Equilibria and control of metabolic networks with enhancers and inhibitors

An, Zheming; Merrill, Nathaniel J.; McQuade, Sean T.; Piccoli, Benedetto

doi:10.3934/mine.2019.3.648

Cited by 3 publications

(4 citation statements)

References 26 publications

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“…The classical computation methods used to solve the qualitative and quantitative problems considered here (see for instance [34]) are based on the equations of the metabolite dynamics (see [3,20]). Let us denote v 0 the level of the virtual intake node, x the concentrations of metabolites and f the exchange flux, the general metabolic dynamics is given by…”

Section: A Classical Methods and Mathematical Representationmentioning

confidence: 99%

“…Because of this characterization, it is possible to write codes for determining the existence of equilibria and thus generate data to train neural networks to identify metabolic networks having such property. The second problem can be solved explicitely for networks with linear dynamics by a matrix inversion, see [3,34], as J −1 (f )ϕ, where J(f ) is the Jacobian matrix of the linear dynamic in terms of the network fluxes f and ϕ is the influx vector. Similarly to the first problem, we can easily generate codes to compute the equilibria and train neural networks.…”

Section: Introductionmentioning

confidence: 99%

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A deep language model to predict metabolic network equilibria

Charton¹,

Hayat²,

McQuade³

et al. 2021

Preprint

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We show that deep learning models, and especially architectures like the Transformer, originally intended for natural language, can be trained on randomly generated datasets to predict to very high accuracy both the qualitative and quantitative features of metabolic networks. Using standard mathematical techniques, we create large sets (40 million elements) of random networks that can be used to train our models. These trained models can predict network equilibrium on random graphs in more than 99% of cases. They can also generalize to graphs with different structure than those encountered at training. Finally, they can predict almost perfectly the equilibria of a small set of known biological networks. Our approach is both very economical in experimental data and uses only small and shallow deep-learning model, far from the large architectures commonly used in machine translation. Such results pave the way for larger use of deep learning models for problems related to biological networks in key areas such as quantitative systems pharmacology, systems biology, and synthetic biology.

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Section: A Classical Methods and Mathematical Representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A deep language model to predict metabolic network equilibria

Charton¹,

Hayat²,

McQuade³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We will provide more detail below about the many results achievable by this approach combining several different methods for modeling chemical systems, including systems biology, zero deficiency theory, laplacian dynamics, and Markov chains [28,1,5,15,10,14,7]. We will also refer the reader to [2,24,25] for a general presentation of the LIFE approach.…”

Section: The Life Methodsmentioning

confidence: 99%

Metabolic graphs, LIFE method and the modeling of drug action on Mycobacterium tuberculosis

McQuade,

Merrill,

Piccoli

2020

Preprint

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This paper serves as a framework for designing advanced models for drug action on metabolism. Drug treatment may affect metabolism by either enhancing or inhibiting metabolic reactions comprising a metabolic network. We introduce the concept of metabolic graphs, a generalization of hypergraphs having specialized features common to metabolic networks. Linear-in-flux-expression (briefly LIFE) is a methodology for analyzing metabolic networks and simulating virtual patients. We extend LIFE dynamics to be compatible with metabolic graphs, including the more complex interactions of enhancer and inhibitor molecules that affect biochemical reactions. We discuss results considering network structure required for existence and uniqueness of equilibria on metabolic graphs and show simulations of drug action on Mycobacterium tuberculosis (briefly MTB).

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“…A complex network is recognized as a powerful tool for revealing the mysteries of complex systems [ 1 ]. It is widely used in metabolic networks [ 2 ], software engineering [ 3 ], ecosystems [ 4 ] and so on. In addition to some topological parameters, such as power-law degree distribution, average path length and clustering coefficient of complex network, the random walks also received widespread attention because the research of random walk theory can disclose dynamic processes on complex networks.…”

Section: Introductionmentioning

confidence: 99%

Mean Hitting Time for Random Walks on a Class of Sparse Networks

Wang

Yao

2021

Entropy

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For random walks on a complex network, the configuration of a network that provides optimal or suboptimal navigation efficiency is meaningful research. It has been proven that a complete graph has the exact minimal mean hitting time, which grows linearly with the network order. In this paper, we present a class of sparse networks G(t) in view of a graphic operation, which have a similar dynamic process with the complete graph; however, their topological properties are different. We capture that G(t) has a remarkable scale-free nature that exists in most real networks and give the recursive relations of several related matrices for the studied network. According to the connections between random walks and electrical networks, three types of graph invariants are calculated, including regular Kirchhoff index, M-Kirchhoff index and A-Kirchhoff index. We derive the closed-form solutions for the mean hitting time of G(t), and our results show that the dominant scaling of which exhibits the same behavior as that of a complete graph. The result could be considered when designing networks with high navigation efficiency.

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Equilibria and control of metabolic networks with enhancers and inhibitors

Cited by 3 publications

References 26 publications

A deep language model to predict metabolic network equilibria

A deep language model to predict metabolic network equilibria

Metabolic graphs, LIFE method and the modeling of drug action on Mycobacterium tuberculosis

Mean Hitting Time for Random Walks on a Class of Sparse Networks

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