Long-term dynamics of multisite phosphorylation

Rubinstein, Boris; Mattingly, Henry H.; Berezhkovskii, Alexander M.; Shvartsman, Stanislav Y.

doi:10.1091/mbc.e16-03-0137

Cited by 36 publications

(58 citation statements)

References 85 publications

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“…They showed that sustained oscillations could be observed in certain parameter regions [6]. Other variants also have been shown to admit oscillations [11,13].…”

Section: Introductionmentioning

confidence: 99%

No oscillations in the Michaelis-Menten approximation of the dual futile cycle under a sequential and distributive mechanism

Morales¹

2017

SIURO

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Protein phosphorylation and dephosphorylation are important intracellular processes. The main object of study in this paper is the dual futile cycle, a network that describes the dual-site phosphorylation/dephosphorylation of a protein by a kinase/phosphatase pair in a sequential and distributive mechanism. Specifically, we analyze the 2-dimensional Michaelis-Menten (M-M) approximation of this system. It has been previously shown that this system is bistable. We also know, from monotone systems theory, that every solution converges to some steady state. Here, we give a new and simpler proof of this convergence result by using Bendixon's criterion to rule out oscillations. Ultimately, understanding the behavior of this system could help us understand the original dual futile cycle (or MAPK cascades that contain it), which has recently been shown to admit oscillations via Hopf bifurcations.

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“…They showed that sustained oscillations could be observed in certain parameter regions [6]. Other variants also have been shown to admit oscillations [11,13].…”

Section: Introductionmentioning

confidence: 99%

No oscillations in the Michaelis-Menten approximation of the dual futile cycle under a sequential and distributive mechanism

Morales¹

2017

SIURO

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“…Indeed, multistep phosphorylation shows several properties that are potentially favorable for regulatory processes. Networks involving multistep phosphorylation can also exhibit bistability [20,21], and can even generate periodic oscillations [22]. Networks involving multistep phosphorylation can also exhibit bistability [20,21], and can even generate periodic oscillations [22].…”

Section: Introductionmentioning

confidence: 99%

“…Thus, it has been shown that a large number of phosphosites can form the basis for an ultrasensitive switch-like response [19]. Networks involving multistep phosphorylation can also exhibit bistability [20,21], and can even generate periodic oscillations [22]. However, a yet unexplored role for multisite phosphorylation is that it may also contribute to make cellular decisions more reliable by filtering noise.…”

Section: Introductionmentioning

confidence: 99%

Multisite phosphorylation provides a reliable mechanism for making decisions in noisy environments

Aledo

2018

The FEBS Journal

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The ability to make decisions at the cellular level is absolutely critical for the survival of organisms. Eukaryotic cells are constantly making binary decisions in response to internal and environmental signals. Among the most notable transducers of information are protein kinases. The regulation of these signaling proteins often relies on the activity of other protein kinases located upstream in the signaling cascade. However, these signaling systems are by their own nature an important source of molecular noise. Herein, we have assessed the role of multisite phosphorylation in detecting signals in the face of molecular noise. To address this issue, we have conceptually envisioned the biochemical transduction machinery as a classifier model that can lead to four possible outputs: true positives and negatives, and false positives and negatives. In this probabilistic framework, we show that multisite phosphorylation represents a mechanism to filter noise during the decision-making process. We present results showing that nonessential phosphorylation sites contribute to increase the rate of true positives while, at the same time, they can lessen the rate of false positives. This simultaneous increase in sensitivity and specificity, makes multisite phosphorylation a valuable and easily implemented mechanism to reliably transduce information in noisy contexts.

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“…A distributive ("hit-and-run") reaction is one 230 that yields only a single product with a given substrate. Processive ("bind-and-slide") 231 reactions, in which the enzyme catalyses multiple modifications while remaining bound 232 to the substrate, can also be accommodated within the grammar, but can yield more 233 complex behaviours [76,77]. Each enzyme has two substrates-S 0 and S 1 for E, and S 1 234 and S 2 for F -and may use a different mechanism from the grammar on each substrate.…”

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confidence: 99%

“…We use this language only as 390 a convenience and note the importance of distinguishing between stationarity and 391 stability. For example, recent work on "mixed-mechanism" PTM systems, which 392 incorporate both distributive and processive mechanisms, has shown the existence of a 393 single unstable steady-state with limit-cycle oscillations [76,77]. Such behaviours are 394 not known to be a feature of PTM systems that employ only distributive mechanisms 395 but checking for them requires testing for stability.…”

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confidence: 99%

Robustness and parameter geography in post-translational modification systems

Nam

Gyori

Amethyst

et al. 2019

Preprint

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AbstractBiological systems are acknowledged to be robust to perturbations but a rigorous understanding of this has been elusive. In a mathematical model, perturbations often exert their effect through parameters, so sizes and shapes of parametric regions offer an integrated global estimate of robustness. Here, we explore this “parameter geography” for bistability in post-translational modification (PTM) systems. We use the previously developed “linear framework” for timescale separation to describe the steady-states of a two-site PTM system as the solutions of two polynomial equations in two variables, with eight non-dimensional parameters. Importantly, this approach allows us to accommodate enzyme mechanisms of arbitrary complexity beyond the conventional Michaelis-Menten scheme, which unrealistically forbids product rebinding. We further use the numerical algebraic geometry tools Bertini, Paramotopy, and alphaCertified to statistically assess the solutions to these equations at ∼109 parameter points in total. Subject to sampling limitations, we find no bistability when substrate amount is below a threshold relative to enzyme amounts. As substrate increases, the bistable region acquires 8-dimensional volume which increases in an apparently monotonic and sigmoidal manner towards saturation. The region remains connected but not convex, albeit with a high visibility ratio. Surprisingly, the saturating bistable region occupies a much smaller proportion of the sampling domain under mechanistic assumptions more realistic than the Michaelis-Menten scheme. We find that bistability is compromised by product rebinding and that unrealistic assumptions on enzyme mechanisms have obscured its parametric rarity. The apparent monotonic increase in volume of the bistable region remains perplexing because the region itself does not grow monotonically: parameter points can move back and forth between monostability and bistability. We suggest mathematical conjectures and questions arising from these findings. Advances in theory and software now permit insights into parameter geography to be uncovered by high-dimensional, data-centric analysis.Author SummaryBiological organisms are often said to have robust properties but it is difficult to understand how such robustness arises from molecular interactions. Here, we use a mathematical model to study how the molecular mechanism of protein modification exhibits the property of multiple internal states, which has been suggested to underlie memory and decision making. The robustness of this property is revealed by the size and shape, or “geography,” of the parametric region in which the property holds. We use advances in reducing model complexity and in rapidly solving the underlying equations, to extensively sample parameter points in an 8-dimensional space. We find that under realistic molecular assumptions the size of the region is surprisingly small, suggesting that generating multiple internal states with such a mechanism is much harder than expected. While the shape of the region appears straightforward, we find surprising complexity in how the region grows with increasing amounts of the modified substrate. Our approach uses statistical analysis of data generated from a model, rather than from experiments, but leads to precise mathematical conjectures about parameter geography and biological robustness.

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Long-term dynamics of multisite phosphorylation

Cited by 36 publications

References 85 publications

No oscillations in the Michaelis-Menten approximation of the dual futile cycle under a sequential and distributive mechanism

No oscillations in the Michaelis-Menten approximation of the dual futile cycle under a sequential and distributive mechanism

Multisite phosphorylation provides a reliable mechanism for making decisions in noisy environments

Robustness and parameter geography in post-translational modification systems

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