Regulation of kinase activity by diffusion and feedback

Kaźmierczak, Bogdan; Lipniacki, Tomasz

doi:10.1016/j.jtbi.2009.03.016

Cited by 31 publications

(50 citation statements)

References 11 publications

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“…In fact, our main theorem is a natural generalization of the main result of [9], where a connection was established between recent PDE and ODE models of synaptic depression. Compare also the model of kinase activity presented in [26] where, much as in our case, fast diffusion combined with feedback from the boundary results in a singular perturbation and a surprising limit. Examples of interesting biological membranes may also be derived from modeling efflux proteins.…”

Section: Intuitionmentioning

confidence: 66%

From Diffusions on Graphs to Markov Chains via Asymptotic State Lumping

Bobrowski

2012

Ann. Henri Poincaré

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Abstract. We show that fast diffusions on finite graphs with semi permeable membranes on vertices may be approximated by finite-state Markov chains provided the related permeability coefficients are appropriately small. The convergence theorem involves a singular perturbation with singularity in both operator and boundary/transmission conditions, and the related semigroups of operators converge in an irregular manner. The result is motivated by recent models of synaptic depression. IntuitionImagine a finite graph G without loops and a Markov process on G obeying the following informal rules.• While on the ith edge, imagined as a C 1 curve in R 3 , the process behaves like a one-dimensional Brownian motion with variance σ i > 0.• Graph's vertices are semipermeable membranes, allowing communication between the edges; permeability coefficients p ij , describing the possibility to filter through the membrane from the ith to the jth edge, depend on the edges. In particular, p ij is in general different from p ji . At each vertex, the process may also be killed and removed from the state space. Now, suppose the diffusion's speed increases while membranes' permeability decreases (i.e., σ i → ∞ and p ij → 0). As a result, points in each edge communicate almost immediately and in the limit are lumped together, but the membranes prevent lumping of points from different edges. We will show, nevertheless, that the assumption that the rate with which permeability coefficients tend to zero is the same as the rate with which the diffusion coefficients tend to infinity, leads to a limit process in which communication between lumped edges is possible. The lumped edges form then the vertices in the

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Section: Intuitionmentioning

confidence: 66%

From Diffusions on Graphs to Markov Chains via Asymptotic State Lumping

Bobrowski

2012

Ann. Henri Poincaré

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“…However, the detailed activation mechanism of RbohD has remained unclear. Kazmierczak and Lipniacki (2009) found that the diffusion coefficient was related to the activation of kinase. Thus, we next investigated the relationship between the mobility and activation of RbohD.…”

Section: Discussionmentioning

confidence: 99%

Clathrin and Membrane Microdomains Cooperatively Regulate RbohD Dynamics and Activity in Arabidopsis

et al. 2014

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Arabidopsis thaliana respiratory burst oxidase homolog D (RbohD) functions as an essential regulator of reactive oxygen species (ROS). However, our understanding of the regulation of RbohD remains limited. By variable-angle total internal reflection fluorescence microscopy, we demonstrate that green fluorescent protein (GFP)-RbohD organizes into dynamic spots at the plasma membrane. These RbohD spots have heterogeneous diffusion coefficients and oligomerization states, as measured by photobleaching techniques. Stimulation with ionomycin and calyculin A, which activate the ROS-producing enzymatic activity of RbohD, increases the diffusion and oligomerization of RbohD. Abscisic acid and flg22 treatments also increase the diffusion coefficient and clustering of GFP-RbohD. Single-particle analysis in clathrin heavy chain2 mutants and a Flotillin1 artificial microRNA line demonstrated that clathrin-and microdomain-dependent endocytic pathways cooperatively regulate RbohD dynamics. Under salt stress, GFP-RbohD assembles into clusters and then internalizes into the cytoplasm. Dual-color fluorescence cross-correlation spectroscopy analysis further showed that salt stress stimulates RbohD endocytosis via membrane microdomains. We demonstrate that microdomain-associated RbohD spots diffuse at the membrane with high heterogeneity, and these dynamics closely relate to RbohD activity. Our results provide insight into the regulation of RbohD activity by clustering and endocytosis, which facilitate the activation of redox signaling pathways.

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“…The operator A 1 given by A 1 f = Af − f, f ∈ C[0, 1] appears implicitly in the recent model of kinase activity in a living cell [17]. In this model, the cell is viewed as a unit ball where the active kinase particles diffuse freely and may be randomly inactivated (hence the term −f in the definition of A 1 f ).…”

Section: A Bessel Process With Mass Inflowmentioning

confidence: 99%

“…The inactive kinase particles perform a similar motion but, upon touching the boundary some of them are being activated. The boundary condition f (1) = μf (1) describes the "inflow" [17] of activated kinase particles reflected from the boundary x = 1. For simplicity, we do not take into account the fact that the number of kinase particles (active and inactive) is limited.…”

Section: A Bessel Process With Mass Inflowmentioning

confidence: 99%

“…This note is devoted to further examples of an application of the method in the theory of semigroups of operators. These include a more direct semigroup-theoretic treatment of abstract delay differential equations [9], a simplified derivation of the form of the McKendrick semigroup [26], and the generation theorem for a semigroup describing kinase activity in the recent model of Kaźmierczak and Lipniacki [17]. For an alternative way of dealing with boundary conditions in semigroup theory see [13].…”

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confidence: 99%

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Lord Kelvin’s method of images in semigroup theory

Bobrowski

2010

Semigroup Forum

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We show that Lord Kelvin's method of images is a way to prove generation theorems for semigroups of operators. To this end we exhibit three examples: a more direct semigroup-theoretic treatment of abstract delay differential equations, a new derivation of the form of the McKendrick semigroup, and a generation theorem The general ideaLord Kelvin's method of images is an ingenious way of solving problems involving boundary conditions, see e.g. [4,7,11,14,18,19,24] and references given there. The idea of employing the method to prove generation theorems for semigroups of operators goes apparently back to W. Feller who constructed the semigroup of the minimal (and the reflected) Brownian motion on R + by noting that the space of odd (even) functions is left invariant by the semigroup of the unrestricted Brownian motion on R, see [12], pp. 341-343, comp. [3]. These semigroups are generated by the one-dimensional Laplacian with Dirichlet and Neumann boundary conditions at the origin, respectively. A question whether a similar construction can be carried out also in the case of more general boundary conditions, seems to have been opened for Communicated

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Regulation of kinase activity by diffusion and feedback

Cited by 31 publications

References 11 publications

From Diffusions on Graphs to Markov Chains via Asymptotic State Lumping

From Diffusions on Graphs to Markov Chains via Asymptotic State Lumping

Clathrin and Membrane Microdomains Cooperatively Regulate RbohD Dynamics and Activity in Arabidopsis

Lord Kelvin’s method of images in semigroup theory

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