Dynamics and growth rate implications of ribosomes and mRNAs interaction in E. coli

Phan, Tin; He, Changhan; Loladze, Irakli; Prater, Clay; Elser, James J.; Kuang, Yang

doi:10.1016/j.heliyon.2022.e09820

Cited by 3 publications

(4 citation statements)

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“…Depend on the types of model identifiability, there are various examples and techniques to address the issues of model identifiability [ 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 ]. Here, we offer our perspective on this issue.…”

Section: Materials and Methodsmentioning

confidence: 99%

Practical Understanding of Cancer Model Identifiability in Clinical Applications

Phan

Bennett

Patten

2023

Life

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Mathematical models are a core component in the foundation of cancer theory and have been developed as clinical tools in precision medicine. Modeling studies for clinical applications often assume an individual’s characteristics can be represented as parameters in a model and are used to explain, predict, and optimize treatment outcomes. However, this approach relies on the identifiability of the underlying mathematical models. In this study, we build on the framework of an observing-system simulation experiment to study the identifiability of several models of cancer growth, focusing on the prognostic parameters of each model. Our results demonstrate that the frequency of data collection, the types of data, such as cancer proxy, and the accuracy of measurements all play crucial roles in determining the identifiability of the model. We also found that highly accurate data can allow for reasonably accurate estimates of some parameters, which may be the key to achieving model identifiability in practice. As more complex models required more data for identification, our results support the idea of using models with a clear mechanism that tracks disease progression in clinical settings. For such a model, the subset of model parameters associated with disease progression naturally minimizes the required data for model identifiability.

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Section: Materials and Methodsmentioning

confidence: 99%

Practical Understanding of Cancer Model Identifiability in Clinical Applications

Phan

Bennett

Patten

2023

Life

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“…Like most growth models,

μ

is defined as the relative increase in protein mass, which is described by the equation

μ goodbreak= \frac{R_{w} k_{el} m_{a}}{P_{m}} .

R_{w} k_{el} m_{a}

is the mass of protein produced by active ribosomes,

R_{w}

, where

k_{el}

is the peptide chain elongation rate,

m_{a}

is the average mass of amino acid and

P_{m}

is the total protein mass in a cell. While not originally formulated as a stoichiometrically explicit model, Phan et al (2021) recently connected the Li et al (2018) model to the GRH by calculating bacterial N:P ratios under each form of limitation, finding good agreement with empirical measurements. Further, they showed that this model is capable of coherently capturing all experimental observations under different nutrient limitation scenarios, providing a powerful framework for identifying physiological mechanisms responsible for weakening GRH coupling under different forms of nutrient limitation.…”

Section: Towards Next‐generation Stoichiometric Modelsmentioning

confidence: 99%

“…That is

\begin{matrix} left μ goodbreak= \frac{R_{w} k_{el} m_{a} + f}{P_{m} + F} goodbreak= \frac{R_{w} k_{el} m_{a} + c ()(, R_{w} k_{el} m_{a})}{P_{m} + c P_{m}} \\ left goodbreak= \frac{R_{w} k_{el} m_{a} ()(, 1 goodbreak+ c)}{P_{m} ()(, 1 goodbreak+ c)} goodbreak= \frac{R_{w} k_{el} m_{a}}{P_{m}} . \end{matrix}

To account for M1, we can omit the constant ratio assumption and explicitly introduce the dynamics of non‐RNA P storage into variables

f

and

F

to study their relationship with growth rate. These two parameters could also be used to incorporate energy costs into this framework (Phan et al, 2021) and to form a comprehensive stoichiometric growth model by considering C pools, including polyesters (Poblete‐Castro et al, 2012), carbohydrates (Liefer et al, 2019), and lipids (Wagner et al, 2015). Such C‐rich molecules can represent a significant proportion (20%–80%) of total biomass under N‐ and/or P limitation, so their inclusion would allow stoichiometric models to better predict C:P and C:N ratios in addition to N:P.…”

Section: Towards Next‐generation Stoichiometric Modelsmentioning

confidence: 99%

Revisiting the growth rate hypothesis: Towards a holistic stoichiometric understanding of growth

et al. 2022

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The growth rate hypothesis (GRH) posits that variation in organismal stoichiometry (C:P and N:P ratios) is driven by growth‐dependent allocation of P to ribosomal RNA. The GRH has found broad but not uniform support in studies across diverse biota and habitats. We synthesise information on how and why the tripartite growth‐RNA‐P relationship predicted by the GRH may be uncoupled and outline paths for both theoretical and empirical work needed to broaden the working domain of the GRH. We found strong support for growth to RNA (r2 = 0.59) and RNA‐P to P (r2 = 0.63) relationships across taxa, but growth to P relationships were relatively weaker (r2 = 0.09). Together, the GRH was supported in ~50% of studies. Mechanisms behind GRH uncoupling were diverse but could generally be attributed to physiological (P accumulation in non‐RNA pools, inactive ribosomes, translation elongation rates and protein turnover rates), ecological (limitation by resources other than P), and evolutionary (adaptation to different nutrient supply regimes) causes. These factors should be accounted for in empirical tests of the GRH and formalised mathematically to facilitate a predictive understanding of growth.

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“…Biochemical interactions of resources can explain the net result of multiple resource limitations, but MRL is likely more complicated due to the diversity of biochemical processes within an organism [14]. For example, it has been demonstrated that E. coli uses different resource allocation strategies to maintain the same growth rate under various resource limitations [15][16][17]. Others have also shown that plant-virus dynamics are altered under different resource treatments [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Rich Dynamics of a General Producer–Grazer Interaction Model under Shared Multiple Resource Limitations

2023

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Organism growth is often determined by multiple resources interdependently. However, growth models based on the Droop cell quota framework have historically been built using threshold formulations, which means they intrinsically involve single-resource limitations. In addition, it is a daunting task to study the global dynamics of these models mathematically, since they employ minimum functions that are non-smooth (not differentiable). To provide an approach to encompass interactions of multiple resources, we propose a multiple-resource limitation growth function based on the Droop cell quota concept and incorporate it into an existing producer–grazer model. The formulation of the producer’s growth rate is based on cell growth process time-tracking, while the grazer’s growth rate is constructed based on optimal limiting nutrient allocation in cell transcription and translation phases. We show that the proposed model captures a wide range of experimental observations, such as the paradox of enrichment, the paradox of energy enrichment, and the paradox of nutrient enrichment. Together, our proposed formulation and the existing threshold formulation provide bounds on the expected growth of an organism. Moreover, the proposed model is mathematically more tractable, since it does not use the minimum functions as in other stoichiometric models.

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Dynamics and growth rate implications of ribosomes and mRNAs interaction in E. coli

Cited by 3 publications

References 50 publications

Practical Understanding of Cancer Model Identifiability in Clinical Applications

Practical Understanding of Cancer Model Identifiability in Clinical Applications

Revisiting the growth rate hypothesis: Towards a holistic stoichiometric understanding of growth

Rich Dynamics of a General Producer–Grazer Interaction Model under Shared Multiple Resource Limitations

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