Spectral clustering of Markov chain transition matrices with complex eigenvalues

Frank, Anna-Simone; Sikorski, Alexander; Röblitz, Susanna

doi:10.48550/arxiv.2206.14537

Cited by 3 publications

(5 citation statements)

References 19 publications

(49 reference statements)

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“…(ii) As in Li et al (2021), we applied a PCCA type algorithm to partition the state space into fewer metastable states. The algorithm, as described in Frank et al (2022), was extended to also deal with irreversible Markov chains, which makes it applicable to a wider range of biological processes. (iii) Instead of applying TPT on all micro-states as in Li et al (2021), we adapted a coarse-grained version of TPT only between the identified phenotypes, which is less computational intensive.…”

Section: Discussionmentioning

confidence: 99%

“…The Matlab code (macro-tpt Frank and Röblitz ( 2022)) for all presented cases is available on GitHub (https://github.com/a-sfrank/macro-tpt.git). The cPCCA+ Matlab code, as described in Frank et al (2022), was downloaded from GitHub (https://github.com/sroeblitz/cPCCA.git), adapted and integrated into our implementation.…”

Section: Credit Authorship Contribution Statementmentioning

confidence: 99%

“…Appendix includes more details on the methods, additional figures and tables describing our results. Matlab code (macro-tpt Frank and Röblitz (2022)) to reproduce the results from this paper is available from https: //github.com/a-sfrank/macro-tpt.git.…”

Section: Introductionmentioning

confidence: 99%

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Macrophage Phenotype Transitions in a Stochastic Gene-Regulatory Network Model

Frank

Larripa

Ryu

et al. 2023

Preprint

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Section: Discussionmentioning

confidence: 99%

Section: Credit Authorship Contribution Statementmentioning

confidence: 99%

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Macrophage Phenotype Transitions in a Stochastic Gene-Regulatory Network Model

Frank

Larripa

Ryu

et al. 2023

Preprint

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“…Accession codes The Matlab codes for all presented cases are available on GitHub (https://github.com/a-sfrank/ macro-tpt.git). The cPCCA+ Matlab code, as described in 34 , was downloaded from GitHub (https://github.com/ sroeblitz/cPCCA.git), adapted and integrated into our implementation.…”

Section: Author Contributions Statementmentioning

confidence: 99%

Macrophage phenotype transitions in a stochastic gene-regulatory network model

Frank

Larripa

Ryu

et al. 2022

Preprint

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Polarization is the process by which a macrophage cell commits to a phenotype based on external signal stimulation. To know how this process is affected by random fluctuations and events within a cell is of utmost importance to better understand the underlying dynamics and predict possible phenotype transitions. For this purpose, we develop a stochastic modeling approach for the macrophage polarization process. We classify phenotype states using the Robust Perron Cluster Analysis and quantify transition pathways and probabilities by applying Transition Path Theory. Depending on the model parameters, we identify four bistable and one tristable phenotype configuration. We find that bistable transitions are fast but their states less robust. In contrast, phenotype transitions in the tristable situation have a comparatively long time duration, which reflects the robustness of the states. The results indicate parallels in the overall transition behavior of macrophage cells with other heterogeneous and plastic cell types, such as cancer cells. Our approach allows for a probabilistic interpretation of macrophage phenotype transitions and biological inference on phenotype robustness. In general, the methodology can easily be adapted to other systems where random state switches are known to occur.

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“…This leads to the maximization problem max ∈A ( ), with ( ) = which is then solved using an efficient optimization algorithm based on the Schur reordering algorithm that takes the side constraints (4.21) and (4.22) into account by projection techniques; see Röblitz andWeber (2013) andSikorski (2015) for details. Moreover, there are several extensions and variants, for example to take into account specifics of non-reversible cases; seeFrank et al (2022).…”

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confidence: 99%

Overcoming the timescale barrier in molecular dynamics: Transfer operators, variational principles and machine learning

Schütte¹,

Klus²,

Hartmann³

2023

Acta Numerica

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One of the main challenges in molecular dynamics is overcoming the ‘timescale barrier’: in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behaviour on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory, as well as the algorithmic development, from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in molecular dynamics. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject.

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Spectral clustering of Markov chain transition matrices with complex eigenvalues

Cited by 3 publications

References 19 publications

Macrophage Phenotype Transitions in a Stochastic Gene-Regulatory Network Model

Macrophage Phenotype Transitions in a Stochastic Gene-Regulatory Network Model

Macrophage phenotype transitions in a stochastic gene-regulatory network model

Overcoming the timescale barrier in molecular dynamics: Transfer operators, variational principles and machine learning

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