Discrete Ricci Flow for Geometric Routing

Gao, Jie; Gu, Xianfeng; Luo, Feng

doi:10.1007/978-1-4939-2864-4_602

Cited by 7 publications

(7 citation statements)

References 9 publications

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“…These two curvature notions are seen to be particularly appealing and give efficient solutions for network geometrizations. In case of undirected networks, Ollivier-Ricci curvature has proved its applicability in various network analyses [17][18][19][20]22,23,38,39]. On the other hand, Forman-Ricci curvature has been introduced as a tool for undirected [29,40] as well as directed [41] network analyses.…”

Section: Curvature-based Methods For Complex Networkmentioning

confidence: 99%

Integrative Computational Framework for Understanding Metabolic Modulation in Leishmania

Chauhan

Singh

2019

Preprint

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The integration of computational and mathematical approaches is used to provide a key insight into the biological systems. Here, we seek to find detailed and more robust information on Leishmanial metabolic network by performing mathematical characterization in terms of Forman/Forman-Ricci curvature measures combined with flux balance analysis (FBA). The model prototype developed largely depends on its structure and topological components. The correlation of curvature measures with various network statistical properties revealed the structural-functional framework. The analyses helped us to identify the importance of several nodes and detect sub-networks. Our results revealed several key high curvature nodes (metabolites) belonging to common yet crucial metabolic, thus, maintaining the integrity of the network which signifies its robustness. Further analysis revealed the presence of some of these metabolites in redox metabolism of the parasite. MGO, an important node, has highly cytotoxic and mutagenic nature that can irreversibly modify DNA, proteins and enzymes, making them nonfunctional, leading to the formation of AGEs and MGO •-. Being a component in the glyoxalase pathway, we further attempted to study the outcome of the deletion of the key enzyme (GLOI) mainly involved in the neutralization of MGO by utilizing FBA. The model and the objective function both kept as simple as possible, demonstrated an interesting emergent behavior. The nonfunctional GLOI in the model contributed to 'zero' flux which signifies the key role of GLOI as a rate limiting enzyme. This has led to several fold increase production of MGO, thereby, causing an increased level of MGO •generation. Hence, the integrated computational approaches has deciphered GLOI as a potential target both from curvature measures as well as FBA which could further be explored for kinetic modeling by implying various redox-dependent constraints on the model. Designing various in vitro experimental perspectives could churn the therapeutic importance of GLOI.Leishmaniasis, one of the most neglected tropical diseases in the world, is of primary concern due to the increased risk of emerging drug resistance. To design novel drugs and search effective molecular drug targets with therapeutic importance, it is important to decipher the relation among the components responsible for leishmanial parasite survival inside the host cell at the metabolic level. Here, we have attempted to get an insight in the leishmanial metabolic network and predict the importance of key metabolites by applying mathematical characterization in terms of curvature measures and flux balance analysis (FBA). Our results identified several metabolites playing significant role in parasite's redox homeostasis. Among these MGO (methylglyoxal) caught our interest due to its highly toxic and reactive nature of irreversibly modifying DNA and proteins. FBA results helped us to look into the important role of GLOI (Glyoxalase I), the enzyme that catalyses the detoxification of MGO, in the pathway tha...

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Section: Curvature-based Methods For Complex Networkmentioning

confidence: 99%

Integrative Computational Framework for Understanding Metabolic Modulation in Leishmania

Chauhan

Singh

2019

Preprint

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“…In particular, Chow and Luo's approach to Discrete Ricci curvature [28], based on circle packings, has proved to be not only theoretically interesting and important, but also extremely useful and influential in various applications -see e.g. [40], [34], [103]. Therefore, a drive to obtain a arXiv: 1902.03438v2 purely metric (in the sense of the first paper in this series [76]) Ricci flow is only natural.…”

Section: Introduction: Why Ricci Curvature?mentioning

confidence: 99%

Metric curvatures and their applications 2: metric Ricci curvature and flow

Saucan

2021

Mathematics, Computation and Geometry of Data

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In this second part of our overview of the different metric curvatures and their various applications, we concentrate on the Ricci curvature and flow for polyhedral surfaces and higher dimensional manifolds, and we largely review our previous studies on the subject, based upon Wald's curvature. In addition to our previous metric approaches to the discretization of Ricci curvature, we consider yet another one, based on the Haantjes curvature, interpreted as a geodesic curvature. We also try to understand the mathematical reasons behind the recent proliferation of discretizations of Ricci curvature. Furthermore, we propose another approach to the metrization of Ricci curvature, based on Forman's discretization, and in particular we propose on that uses our graph version of Forman's Ricci curvature.

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“…Ollivier-Ricci (Ollivier, 2009, 2011) and Forman-Ricci (Forman, 2003), two different discretization of Ricci curvature, give efficient solutions for network geometrizations. In case of undirected networks, Ollivier-Ricci curvature has proved its applicability in various network analyses (Loisel and Romon, 2014; Ni et al, 2015; Sandhu et al, 2015; Gao et al, 2016). On the other hand, Forman-Ricci curvature has been introduced as a tool for undirected (Sreejith et al, 2016, 2017a,b) as well as directed (Weber et al, 2017a,b) network analyses.…”

Section: Introductionmentioning

confidence: 99%

Integrative Computational Framework for Understanding Metabolic Modulation in Leishmania

Chauhan

Singh

2019

Front. Bioeng. Biotechnol.

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Background: The integration of computational and mathematical approaches is used to provide a key insight into the biological systems. Through systems biology approaches we seek to find detailed and more robust information on Leishmanial metabolic network. Forman/Forman-Ricci curvature measures were applied to identify important nodes in the network(s). This was followed by flux balance analysis (FBA) to decipher important drug targets.Results: Our results revealed several key high curvature nodes (metabolites) belonging to common yet crucial metabolic networks, thus, maintaining the integrity of the network which signifies its robustness. Further analysis revealed the presence of some of these metabolites, MGO, in redox metabolism of the parasite. Being a component in the glyoxalase pathway and highly cytotoxic, we further attempted to study the outcome of the deletion of the key enzyme (GLOI) mainly involved in the neutralization of MGO by utilizing FBA. The model and the objective function kept as simple as possible demonstrated an interesting emergent behavior. The non-functional GLOI in the model contributed to “zero” flux which signifies the key role of GLOI as a rate limiting enzyme. This has led to several fold increase production of MGO, thereby, causing an increased level of MGO•− generation.Conclusions: The integrated computational approaches have deciphered GLOI as a potential target both from curvature measures as well as FBA which could further be explored for kinetic modeling by implying various redox-dependent constraints on the model. Furthermore, a constraint-based FBA on a larger model could further be explored to get broader picture to understand the exact underlying mechanisms. Designing various in vitro experimental perspectives could churn the therapeutic importance of GLOI.

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Discrete Ricci Flow for Geometric Routing

Cited by 7 publications

References 9 publications

Integrative Computational Framework for Understanding Metabolic Modulation in Leishmania

Integrative Computational Framework for Understanding Metabolic Modulation in Leishmania

Metric curvatures and their applications 2: metric Ricci curvature and flow

Integrative Computational Framework for Understanding Metabolic Modulation in Leishmania

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