Mathematical Model of a Bacteria-Immunity System with the Influence of Quorum Sensing Signal Molecule

Zhang, Zhiwen

doi:10.4236/jamp.2016.45097

Cited by 4 publications

(4 citation statements)

References 13 publications

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Section: Resultsmentioning

confidence: 99%

“…This model describes the influence of quorum sensing signaling molecules (QSSM) on the competition between bacteria and the immune system, as studied in [58]. The following differential equations depict the dynamics for the concentrations of bacteria and immune cells : where it is assumed that bacteria grow logistically at rate a with an effective carrying capacity of the environment given by parameter k , and that they are cleared by the immune system following a mass action term ex 1 x 2 .…”

Section: Resultsmentioning

confidence: 99%

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Distilling identifiable and interpretable dynamic models from biological data

Banga

Massonis

Villaverde

2023

Preprint

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Mechanistic dynamical models allow us to study the behavior of complex biological systems. They can provide an objective and quantitative understanding that would be difficult to achieve through other means. However, the systematic development of these models is a non-trivial exercise and an open problem in computational biology. Currently, many research efforts are focused on model discovery, i.e. automating the development of interpretable models from data. One of the main frameworks is sparse regression, where the sparse identification of nonlinear dynamics (SINDy) algorithm and its variants have enjoyed great success. SINDy-PI is an extension which allows the discovery of rational nonlinear terms, thus enabling the identification of kinetic functions common in biochemical networks, such as Michaelis-Menten. SINDy-PI also pays special attention to the recovery of parsimonious models (Occam's razor). Here we focus on biological models composed of sets of deterministic nonlinear ordinary differential equations. We present a methodology that, combined with SINDy-PI, allows the automatic discovery of structurally identifiable and observable models which are also mechanistically interpretable. The lack of structural identifiability and observability makes it impossible to uniquely infer parameter and state variables, which can compromise the usefulness of a model by distorting its mechanistic significance and hampering its ability to produce biological insights. We illustrate the performance of our method with six case studies. We find that, despite enforcing sparsity, SINDy-PI sometimes yields models that are unidentifiable. In these cases we show how our method transforms their equations in order to obtain a structurally identifiable and observable model which is also interpretable.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Distilling identifiable and interpretable dynamic models from biological data

Banga

Massonis

Villaverde

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…This model describes the influence of quorum sensing signaling molecules (QSSM) on the competition between bacteria and the immune system, as studied in [ 58 ]. The following differential equations depict the dynamics for the concentrations of bacteria ( ) and immune cells ( ): where it is assumed that bacteria grow logistically at rate a with an effective carrying capacity of the environment given by parameter k , and that they are cleared by the immune system following a mass action term ex 1 x 2 .…”

Section: Resultsmentioning

confidence: 99%

Section: Competition Between Bacteria and The Immune System (Immunity)mentioning

confidence: 99%

Distilling identifiable and interpretable dynamic models from biological data

Massonis,

Villaverde,

Banga

2023

PLoS Comput Biol

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Mechanistic dynamical models allow us to study the behavior of complex biological systems. They can provide an objective and quantitative understanding that would be difficult to achieve through other means. However, the systematic development of these models is a non-trivial exercise and an open problem in computational biology. Currently, many research efforts are focused on model discovery, i.e. automating the development of interpretable models from data. One of the main frameworks is sparse regression, where the sparse identification of nonlinear dynamics (SINDy) algorithm and its variants have enjoyed great success. SINDy-PI is an extension which allows the discovery of rational nonlinear terms, thus enabling the identification of kinetic functions common in biochemical networks, such as Michaelis-Menten. SINDy-PI also pays special attention to the recovery of parsimonious models (Occam’s razor). Here we focus on biological models composed of sets of deterministic nonlinear ordinary differential equations. We present a methodology that, combined with SINDy-PI, allows the automatic discovery of structurally identifiable and observable models which are also mechanistically interpretable. The lack of structural identifiability and observability makes it impossible to uniquely infer parameter and state variables, which can compromise the usefulness of a model by distorting its mechanistic significance and hampering its ability to produce biological insights. We illustrate the performance of our method with six case studies. We find that, despite enforcing sparsity, SINDy-PI sometimes yields models that are unidentifiable. In these cases we show how our method transforms their equations in order to obtain a structurally identifiable and observable model which is also interpretable.

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Abrupt and gradual onset of synchronized oscillations due to dynamical quorum sensing in the single-cathode multi-anode nickel electrodissolution system

Hankins

Gáspár

Kiss

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The nonlinear dynamics of an oscillatory Ni electrodissolution–hydrogen ion reduction system are explored in a multi-electrode anode–single cathode system. A mathematical analysis of the charge balance equations reveals that the coupling scheme is similar to dynamical quorum sensing, where the number of anode wires affects a parameter related to the population density. In a parameter region where the large population exhibits stationary behavior, with sufficiently strong coupling (with small individual resistances attached to the anode wires), synchronized oscillations emerge abruptly with decreasing the number of anodes. Therefore, an “inverse” dynamical quorum sensing takes place. With weak coupling the transition is gradual. The experiments are supported by numerical simulation of a kinetic model of the process. The results thus show that the description of nontrivial cathode-anode interactions in the form of dynamical quorum sensing provides an efficient way of analyzing the dynamical response of complex, interacting electrochemical reactions.

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Mathematical Model of a Bacteria-Immunity System with the Influence of Quorum Sensing Signal Molecule

Cited by 4 publications

References 13 publications

Distilling identifiable and interpretable dynamic models from biological data

Distilling identifiable and interpretable dynamic models from biological data

Distilling identifiable and interpretable dynamic models from biological data

Abrupt and gradual onset of synchronized oscillations due to dynamical quorum sensing in the single-cathode multi-anode nickel electrodissolution system

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