Dynamical Signatures of Multifunnel Energy Landscapes

Wales, David J.

doi:10.1021/acs.jpclett.2c01258

Cited by 17 publications

(33 citation statements)

References 61 publications

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“…All the distributions are approximately Poissonian, suggesting that the transitions to the N* states do not involve any long-lived intermediates, and the underlying kinetics can be appropriately described by a two-state model. To further assess the validity of the two-state kinetics, we analyzed the log(τ FPT ) distributions, which can resolve signatures corresponding to multiple relaxation time scales ( 70 ). For both Aβ40 and Aβ42, the log(τ FPT ) distributions are largely unimodal and can be fit using single Gaussian functions (figs.…”

Section: Resultsmentioning

confidence: 99%

Energy landscapes of Aβ monomers are sculpted in accordance with Ostwald’s rule of stages

2023

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The transition from a disordered to an assembly-competent monomeric state (N*) in amyloidogenic sequences is a crucial event in the aggregation cascade. Using a well-calibrated model for intrinsically disordered proteins (IDPs), we show that the N* states, which bear considerable resemblance to the polymorphic fibril structures found in experiments, not only appear as excitations in the free energy landscapes of Aβ40 and Aβ42, but also initiate the aggregation cascade. For Aβ42, the transitions to the different N* states are in accord with Ostwald’s rule of stages, with the least stable structures forming ahead of thermodynamically favored ones. The Aβ40 and Aβ42 monomer landscapes exhibit different extents of local frustration, which we show have profound implications in dictating subsequent self-assembly. Using kinetic transition networks, we illustrate that the most favored dimerization routes proceed via N* states. We argue that Ostwald’s rule also holds for the aggregation of fused in sarcoma and polyglutamine proteins.

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Section: Resultsmentioning

confidence: 99%

Energy landscapes of Aβ monomers are sculpted in accordance with Ostwald’s rule of stages

2023

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“…where {−λ ,S } are the eigenvalues of Q S , so that λ ,S > 0, and w R ,S and w L ,S are the corresponding right (column) and left (row) eigenvectors. The logarithmic time distribution clearly shows distinct peaks for competing pathways [30,33,63]. The probability vector P S (0) has dimension |S| but the elements are non-zero only for source states in B.…”

Section: (A) First Passage Time Distributionsmentioning

confidence: 99%

Analysing ill-conditioned Markov chains

Woods

Kannan

Sharpe

et al. 2023

Phil. Trans. R. Soc. A.

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Discrete state Markov chains in discrete or continuous time are widely used to model phenomena in the social, physical and life sciences. In many cases, the model can feature a large state space, with extreme differences between the fastest and slowest transition timescales. Analysis of such ill-conditioned models is often intractable with finite precision linear algebra techniques. In this contribution, we propose a solution to this problem, namely partial graph transformation, to iteratively eliminate and renormalize states, producing a low-rank Markov chain from an ill-conditioned initial model. We show that the error induced by this procedure can be minimized by retaining both the renormalized nodes that represent metastable superbasins, and those through which reactive pathways concentrate, i.e. the dividing surface in the discrete state space. This procedure typically returns a much lower rank model, where trajectories can be efficiently generated with kinetic path sampling. We apply this approach to an ill-conditioned Markov chain for a model multi-community system, measuring the accuracy by direct comparison with trajectories and transition statistics. This article is part of a discussion meeting issue ‘Supercomputing simulations of advanced materials’.

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“…Hierarchical metamaterials (HMMs) endowed with complex architectures and multi-component compositions have drawn much attention in the scientific community. [1][2][3][4] This is because the very existence of designed (intra-material and material-environment) interfaces with specific properties makes HMMs superior to simpler, often single-component, materials. The list of actual applications of HMMs is enormous, with the most relevant ones being biotechnology, 5,6 sensors [7][8][9] and biosensors, 10,11 energy harvesting systems, 12,13 nanomedicine, 14,15 photocatalysis 16 and chemical catalysis, 17,18 hydrogen energy, 19 water purification, 20 environmental protection 21 and space exploration.…”

Section: Introductionmentioning

confidence: 99%