Modelling in systems biology

Lecca, Paola; Laurenzi, Ian J.; Jordán, Ferenc

doi:10.1533/9781908818218.117

Cited by 4 publications

(4 citation statements)

References 53 publications

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“…Mathematical modelling and simulating is an important phase in studying many processes that are not easily or are not yet accessible by experimental procedures such as is in the field of biology [1]. For decades, mathematical models have been used to provide a better understanding of biological and pathological systems [2, 3]. For the special case of acute myeloid leukaemia (AML), there is a need to improve the understanding of the relationship between healthy and cancerous stem cells [4] in addition to the requirement of finding theoretical conditions for an efficient drug delivery [5, 6].…”

Section: Introductionmentioning

confidence: 99%

Study of cohabitation and interconnection effects on normal and leukaemic stem cells dynamics in acute myeloid leukaemia

Zenati

Chakir

Tadjine

2018

IET Systems Biology

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On the basis of recent studies, understanding the intimate relationship between normal and leukaemic stem cells is very important in leukaemia treatment. The authors' aim in this work is to clarify and assess the effect of coexistence and interconnection phenomenon on the healthy and cancerous stem cell dynamics. To this end, they perform the analysis of two time-delayed stem cell models in acute myeloid leukaemia. The first model is based on decoupled healthy and cancerous stem cell populations (i.e. there is no interaction between cell dynamics) and the second model includes interconnection between both population's dynamics. By using the positivity of both systems, they build new linear functions that permit to derive global stability conditions for each model. Moreover, knowing that most common types of haematological diseases are characterised by the existence of oscillations, they give conditions for the existence of a limit cycle (oscillations) in a particularly interesting healthy situation based on Poincare-Bendixson theorem. The obtained results are simulated and interpreted to be significant in understanding the effect of interconnection and would lead to an improvement in leukaemia treatment.

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Section: Introductionmentioning

confidence: 99%

Study of cohabitation and interconnection effects on normal and leukaemic stem cells dynamics in acute myeloid leukaemia

Zenati

Chakir

Tadjine

2018

IET Systems Biology

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“…Since the vector P 0 multiplies [ s I − M ] −1 , therefore, the first column of [ s I − M ] −1 will contribute exclusively to the multiplication output. 35 The first three rows of the latter correspond to the probabilities of three conformers of the specie E, while its last three rows yield the probabilities of ES conformers in the Laplace domain. Because the definition of waiting-time distribution, eqn (3), involves the P ES i ( t ) terms, it is evident that the first column of the block matrix, − Z −1 W ( G − HZ −1 W ) −1 in eqn (16) will be our only concern.…”

Section: Kinetic Modelmentioning

confidence: 99%

A minimal kinetic model for the interpretation of complex catalysis in single enzyme molecules

Kundu,

Saha,

Gangopadhyay

2024

Phys. Chem. Chem. Phys.

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“…The SSA is an example of stochastic modeling, as opposed to the deterministic modeling approach [ 9 ]. In a deterministic approach, the time-continuous processes are wholly predictable and can be governed by the reaction-rate equations [ 10 ], a set of coupled ordinary differential equations (ODEs).…”

Section: Introductionmentioning

confidence: 99%

Approximate simulation of cortical microtubule models using dynamical graph grammars

Medwedeff

Mjolsness

2023

Phys. Biol.

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Dynamical graph grammars (DGGs) are capable of modelling and simulating the dynamics of the cortical microtubule array (CMA) in plant cells by using an exact simulation algorithm derived from a master equation; however, the exact method is slow for large systems. We present preliminary work on an approximate simulation algorithm that is compatible with the DGG formalism. The approximate simulation algorithm uses a spatial decomposition of the domain at the level of the system’s time-evolution operator, to gain efficiency at the cost of some reactions firing out of order, which may introduce errors. The decomposition is more coarsely partitioned by effective dimension 1 (d=0 to 2 or 0 to 3), to promote exact parallelism between different subdomains within a dimension, where most computing will happen, and to confine errors to the interactions between adjacent subdomains of different effective dimensions. To demonstrate these principles we implement a prototype simulator, and run three simple experiments using a DGG for testing the viability of simulating the CMA. We find evidence indicating the initial formulation of the approximate algorithm is substantially faster than the exact algorithm, and one experiment leads to network formation in the long-time behavior, whereas another leads to a long-time behavior of local alignment.

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Modelling in systems biology

Cited by 4 publications

References 53 publications

Study of cohabitation and interconnection effects on normal and leukaemic stem cells dynamics in acute myeloid leukaemia

Study of cohabitation and interconnection effects on normal and leukaemic stem cells dynamics in acute myeloid leukaemia

A minimal kinetic model for the interpretation of complex catalysis in single enzyme molecules

Approximate simulation of cortical microtubule models using dynamical graph grammars

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