Ghag G, Ghosh P, Mauro A, Rangachari V, Vaidya A
Department of Chemistry and Biochemistry, University of Southern Mississippi, 118 College Dr, # 5043, Hattiesburg, MS 39406, United States.
Department of Computer Science, Virginia Commonwealth University, Richmond, VA 23220, United States.
Appl Math Comput. 2013 Nov 1;224:205-215. doi: 10.1016/j.amc.2013.08.053.
Protein misfolding and concomitant aggregation towards amyloid formation is the underlying biochemical commonality among a wide range of human pathologies. Amyloid formation involves the conversion of proteins from their native monomeric states (intrinsically disordered or globular) to well-organized, fibrillar aggregates in a nucleation-dependent manner. Understanding the mechanism of aggregation is important not only to gain better insight into amyloid pathology but also to simulate and predict molecular pathways. One of the main impediments in doing so is the stochastic nature of interactions that impedes thorough experimental characterization and the development of meaningful insights. In this study, we have utilized a well-known intermediate state along the amyloid- peptide aggregation pathway called as a model system to investigate the molecular mechanisms by which they form fibrils using stability and perturbation analysis. Investigation of protofibril aggregation mechanism limits both the number of species to be modeled (monomers, and protofibrils), as well as the reactions to two (elongation by monomer addition, and protofibril-protofibril lateral association). Our new model is a reduced order four species model grounded in mass action kinetics. Our prior study required 3200 reactions, which makes determining the reaction parameters prohibitively difficult. Using this model, along with a linear perturbation argument, we rigorously determine stable ranges of rate constants for the reactions and ensure they are physically meaningful. This was accomplished by finding the ranges in which the perturbations dieout in a five-parameter sweep, which includes the monomer and protofibril equilibrium concentrations and three of the rate constants. The results presented are a proof-of-concept method in determining meaningful rate constants that can be used as a bonafide way for determining accurate rate constants for other models involving complex biological reactions such as amyloid aggregation.
蛋白质错误折叠以及随之而来的向淀粉样蛋白形成的聚集是多种人类疾病潜在的生化共性。淀粉样蛋白形成涉及蛋白质从其天然单体状态（内在无序或球状）以成核依赖的方式转变为组织良好的纤维状聚集体。了解聚集机制不仅对于更好地洞察淀粉样蛋白病理学很重要，而且对于模拟和预测分子途径也很重要。这样做的主要障碍之一是相互作用的随机性，这阻碍了全面的实验表征和有意义见解的发展。在本研究中，我们利用了淀粉样肽聚集途径中一个著名的中间状态作为模型系统，通过稳定性和微扰分析来研究它们形成纤维的分子机制。对原纤维聚集机制的研究将需要建模的物种数量限制为两种（单体和原纤维），反应也限制为两种（通过单体添加进行延伸以及原纤维 - 原纤维横向缔合）。我们的新模型是一个基于质量作用动力学的降阶四物种模型。我们之前的研究需要3200个反应，这使得确定反应参数极其困难。使用这个模型，结合线性微扰论证，我们严格确定了反应速率常数的稳定范围，并确保它们在物理上是有意义的。这是通过在一个五参数扫描中找到微扰消失的范围来实现的，该扫描包括单体和原纤维的平衡浓度以及三个速率常数。所呈现的结果是一种概念验证方法，用于确定有意义的速率常数，可作为确定其他涉及复杂生物反应（如淀粉样蛋白聚集）模型准确速率常数的可靠方法。
