Stochastic Lag Time in Nucleated Linear Self-Assembly

Protein aggregation is of great importance in biology, e.g., in amyloid fibrillation. The aggregation processes that occur at the cellular scale must be highly stochastic in nature because of the statistical number fluctuations that arise on account of the small system size at the cellular scale. We study the nucleated reversible self-assembly of monomeric building blocks into polymer-like aggregates using the method of kinetic Monte Carlo. Kinetic Monte Carlo, being inherently stochastic, allows us to study the impact of fluctuations on the polymerisation reactions. One of the most important characteristic features in this kind of problem is the existence of a lag phase before self-assembly takes off, which is what we focus attention on. We study the associated lag time as a function of the system size and kinetic pathway. We find that the leading order stochastic contribution to the lag time before polymerisation commences is inversely proportional to the system volume for large-enough system size for all nine reaction pathways tested. Finite-size corrections to this do depend on the kinetic pathway

Information Content in Data Sets for a Nucleated-Polymerization Model

We illustrate the use of tools (asymptotic theories of standard error quantification using appropriate statistical models, bootstrapping, model comparison techniques) in addition to sensitivity that may be employed to determine the information content in data sets. We do this in the context of recent models [23] for nucleated polymerization in proteins, about which very little is known regarding the underlying mechanisms; thus the methodology we develop here may be of great help to experimentalists

High-order WENO scheme for Polymerization-type equations

Polymerization of proteins is a biochimical process involved in different diseases. Mathematically, it is generally modeled by aggregation-fragmentation-type equations. In this paper we consider a general polymerization model and propose a high-order numerical scheme to investigate the behavior of the solution. An important property of the equation is the mass conservation. The fifth-order WENO scheme is built to preserve the total mass of proteins along time

Characterization of Oligomers of Heterogeneous Size as Precursors of Amyloid Fibril Nucleation of an SH3 Domain: An Experimental Kinetics Study

Correction: Characterization of Oligomers of Heterogeneous Size as Precursors of Amyloid Fibril Nucleation of an SH3 Domain: An Experimental Kinetics Study. PLoS ONE 9(1): 10.1371/annotation/dbb84118-9ada-43e4-8734-8f8322be1a59. doi: 10.1371/annotation/dbb84118-9ada-43e4-8734-8f8322be1a59Understanding the earliest molecular events during nucleation of the amyloid aggregation cascade is of fundamental significance to prevent amyloid related disorders. We report here an experimental kinetic analysis of the amyloid aggregation of the N47A mutant of the α-spectrin SH3 domain (N47A Spc-SH3) under mild acid conditions, where it is governed by rapid formation of amyloid nuclei. The initial rates of formation of amyloid structures, monitored by thioflavine T fluorescence at different protein concentrations, agree quantitatively with high-order kinetics, suggesting an oligomerization pre-equilibrium preceding the rate-limiting step of amyloid nucleation. The curves of native state depletion also follow high-order irreversible kinetics. The analysis is consistent with the existence of low-populated and heterogeneous oligomeric precursors of fibrillation that form by association of partially unfolded protein monomers. An increase in NaCl concentration accelerates fibrillation but reduces the apparent order of the nucleation kinetics; and a double mutant (K43A, N47A) Spc-SH3 domain, largely unfolded under native conditions and prone to oligomerize, fibrillates with apparent first order kinetics. On the light of these observations, we propose a simple kinetic model for the nucleation event, in which the monomer conformational unfolding and the oligomerization of an amyloidogenic intermediate are rapidly pre-equilibrated. A conformational change of the polypeptide chains within any of the oligomers, irrespective of their size, is the rate-limiting step leading to the amyloid nuclei. This model is able to explain quantitatively the initial rates of aggregation and the observed variations in the apparent order of the kinetics and, more importantly, provides crucial thermodynamic magnitudes of the processes preceding the nucleation. This kinetic approach is simple to use and may be of general applicability to characterize the amyloidogenic intermediates and oligomeric precursors of other disease-related proteins.This work was financed by the Andalucía Government (grant FQM-02838), the Spanish Ministry of Science and Innovation (grant BIO2009-07317), and the European Regional Development Fund of the European Union. D. Ruzafa is recipient of a research fellowship from the F.P.U. program of the Spanish Ministry of Education. L. Varela is financed by the G.R.E.I.B. program of the University of Granada

Kinetics of spontaneous filament nucleation via oligomers: Insights from theory and simulation

Nucleation processes are at the heart of a large number of phenomena, from cloud formation to protein crystallization. A recently emerging area where nucleation is highly relevant is the initiation of filamentous protein self-assembly, a process that has broad implications in many research areas ranging from medicine to nanotechnology. As such, spontaneous nucleation of protein fibrils has received much attention in recent years with many theoretical and experimental studies focussing on the underlying physical principles. In this paper we make a step forward in this direction and explore the early time behaviour of filamentous protein growth in the context of nucleation theory. We first provide an overview of the thermodynamics and kinetics of spontaneous nucleation of protein filaments in the presence of one relevant degree of freedom, namely the cluster size. In this case, we review how key kinetic observables, such as the reaction order of spontaneous nucleation, are directly related to the physical size of the critical nucleus. We then focus on the increasingly prominent case of filament nucleation that includes a conformational conversion of the nucleating building-block as an additional slow step in the nucleation process. Using computer simulations, we study the concentration dependence of the nucleation rate. We find that, under these circumstances, the reaction order of spontaneous nucleation with respect to the free monomer does no longer relate to the overall physical size of the nucleating aggregate but rather to the portion of the aggregate that actively participates in the conformational conversion. Our results thus provide a novel interpretation of the common kinetic descriptors of protein filament formation, including the reaction order of the nucleation step or the scaling exponent of lag times, and put into perspective current theoretical descriptions of protein aggregation.We acknowledge support from the Human Frontier Science Program and Emmanuel College (A.Š.), St John’s and Peterhouse Colleges (T.C.T.M.), the Swiss National Science Foundation (T.C.T.M.), the Biotechnology and Biological Sciences Research Council (T.P.J.K.), the Frances and Augustus Newman Foundation (T.P.J.K.), the European Research Council (T.C.T.M., T.P.J.K., and D.F.), and the Engineering and Physical Sciences Research Council (D.F.)