Dynamics of heteromolecular filament formation

Directionality of growth and kinetics of branched fibril formation

The self-assembly of fibrils is a subject of intense interest, primarily due to its relevance to the formation of pathological structures. Some fibrils develop branches via the so-called secondary nucleation. In this paper, we use the master equation approach to model the kinetics of formation of branched fibrils. In our model, a branched fibril consists of one mother branch and several daughter branches. We consider five basic processes of fibril formation, namely, nucleation, elongation, branching, fragmentation, and dissociation of the primary nucleus of fibrils into free monomers. Our main focus is on the effect of the directionality of growth on the kinetics of fibril formation. We consider several cases. At first, the mother branch may elongate from one or from both ends, while the daughter branch elongates only from one end. We also study the case of branched fibrils with bidirectionally growing daughter branches, tangentially to the main stem, which resembles the intertwining process. We derive a set of ordinary differential equations for the moments of the number concentration of fibrils, which can be solved numerically. Assuming that the primary nucleus of fibrils dissociates with the fragmentation rate, in the limit of the zero branching rate, our model reproduces the results of a previous model that considers only the three basic processes of nucleation, elongation, and fragmentation. We also use the experimental parameters for the fibril formation of Huntingtin fragments to investigate the effect of unidirectional vs bidirectional elongation of the filaments on the kinetics of fibrillogenesis.

Chemical Kinetics for Bridging Molecular Mechanisms and Macroscopic Measurements of Amyloid Fibril Formation

Understanding how normally soluble peptides and proteins aggregate to form amyloid fibrils is central to many areas of modern biomolecular science, ranging from the development of functional biomaterials to the design of rational therapeutic strategies against increasingly prevalent medical conditions such as Alzheimer's and Parkinson's diseases. As such, there is a great need to develop models to mechanistically describe how amyloid fibrils are formed from precursor peptides and proteins. Here we review and discuss how ideas and concepts from chemical reaction kinetics can help to achieve this objective. In particular, we show how a combination of theory, experiments, and computer simulations, based on chemical kinetics, provides a general formalism for uncovering, at the molecular level, the mechanistic steps that underlie the phenomenon of amyloid fibril formation.

Physical principles of filamentous protein self-assembly kinetics

The polymerization of proteins and peptides into filamentous supramolecular structures is an elementary form of self-organization of key importance to the functioning biological systems, as in the case of actin biofilaments that compose the cellular cytoskeleton. Aberrant filamentous protein self-assembly, however, is associated with undesired effects and severe clinical disorders, such as Alzheimer's and Parkinson's diseases, which, at the molecular level, are associated with the formation of certain forms of filamentous protein aggregates known as amyloids. Moreover, due to their unique physicochemical properties, protein filaments are finding extensive applications as biomaterials for nanotechnology. With all these different factors at play, the field of filamentous protein self-assembly has experienced tremendous activity in recent years. A key question in this area has been to elucidate the microscopic mechanisms through which filamentous aggregates emerge from dispersed proteins with the goal of uncovering the underlying physical principles. With the latest developments in the mathematical modeling of protein aggregation kinetics as well as the improvement of the available experimental techniques it is now possible to tackle many of these complex systems and carry out detailed analyses of the underlying microscopic steps involved in protein filament formation. In this paper, we review some classical and modern kinetic theories of protein filament formation, highlighting their use as a general strategy for quantifying the molecular-level mechanisms and transition states involved in these processes.