Search

Abstract Background Proteins search along the DNA for targets, such as transcription initiation sequences, according to one-dimensional diffusion, which is interrupted by micro- and macro-hopping events and intersegmental transfers that occur under close packing conditions. Results A one-dimensional diffusion-reaction model in the form of difference-differential equations is proposed to analyze the nonequilibrium protein sliding kinetics along a segment of bacterial DNA. A renormalization approach is used to derive an expression for the mean first-passage time to arrive at sites downstream of the origin from the occupation probabilities given by the individual transport equations. Monte Carlo simulations are employed to assess the validity of the proposed approach, and all results are interpreted within the context of bacterial transcription. Conclusions Mean first-passage times decrease with increasing reaction rates, indicating that, on average, surviving proteins more rapidly locate downstream targets than their reaction-free counterparts, but at the price of increasing rarity. Two qualitatively different screening regimes are identified according to whether the search process operates under “small” or “large” values for the dissociation rate of the protein-DNA complex. Lower bounds are placed on the overall search time for varying reactive conditions. Good agreement with experimental estimates requires the reaction rate reside near the transition between both screening regimes, suggesting that biology balances a need for rapid searches against maximum exploration during each round of the sliding phase.

Abstract Background In all amyloid diseases, protein aggregates have been implicated fully or partly, in the etiology of the disease. Due to their significance in human pathologies, there have been unprecedented efforts towards physiochemical understanding of aggregation and amyloid formation over the last two decades. An important relation from which hydrodynamic radii of the aggregate is routinely measured is the classic Stokes-Einstein equation. Here, we report a modification in the classical Stokes-Einstein equation using a mixture theory approach, in order to accommodate the changes in viscosity of the solvent due to the changes in solute size and shape, to implement a more realistic model for Aβ aggregation involved in Alzheimer’s disease. Specifically, we have focused on validating this model in protofibrill lateral association reactions along the aggregation pathway, which has been experimentally well characterized. Results The modified Stokes-Einstein equation incorporates an effective viscosity for the mixture consisting of the macromolecules and solvent where the lateral association reaction occurs. This effective viscosity is modeled as a function of the volume fractions of the different species of molecules. The novelty of our model is that in addition to the volume fractions, it incorporates previously published reports on the dimensions of the protofibrils and their aggregates to formulate a more appropriate shape rather than mere spheres. The net result is that the diffusion coefficient which is inversely proportional to the viscosity of the system is now dependent on the concentration of the different molecules as well as their proper shapes. Comparison with experiments for variations in diffusion coefficients over time reveals very similar trends. Conclusions We argue that the standard Stokes-Einstein’s equation is insufficient to understand the temporal variations in diffusion when trying to understand the aggregation behavior of Aβ42 proteins. Our modifications also involve inclusion of improved shape factors of molecules and more appropriate viscosities. The modification we are reporting is not only useful in Aβ aggregation but also will be important for accurate measurements in all protein aggregation systems.

Abstract Background The aggregates of a protein called, ‘Aβ’ found in brains of Alzheimer’s patients are strongly believed to be the cause for neuronal death and cognitive decline. Among the different forms of Aβ aggregates, smaller aggregates called ‘soluble oligomers’ are increasingly believed to be the primary neurotoxic species responsible for early synaptic dysfunction. Since it is well known that the Aβ aggregation is a nucleation dependant process, it is widely believed that the toxic oligomers are intermediates to fibril formation, or what we call the ‘on-pathway’ products. Modeling of Aβ aggregation has been of intense investigation during the last decade. However, precise understanding of the process, pre-nucleation events in particular, are not yet known. Most of these models are based on curve-fitting and overlook the molecular-level biophysics involved in the aggregation pathway. Hence, such models are not reusable, and fail to predict the system dynamics in the presence of other competing pathways. Results In this paper, we present a molecular-level simulation model for understanding the dynamics of the amyloid-β (Aβ) peptide aggregation process involved in Alzheimer’s disease (AD). The proposed chemical kinetic theory based approach is generic and can model most nucleation-dependent protein aggregation systems that cause a variety of neurodegenerative diseases. We discuss the challenges in estimating all the rate constants involved in the aggregation process towards fibril formation and propose a divide and conquer strategy by dissecting the pathway into three biophysically distinct stages: 1) pre-nucleation stage 2) post-nucleation stage and 3) protofibril elongation stage. We next focus on estimating the rate constants involved in the protofibril elongation stages for Aβ42 supported by in vitro experimental data. This elongation stage is further characterized by elongation due to oligomer additions and lateral association of protofibrils (13) and to properly validate the rate constants involved in these phases we have presented three distinct reaction models. We also present a novel scheme for mapping the fluorescence sensitivity and dynamic light scattering based in vitro experimental plots to estimates of concentration variation with time. Finally, we discuss how these rate constants will be incorporated into the overall simulation of the aggregation process to identify the parameters involved in the complete Aβ pathway in a bid to understand its dynamics. Conclusions We have presented an instance of the top-down modeling paradigm where the biophysical system is approximated by a set of reactions for each of the stages that have been modeled. In this paper, we have only reported the kinetic rate constants of the fibril elongation stage that were validated by in vitro biophysical analyses. The kinetic parameters reported in the paper should be at least accurate upto the first two decimal places of the estimate. We sincerely believe that our top-down models and kinetic parameters will be able to accurately model the biophysical phenomenon of Aβ protein aggregation and identify the nucleation mass and rate constants of all the stages involved in the pathway. Our model is also reusable and will serve as the basis for making computational predictions on the system dynamics with the incorporation of other competing pathways introduced by lipids and fatty acids.