesize collagen-based biomimetic tissues with tailored mechanical properties.

Particles in simulations are traditionally endowed with fixed interactions. While this is appropriate for particles representing atoms or molecules, objects with significant internal dynamics—like sequences of amino acids or even an entire protein—are poorly modelled by invariable particles. We develop a highly coarse grained polymorph patchy particle with the ultimate aim of simulating proteins as chains of particles at the secondary structure level. Conformational changes, e.g., a transition between disordered and β-sheet states, are accommodated by internal coordinates that determine the shape and interaction characteristics of the particles. The internal coordinates, as well as the particle positions and orientations, are propagated by Brownian Dynamics in response to their local environment. As an example of the potential offered by polymorph particles, we model the amyloidogenic intrinsically disordered protein α-synuclein, involved in Parkinson’s disease, as a single particle with two internal states. The simulations yield oligomers of particles in the disordered state and fibrils of particles in the “misfolded” cross-β-sheet state. The aggregation dynamics is complex, as aggregates can form by a direct nucleation-and-growth mechanism and by two-step-nucleation through conversions between the two cluster types. The aggregation dynamics is complex, with fibrils formed by direct nucleation-and-growth, by two-step-nucleation through the conversion of an oligomer and by auto-catalysis of this conversion.