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Ghosh D, Biswas A, Radhakrishna M. Advanced computational approaches to understand protein aggregation. BIOPHYSICS REVIEWS 2024; 5:021302. [PMID: 38681860 PMCID: PMC11045254 DOI: 10.1063/5.0180691] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2023] [Accepted: 03/18/2024] [Indexed: 05/01/2024]
Abstract
Protein aggregation is a widespread phenomenon implicated in debilitating diseases like Alzheimer's, Parkinson's, and cataracts, presenting complex hurdles for the field of molecular biology. In this review, we explore the evolving realm of computational methods and bioinformatics tools that have revolutionized our comprehension of protein aggregation. Beginning with a discussion of the multifaceted challenges associated with understanding this process and emphasizing the critical need for precise predictive tools, we highlight how computational techniques have become indispensable for understanding protein aggregation. We focus on molecular simulations, notably molecular dynamics (MD) simulations, spanning from atomistic to coarse-grained levels, which have emerged as pivotal tools in unraveling the complex dynamics governing protein aggregation in diseases such as cataracts, Alzheimer's, and Parkinson's. MD simulations provide microscopic insights into protein interactions and the subtleties of aggregation pathways, with advanced techniques like replica exchange molecular dynamics, Metadynamics (MetaD), and umbrella sampling enhancing our understanding by probing intricate energy landscapes and transition states. We delve into specific applications of MD simulations, elucidating the chaperone mechanism underlying cataract formation using Markov state modeling and the intricate pathways and interactions driving the toxic aggregate formation in Alzheimer's and Parkinson's disease. Transitioning we highlight how computational techniques, including bioinformatics, sequence analysis, structural data, machine learning algorithms, and artificial intelligence have become indispensable for predicting protein aggregation propensity and locating aggregation-prone regions within protein sequences. Throughout our exploration, we underscore the symbiotic relationship between computational approaches and empirical data, which has paved the way for potential therapeutic strategies against protein aggregation-related diseases. In conclusion, this review offers a comprehensive overview of advanced computational methodologies and bioinformatics tools that have catalyzed breakthroughs in unraveling the molecular basis of protein aggregation, with significant implications for clinical interventions, standing at the intersection of computational biology and experimental research.
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Affiliation(s)
- Deepshikha Ghosh
- Department of Biological Sciences and Engineering, Indian Institute of Technology (IIT) Gandhinagar, Palaj, Gujarat 382355, India
| | - Anushka Biswas
- Department of Chemical Engineering, Indian Institute of Technology (IIT) Gandhinagar, Palaj, Gujarat 382355, India
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Michaels TCT, Lazell HW, Arosio P, Knowles TPJ. Dynamics of protein aggregation and oligomer formation governed by secondary nucleation. J Chem Phys 2016; 143:054901. [PMID: 26254664 DOI: 10.1063/1.4927655] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
The formation of aggregates in many protein systems can be significantly accelerated by secondary nucleation, a process where existing assemblies catalyse the nucleation of new species. In particular, secondary nucleation has emerged as a central process controlling the proliferation of many filamentous protein structures, including molecular species related to diseases such as sickle cell anemia and a range of neurodegenerative conditions. Increasing evidence suggests that the physical size of protein filaments plays a key role in determining their potential for deleterious interactions with living cells, with smaller aggregates of misfolded proteins, oligomers, being particularly toxic. It is thus crucial to progress towards an understanding of the factors that control the sizes of protein aggregates. However, the influence of secondary nucleation on the time evolution of aggregate size distributions has been challenging to quantify. This difficulty originates in large part from the fact that secondary nucleation couples the dynamics of species distant in size space. Here, we approach this problem by presenting an analytical treatment of the master equation describing the growth kinetics of linear protein structures proliferating through secondary nucleation and provide closed-form expressions for the temporal evolution of the resulting aggregate size distribution. We show how the availability of analytical solutions for the full filament distribution allows us to identify the key physical parameters that control the sizes of growing protein filaments. Furthermore, we use these results to probe the dynamics of the populations of small oligomeric species as they are formed through secondary nucleation and discuss the implications of our work for understanding the factors that promote or curtail the production of these species with a potentially high deleterious biological activity.
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Affiliation(s)
- Thomas C T Michaels
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Hamish W Lazell
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Paolo Arosio
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Tuomas P J Knowles
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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Shoffner SK, Schnell S. Estimation of the lag time in a subsequent monomer addition model for fibril elongation. Phys Chem Chem Phys 2016; 18:21259-68. [DOI: 10.1039/c5cp07845h] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
The lag time for dock–lock fibril elongation can be estimated from kinetic parameters.
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Affiliation(s)
- Suzanne K. Shoffner
- Department of Molecular & Integrative Physiology
- University of Michigan Medical School
- Ann Arbor
- USA
| | - Santiago Schnell
- Department of Molecular & Integrative Physiology
- University of Michigan Medical School
- Ann Arbor
- USA
- Department of Computational Medicine & Bioinformatics
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Michaels TCT, Garcia GA, Knowles TPJ. Asymptotic solutions of the Oosawa model for the length distribution of biofilaments. J Chem Phys 2014; 140:194906. [PMID: 24852562 DOI: 10.1063/1.4875897] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
Nucleated polymerisation phenomena are general linear growth processes that underlie the formation of a range of biofilaments in nature, including actin and tubulin that are key components of the cellular cytoskeleton. The conventional theoretical framework for describing this process is the Oosawa model that takes into account homogeneous nucleation coupled to linear growth. In his original work, Oosawa provided an analytical solution to the total mass concentration of filaments; the time evolution of the full length distribution has, however, been challenging to access, in large part due to the nonlinear nature of the rate equations inherent in the description of such phenomena and to date analytical solutions for the filament distribution are known only in certain special cases. Here, by exploiting a technique based on the method of matched asymptotics, we present an analytical treatment of the Oosawa model that describes the shape of the length distribution of biofilaments reversibly growing through primary nucleation and filament elongation. Our work highlights the power of matched asymptotics for obtaining closed-form analytical solutions to nonlinear master equations in biophysics and allows us to identify the key time scales that characterize biological polymerization processes.
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Affiliation(s)
- Thomas C T Michaels
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Gonzalo A Garcia
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Tuomas P J Knowles
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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Morris AM, Watzky MA, Finke RG. Protein aggregation kinetics, mechanism, and curve-fitting: A review of the literature. BIOCHIMICA ET BIOPHYSICA ACTA-PROTEINS AND PROTEOMICS 2009; 1794:375-97. [DOI: 10.1016/j.bbapap.2008.10.016] [Citation(s) in RCA: 507] [Impact Index Per Article: 33.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2008] [Revised: 10/17/2008] [Accepted: 10/27/2008] [Indexed: 11/25/2022]
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Morris AM, Watzky MA, Agar JN, Finke RG. Fitting neurological protein aggregation kinetic data via a 2-step, minimal/"Ockham's razor" model: the Finke-Watzky mechanism of nucleation followed by autocatalytic surface growth. Biochemistry 2008; 47:2413-27. [PMID: 18247636 DOI: 10.1021/bi701899y] [Citation(s) in RCA: 216] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The aggregation of proteins has been hypothesized to be an underlying cause of many neurological disorders including Alzheimer's, Parkinson's, and Huntington's diseases; protein aggregation is also important to normal life function in cases such as G to F-actin, glutamate dehydrogenase, and tubulin and flagella formation. For this reason, the underlying mechanism of protein aggregation, and accompanying kinetic models for protein nucleation and growth (growth also being called elongation, polymerization, or fibrillation in the literature), have been investigated for more than 50 years. As a way to concisely present the key prior literature in the protein aggregation area, Table 1 in the main text summarizes 23 papers by 10 groups of authors that provide 5 basic classes of mechanisms for protein aggregation over the period from 1959 to 2007. However, and despite this major prior effort, still lacking are both (i) anything approaching a consensus mechanism (or mechanisms), and (ii) a generally useful, and thus widely used, simplest/"Ockham's razor" kinetic model and associated equations that can be routinely employed to analyze a broader range of protein aggregation kinetic data. Herein we demonstrate that the 1997 Finke-Watzky (F-W) 2-step mechanism of slow continuous nucleation, A --> B (rate constant k1), followed by typically fast, autocatalytic surface growth, A + B --> 2B (rate constant k2), is able to quantitatively account for the kinetic curves from all 14 representative data sets of neurological protein aggregation found by a literature search (the prion literature was largely excluded for the purposes of this study in order provide some limit to the resultant literature that was covered). The F-W model is able to deconvolute the desired nucleation, k1, and growth, k2, rate constants from those 14 data sets obtained by four different physical methods, for three different proteins, and in nine different labs. The fits are generally good, and in many cases excellent, with R2 values >or=0.98 in all cases. As such, this contribution is the current record of the widest set of protein aggregation data best fit by what is also the simplest model offered to date. Also provided is the mathematical connection between the 1997 F-W 2-step mechanism and the 2000 3-step mechanism proposed by Saitô and co-workers. In particular, the kinetic equation for Saitô's 3-step mechanism is shown to be mathematically identical to the earlier, 1997 2-step F-W mechanism under the 3 simplifying assumptions Saitô and co-workers used to derive their kinetic equation. A list of the 3 main caveats/limitations of the F-W kinetic model is provided, followed by the main conclusions from this study as well as some needed future experiments.
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Affiliation(s)
- Aimee M Morris
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
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Abstract
Given a set of kinetic data, then, the preceding discussions suggest the following approach to its analysis. 1. For purposes of establishing the reaction, ignore the final stages and concentrate on the initial 10-20% of the reaction at first. A globally optimized model may be based on a faulty assumption for the initial steps. Thus, although the whole data set may look reasonably well fit, the reaction could be misrepresented, and thus the fit unhelpful if accuracy at the later stages has come at the expense of the initial phase of the reaction. 2. What is the time course of the initial reaction? (A) Is the reaction exponential? Exponential growth gives dramatic lag times (see Fig. 3), whereas nonexponential "lag times" have a visible signal from time 0 (i.e., Fig. 2). If the data set shows the abrupt appearance of signals after a period of quiescence, the chances are excellent that the time course is exponential. High sensitivity measurement of the signal at times during the lag phase should be used to confirm the exponential nature quantitatively. Exponential reactions mean a secondary pathway is operative. (a) A cascade (tn) can look similar to an exponential, but may proceed from a multistep single-path reaction. Thus the exponential needs to be ascertained with some accuracy. (b) It is possible that some or all of the lag results from a stochastic process, i.e., formation of a single nucleus being observed. This, however, is likely to be accompanied by a secondary process, as few techniques are sensitive enough to detect a single polymer at a time, and having one nucleus form many polymers is a hallmark of a secondary process. Thus, the reproducibility of the kinetics must be established to rule out stochastics. If data show wide variation, stochastic methods as described earlier may be employed. (c) Given a secondary process, one must separate the primary nucleation process from the secondary process (by stochastic means or by use of the product B2A, as described earlier). (B) If the reaction does not begin with an exponential, is it parabolic? If so, it falls in the general class of linear polymerizations. 3. What is the concentration dependence of the reaction(s)? This will separate nucleation processes from growth, and so on. 4. If the initial reaction is neither exponential nor parabolic, a reaction mechanism needs to be proposed and evaluated. Solving the resulting equations is best done by linearization, which has the best chance of giving equations whose solutions and their sensitivity to parameters are readily understood. If this proves fruitful, full numeric solutions may be useful. 5. At this point, the full reaction may be considered to completion. 6. The physical basis of the description (sizes of parameters and their dependencies) needs to be finally considered to ensure that the mathematical success of the description rests on tenable physical grounds.
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Affiliation(s)
- F Ferrone
- Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA
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Bhattacharjee B, Rangarajan S. Multicomponent multilayer random irreversible deposition model. J Electroanal Chem (Lausanne) 1994. [DOI: 10.1016/0022-0728(93)03187-t] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Zhou HX, Ferrone FA. Theoretical description of the spatial dependence of sickle hemoglobin polymerization. Biophys J 1990; 58:695-703. [PMID: 2207259 PMCID: PMC1281010 DOI: 10.1016/s0006-3495(90)82412-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
We have generalized the double nucleation mechanism of Ferrone et al. (Ferrone, F. A., J. Hofrichter, H. Sunshine, and W. A. Eaton. 1980. Biophys. J. 32:361-377; Ferrone, F. A., J. Hofrichter, and W. A. Eaton. 1985. J. Mol. Biol. 183:611-631) to describe the spatial dependence of the radial growth of polymer domains of sickle hemoglobin. Although this extended model requires the consideration of effects such as monomer diffusion, which are irrelevant to a spatially uniform description, no new adjustable parameters are required because diffusion constants are known independently. We find that monomer diffusion into the growing domain can keep the net unpolymerized monomer concentration approximately constant, and in that limit we present an analytic solution of the model. The model shows the features reported by Basak, S., F. A. Ferrone, and J. T. Wang (1988. Biophys J. 54:829-843) and provides a new means of determining the rate of polymer growth. When spatially integrated, the model exhibits the exponential growth seen in previous studies, although molecular parameters derived from analysis of the kinetics assuming uniformity must be modified in some cases to account for the spatially nonuniform growth. The model developed here can be easily adapted to any spatially dependent polymerization process.
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Affiliation(s)
- H X Zhou
- Department of Physics and Atmospheric Science, Drexel University, Philadelphia, Pennsylvania 19104
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Firestone MP, de Levie R, Rangarajan SK. On one-dimensional nucleation and growth of "living" polymers I. Homogeneous nucleation. J Theor Biol 1983; 104:535-52. [PMID: 6645560 DOI: 10.1016/0022-5193(83)90244-8] [Citation(s) in RCA: 29] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
The kinetics of one-dimensional polymerization are described in terms of successive monomer additions. During homogeneous nucleation, the concentration cn of critical nuclei is proportional to the nth power of monomer concentration c1 and, initially, to the (n - 1)th power of time.
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