scholarly journals A Unifying Mathematical Framework for Genetic Robustness, Environmental Robustness, Network Robustness and their Tradeoff on Phenotype Robustness in Biological Networks Part II: Ecological Networks

2013 ◽  
Vol 9 ◽  
pp. EBO.S10685 ◽  
Author(s):  
Bor-Sen Chen ◽  
Ying-Po Lin
Keyword(s):  
Biological Networks ◽  
Ecological Networks ◽  
Network Robustness ◽  
Mathematical Framework ◽  
Genetic Robustness ◽  
Environmental Robustness

scholarly journals Adaptation of turnip mosaic potyvirus to a specific niche reduces its genetic and environmental robustness

2020 ◽  
Vol 6 (2) ◽  
Author(s):  
Anamarija Butković ◽  
Rubén González ◽  
Inés Cobo ◽  
Santiago F Elena
Keyword(s):  
Mutation Rates ◽  
Permissive Temperature ◽  
Fitness Component ◽  
Temperature Conditions ◽  
Environmental Perturbations ◽  
Genetic Robustness ◽  
Congruence Theory ◽  
The Face ◽  
Environmental Robustness ◽  
Two Sides

Abstract Robustness is the preservation of the phenotype in the face of genetic and environmental perturbations. It has been argued that robustness must be an essential fitness component of RNA viruses owed to their small and compacted genomes, high mutation rates and living in ever-changing environmental conditions. Given that genetic robustness might hamper possible beneficial mutations, it has been suggested that genetic robustness can only evolve as a side-effect of the evolution of robustness mechanisms specific to cope with environmental perturbations, a theory known as plastogenetic congruence. However, empirical evidences from different viral systems are contradictory. To test how adaptation to a particular environment affects both environmental and genetic robustness, we have used two strains of turnip mosaic potyvirus (TuMV) that differ in their degree of adaptation to Arabidopsis thaliana at a permissive temperature. We show that the highly adapted strain is strongly sensitive to the effect of random mutations and to changes in temperature conditions. In contrast, the non-adapted strain shows more robustness against both the accumulation of random mutations and drastic changes in temperature conditions. Together, these results are consistent with the predictions of the plastogenetic congruence theory, suggesting that genetic and environmental robustnesses may be two sides of the same coin for TuMV.

scholarly journals The relationship between modularity and robustness in signalling networks

2013 ◽  
Vol 10 (88) ◽  
pp. 20130771 ◽  
Author(s):  
Tien-Dzung Tran ◽  
Yung-Keun Kwon
Keyword(s):  
Negative Correlation ◽  
Biological Networks ◽  
Boolean Network ◽  
Negative Relationship ◽  
Network Robustness ◽  
Network Density ◽  
Boolean Network Model ◽  
Signalling Network ◽  
Network Modularity ◽  
The Relationship

Many biological networks tend to have a high modularity structural property and the dynamic characteristic of high robustness against perturbations. However, the relationship between modularity and robustness is not well understood. To investigate this relationship, we examined real signalling networks and conducted simulations using a random Boolean network model. As a result, we first observed that the network robustness is negatively correlated with the network modularity. In particular, this negative correlation becomes more apparent as the network density becomes sparser. Even more interesting is that, the negative relationship between the network robustness and the network modularity occurs mainly because nodes in the same module with the perturbed node tend to be more sensitive to the perturbation than those in other modules. This result implies that dynamically similar nodes tend to be located in the same module of a network. To support this, we show that a pair of genes associated with the same disease or a pair of functionally similar genes is likely to belong to the same module in a human signalling network.

scholarly journals Hyperbolic matrix factorization reaffirms the negative curvature of the native biological space

2020 ◽  
Author(s):  
Aleksandar Poleksic
Keyword(s):  
Hyperbolic Space ◽  
Matrix Factorization ◽  
Biological Networks ◽  
Hierarchical Structures ◽  
Past Research ◽  
Computational Procedure ◽  
Mathematical Framework ◽  
Biological Databases ◽  
Latent Dimension ◽  
Hyperbolic Embedding

AbstractPast research in systems biology has taken for granted the Euclidean geometry of biological space. This has not only drawn parallels to other fields but has also been convenient due to the ample statistical and numerical optimization tools available to address the core task and downstream machine learning problems. However, emerging theoretical studies now demonstrate that biological databases exhibit hierarchical topology, characterized by heterogeneous degree distribution and a high degree of clustering, thus contradicting the flat geometry assumption. Namely, since the number of nodes in hierarchical structures grows exponentially with node depth, the biological networks naturally reside in a hyperbolic space where the circle circumference and disk area are the exponential functions of the radius. To test these claims and assess potential benefits of the applications grounded in the above hypothesis, we have developed a mathematical framework and an accompanying computational procedure for matrix factorization and implied biological relationship inference in hyperbolic space. Not only does our study demonstrate a significant increase in the accuracy of hyperbolic embedding compared to Euclidean embedding, but it also shows that the latent dimension of an optimal hyperbolic embedding is by more than an order of magnitude smaller than the latent dimension of an optimal Euclidean embedding. We see this as additional evidence that hyperbolic geometry, rather than Euclidean, underlines the biological system.

scholarly journals A Mathematical Framework for Agent Based Models of Complex Biological Networks

2010 ◽  
Vol 73 (7) ◽  
pp. 1583-1602 ◽  
Author(s):  
Franziska Hinkelmann ◽  
David Murrugarra ◽  
Abdul Salam Jarrah ◽  
Reinhard Laubenbacher
Keyword(s):  
Biological Networks ◽  
Mathematical Framework ◽  
Agent Based Models ◽  
Agent Based ◽  
Complex Biological Networks

Testing early-warning signals for the transition of ecological network properties in wetland complex

2020 ◽  
Author(s):  
Bin Kim ◽  
Hyojeong Lee ◽  
Khawon Lee ◽  
Jeryang Park
Keyword(s):  
Early Warning ◽  
Human Activities ◽  
Land Development ◽  
Warning Signal ◽  
Climatic Conditions ◽  
Ecological Networks ◽  
Clustering Coefficient ◽  
Network Robustness ◽  
Network Characteristics ◽  
Early Warning Signal

<p>Wetlands, which exist in both natural and man-made landscapes, play a critical role in providing various ecosystem services for both ecology and human-being. These services are affected not only by regional hydro-climatic and geologic conditions but also by human activities. On a landscape scale, wetlands form a complex spatial structure by their spatial distribution in a specific geological setting. Consequently, dispersal of inhabiting species between spatially distributed wetlands organizes ecological networks that are consisted of nodes (wetlands) and links (pathways of movement). In this study, we generated and analyzed the ecological networks by introducing deterministic (e.g., threshold distance) or stochastic (e.g., exponential kernel and heavy-tailed model) dispersal models. From these networks, we evaluated structural or functional characteristics including degree, efficiency, and clustering coefficient, all of which are affected by disturbances such as seasonal hydro-climatic conditions that change wetland surface area, and shocks that may remove nodes from the network (e.g., human activities for land development). Specifically, by using the characteristics of the corresponding ecological networks, we analyzed (1) their network robustness by simulating the removal of nodes selected by their degree or area; and (2) the change of variance as the early-warning signal to predict where critical point may occur in global network characteristics affected by disturbances. The results showed that there was not a clear relationship between network robustness and wetland size for node removal. However, when nodes were removed in the order of degree, the network fragmented rapidly. Also, we observed that the variance of network characteristics in the time-series increased in drier hydro-climatic conditions for all the three network models we tested. This result indicates a possibility of using increasing variance as the early-warning signal for detecting a critical transition in network characteristics as the hydro-climatic condition becomes dry. In sum, the observed characteristics of ecological networks are vulnerable to target attack on hubs (structurally important nodes) or drought. Also, the resilience of a wetlandscape can be low after hubs were destroyed or in a dry season causing the fragmentation of habitats. Implications of these results for modeling ecological networks depending on hydrologic systems and influenced by human activities will provide a new decision-making process, especially for restoring and conservation purposes.</p>

scholarly journals Topology and static response of interaction networks in molecular biology

2005 ◽  
Vol 3 (6) ◽  
pp. 185-196 ◽  
Author(s):  
Ovidiu Radulescu ◽  
Sandrine Lagarrigue ◽  
Anne Siegel ◽  
Philippe Veber ◽  
Michel Le Borgne
Keyword(s):  
Molecular Biology ◽  
Biological Networks ◽  
Genetic Regulation ◽  
Mathematical Framework ◽  
Interaction Graph ◽  
Static Response ◽  
Electrical Networks ◽  
Kirchhoff Equations ◽  
Neumann Problems ◽  
External Perturbations

We introduce a mathematical framework describing static response of networks occurring in molecular biology. This formalism has many similarities with the Laplace–Kirchhoff equations for electrical networks. We introduce the concept of graph boundary and we show how the response of the biological networks to external perturbations can be related to the Dirichlet or Neumann problems for the corresponding equations on the interaction graph. Solutions to these two problems are given in terms of path moduli (measuring path rigidity with respect to the propagation of interaction along the graph). Path moduli are related to loop products in the interaction graph via generalized Mason–Coates formulae. We apply our results to two specific biological examples: the lactose operon and the genetic regulation of lipogenesis. Our applications show consistency with experimental results and in the case of lipogenesis check some hypothesis on the behaviour of hepatic fatty acids on fasting.

LPCD framework: Analytical tool or psychological model?

2018 ◽  
Vol 41 ◽  
Author(s):  
David Danks
Keyword(s):  
Decision Making ◽  
Analytical Tool ◽  
Mathematical Framework ◽  
Bayesian Decision ◽  
Perceptual Decision Making ◽  
Psychological Model ◽  
Psychological Reality ◽  
Psychological Theories ◽  
Target Article ◽  
Bayesian Decision Making

AbstractThe target article uses a mathematical framework derived from Bayesian decision making to demonstrate suboptimal decision making but then attributes psychological reality to the framework components. Rahnev & Denison's (R&D) positive proposal thus risks ignoring plausible psychological theories that could implement complex perceptual decision making. We must be careful not to slide from success with an analytical tool to the reality of the tool components.

Determination and prediction of the stress-strain state of pipeline, taking into account soil changes during operation

2020 ◽  
Vol 10 (4) ◽  
pp. 372-378
Author(s):  
Aydar К. Gumerov ◽  
◽  
Rinat M. Karimov ◽  
Robert М. Askarov ◽  
Khiramagomed Sh. Shamilov ◽  
...  
Keyword(s):  
Strain State ◽  
Mathematical Framework ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Optimal Method ◽  
Initial Stress State ◽  
Soil Response ◽  
Stress Strain State ◽  
Support Reaction ◽  
Key Factor

The key factor determining the strength, reliability, service life and fail-safe operation of the main pipeline is its stress-strain state. The purpose of this article is to develop a mathematical framework and methodology for calculating the stress-strain state of a pipeline section laid in complex geotechnical conditions, taking into account all planned and altitude changes and impacts at various points of operation, as well as during repair and after its completion. The mathematical framework is based on differential equations reflecting the equilibrium state of the pipeline, taking into account the features of the sections (configuration, size, initial stress state, acting forces, temperature conditions, interaction with soil, supports, and pipe layers). The equilibrium equations are drawn up in a curvilinear coordinate system – the same one that is used for in-pipe diagnostics. According to the results of the solution, all stress components are determined at each point both along the length of the pipeline and along the circumference of any section. At the same time, transverse and longitudinal forces, bending moments, shearing forces, pipeline displacements relative to the ground and soil response to displacements are determined. As an example, a solution is given using the developed mathematical framework. During the course of calculation, the places where the lower form of the pipe does not touch the ground and the places where the support reaction becomes higher than a predetermined limit are determined. A comparative analysis was accomplished, and the optimal method for section repair has been selected.

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