Spatial modeling of the membrane-cytosolic interface in protein kinase signal transduction

Giese, Wolfgang; Milicic, Gregor; Schröder, Jörg; Klipp, Edda

doi:10.1101/191940

Cited by 3 publications

(4 citation statements)

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“…While we have used a relatively simple model for ligand-receptor binding to demonstrate the possibilities of the computational framework, the same techniques could be used to investigate the effect of local extracellular ligand depletion by membrane bound enzymes and intracelluar signalling pathways [41]. The method could also be used to consider the effect of cell shape changes on intracellular signalling from the cell cytoplasm to the cell nucleus [22,5,67]. In future work we also plan to couple the GTPase module to a mechanical model for the bulk material velocity which will be driven by the intracellular forces generated by the interaction of actin and myosin and substrate adhesion.…”

Section: Discussionmentioning

confidence: 99%

“…For example, Cusseddu et al [6] recently proposed a bulk-surface extension of the classical wave-pinning (WP) model [49] to investigate cell polarisation in three dimensions. Giese et al [21,22] constructed a two-dimensional model to study the effect of cell size and cell shape on the signalling pathway from the cell membrane to the nucleus. Diegmiller et al [10] used a bulk-surface model to look at pattern formation on the surface of a spherical geometry.…”

Section: Introductionmentioning

confidence: 99%

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A Conservative Finite Element ALE Scheme for Mass-Conserving Reaction-Diffusion Equations on Evolving Two-Dimensional Domains

Mackenzie¹,

Rowlatt²,

Insall³

2019

Preprint

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Mass-conservative reaction-diffusion systems have recently been proposed as a general framework to describe intracellular pattern formation. These systems have been used to model the conformational switching of proteins as they cycle from an inactive state in the cell cytoplasm, to an active state at the cell membrane. The active state then acts as input to downstream effectors. The paradigm of activation by recruitment to the membrane underpins a range of biological pathwaysincluding G-protein signalling, growth control through Ras and PI 3-kinase, and cell polarity through Rac and Rho; all activate their targets by recruiting them from the cytoplasm to the membrane. Global mass conservation lies at the heart of these models reflecting the property that the total number of active and inactive forms, and targets, remains constant. Here we present a conservative arbitrary Lagrangian Eulerian (ALE) finite element method for the approximate solution of systems of bulk-surface reaction-diffusion equations on an evolving two-dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a moving mesh partial differential equation (MMPDE) approach. Global conservation of the fully discrete finite element solution is established independently of the ALE velocity field and the time step size. The developed method is applied to model problems with known analytical solutions; these experiments indicate that the method is second-order accurate and globally conservative. The method is further applied to a model of a single cell migrating in the presence of an external chemotactic signal.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Conservative Finite Element ALE Scheme for Mass-Conserving Reaction-Diffusion Equations on Evolving Two-Dimensional Domains

Mackenzie¹,

Rowlatt²,

Insall³

2019

Preprint

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“…Bitki hücrelerinin biyotik bir sinyali hücre yüzey reseptörleriyle algıladıktan sonra sitosolik reseptörlerle bağlantılı olarak karmaşık bir ağ mekanizmasıyla nükleusa kadar ilettiği bilinmektedir [7]. Bu sinyaller yoluyla bitkiler kendi hücrelerinde önceden mevcut olan sekonder antimikrobiyal kimyasalları kullanarak ve savunma tepkimelerini teşvik ederek, patojen saldırılarına karşı koymaktadırlar [8].…”

Section: Introductionunclassified

Bitki Hastalık Dayanıklılık Proteinleri; İmmün Savunma Molekülleri Olarak R-gen Ürünleri

Baş

2021

International Journal of Life Sciences and Biotechnology

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Çoğu bitkinin NBS-LRR proteinlerini kodlayan hastalık dayanıklılığı ile ilgili R genleri, sistemik olarak kazanılmış immünitede işlevseldir, kısaca ETI olarakta bilinir. Patojen organizmalar hücre yüzey reseptörleri ile harekete geçirilen PTI immüniteyi bertaraf ettikten sonra, daha sonraki aşamada ETI immünite aktif hale geçmektedir. Aynı zamanda patojen organizmaların efektörleri direkt sitoplazmaya ulaşınca, efektörleri tanıyan R proteinleri aracılığı ile PTI'nin etkisinden daha hızlı ve güçlü bir ETI immün tepki gelişmektedir. Patojen efektörlerinin çoğu, epitop-paratop ilişkisindeki yapısal interaksiyona benzer şekilde direkt veya indirekt olarak R-gen proteinleri ile reaksiyona girerler. Bilinen bütün biyotik faktörlere, birbirine benzer tepki veren bitkiler ne tür mekanizmalarla çok çeşitli patojen efektörlerini tanımaktadırlar? Ancak bitkilerdeki hücre içi örnek-tanıma reseptörlerinin moleküler mekanizmalarıyla ilgili birçok yaklaşım mevcut olmakla beraber, her mekanizmaya ait sonuçlar, kişisel olarak araştırmacıların kendi özel çalışmalarından elde edilmiştir. Çok çeşitli efektörreseptör tanımanın moleküler interaksiyonunda geçerli olan toplam kaç farklı strateji modelinin işlevsel olduğu bilinmemektedir. Bu nedenle sunulan derlemede, birçok farklı efektörler ile intraselüler reseptörleri arasındaki fiziki bağlantının moleküler mekanizma çeşitlerine odaklanılmıştır.

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“…An especially challenging issue in studying intracellular signaling pathways stems from the complicated geometry of the cytosolic space [24]. While mathematical models often depict the cytoplasm as an empty space [21,41,42], it is actually crowded, tortuous, and highly heterogeneous [9,23]. In fact, several important works have found that such tortuous and crowded geometries can drastically affect FPTs [8,29,57].…”

Section: Introductionmentioning

confidence: 99%

The effects of fast inactivation on conditional first passage times of mortal diffusive searchers

Lawley¹

2020

Preprint

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The first time a searcher finds a target is called a first passage time (FPT). In many physical, chemical, and biological processes, the searcher is "mortal," which means that the searcher might become inactivated (degrade, die, etc.) before finding the target. In the context of intracellular signaling, an important recent work discovered that fast inactivation can drastically alter the conditional FPT distribution of a mortal diffusive searcher, if the searcher is conditioned to find the target before inactivation. In this paper, we prove a general theorem which yields an explicit formula for all the moments of such conditional FPTs in the fast inactivation limit. This formula is quite universal, as it holds under very general conditions on the diffusive searcher dynamics, the target, and the spatial domain. These results prove in significant generality that if inactivation is fast, then the conditional FPT compared to the FPT without inactivation is (i) much faster, (ii) much less affected by spatial heterogeneity, and (iii) much less variable. Our results agree with recent computational and theoretical analysis of a certain discrete intracellular diffusion model and confirm a conjecture related to the effect of spatial heterogeneity on intracellular signaling.

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Spatial modeling of the membrane-cytosolic interface in protein kinase signal transduction

Abstract: The spatial architecture of signaling pathways and the inter-

Cited by 3 publications

References 50 publications

A Conservative Finite Element ALE Scheme for Mass-Conserving Reaction-Diffusion Equations on Evolving Two-Dimensional Domains

A Conservative Finite Element ALE Scheme for Mass-Conserving Reaction-Diffusion Equations on Evolving Two-Dimensional Domains

Bitki Hastalık Dayanıklılık Proteinleri; İmmün Savunma Molekülleri Olarak R-gen Ürünleri

The effects of fast inactivation on conditional first passage times of mortal diffusive searchers

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