Metastable regimes and tipping points of biochemical networks with potential applications in precision medicine

Samal, Satya Swarup; Krishnan, Jeyashree; Esfahan, Ali i Hadizadeh; Lueders, Christoph; Weber, Andreas; Radulescu, Ovidiu

doi:10.1101/466714

Cited by 4 publications

(2 citation statements)

References 30 publications

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“…In the final Section 5, we approximate the stochastic protein distribution by a mixture of Gaussians with means at deterministic fixed points and variances given by the linear-noise approximation [8,30]. Additionally, we study the rates of metastable transitions [40,43] between the Gaussian modes in the one-dimensional and structured settings.…”

Section: Introductionmentioning

confidence: 99%

Stationary distributions and metastable behaviour for self-regulating proteins with general lifetime distributions

Çelik

Bokes

Singh

2020

Preprint

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Regulatory molecules such as transcription factors are often present at relatively small copy numbers in living cells. The copy number of a particular molecule fluctuates in time due to the random occurrence of production and degradation reactions. Here we consider a stochastic model for a self-regulating transcription factor whose lifespan (or time till degradation) follows a general distribution modelled as per a multidimensional phase-type process. We show that at steady state the protein copy-number distribution is the same as in a one-dimensional model with exponentially distributed lifetimes. This invariance result holds only if molecules are produced one at a time: we provide explicit counterexamples in the bursty production regime. Additionally, we consider the case of a bistable genetic switch constituted by a positively autoregulating transcription factor. The switch alternately resides in states of up-and downregulation and generates bimodal protein distributions. In the context of our invariance result, we investigate how the choice of lifetime distribution affects the rates of metastable transitions between the two modes of the distribution. The phase-type model, being non-linear and multi-dimensional whilst possessing an explicit stationary distribution, provides a valuable test example for exploring dynamics in complex biological systems.

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Section: Introductionmentioning

confidence: 99%

Stationary distributions and metastable behaviour for self-regulating proteins with general lifetime distributions

Çelik

Bokes

Singh

2020

Preprint

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“…Certain biological systems exhibit nonlinear dynamics that undergo sudden regime transitions at tipping points 1,2 . In a medical context, these transitions often indicate changes in clinical phenotypes, e.g., disease-onset 3 .…”

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confidence: 99%

Critical Transitions in Intensive Care Units: A Sepsis Case Study

Ghalati

Samal

Bhat

et al. 2019

Sci Rep

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The progression of complex human diseases is associated with critical transitions across dynamical regimes. These transitions often spawn early-warning signals and provide insights into the underlying disease-driving mechanisms. In this paper, we propose a computational method based on surprise loss (SL) to discover data-driven indicators of such transitions in a multivariate time series dataset of septic shock and non-sepsis patient cohorts (MIMIC-III database). The core idea of SL is to train a mathematical model on time series in an unsupervised fashion and to quantify the deterioration of the model’s forecast (out-of-sample) performance relative to its past (in-sample) performance. Considering the highest value of the moving average of SL as a critical transition, our retrospective analysis revealed that critical transitions occurred at a median of over 35 hours before the onset of septic shock, which suggests the applicability of our method as an early-warning indicator. Furthermore, we show that clinical variables at critical-transition regions are significantly different between septic shock and non-sepsis cohorts. Therefore, our paper contributes a critical-transition-based data-sampling strategy that can be utilized for further analysis, such as patient classification. Moreover, our method outperformed other indicators of critical transition in complex systems, such as temporal autocorrelation and variance.

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Tropical Geometry of Biological Systems (Invited Talk)

Radulescu

2020

Lecture Notes in Computer Science

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Metastable regimes and tipping points of biochemical networks with potential applications in precision medicine

Cited by 4 publications

References 30 publications

Stationary distributions and metastable behaviour for self-regulating proteins with general lifetime distributions

Stationary distributions and metastable behaviour for self-regulating proteins with general lifetime distributions

Critical Transitions in Intensive Care Units: A Sepsis Case Study

Tropical Geometry of Biological Systems (Invited Talk)

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