scholarly journals Mathematical Model Explaining the Role of CDC6 in the Diauxic Growth of CDK1 Activity during the M-Phase of the Cell Cycle

Cells ◽  
2019 ◽  
Vol 8 (12) ◽  
pp. 1537 ◽  
Author(s):  
Mateusz Dębowski ◽  
Zuzanna Szymańska ◽  
Jacek Z. Kubiak ◽  
Mirosław Lachowicz

In this paper we propose a role for the CDC 6 protein in the entry of cells into mitosis. This has not been considered in the literature so far. Recent experiments suggest that CDC 6 , upon entry into mitosis, inhibits the appearance of active CDK 1 and cyclin B complexes. This paper proposes a mathematical model which incorporates the dynamics of kinase CDK 1 , its regulatory protein cyclin B, the regulatory phosphatase CDC 25 and the inhibitor CDC 6 known to be involved in the regulation of active CDK 1 and cyclin B complexes. The experimental data lead us to formulate a new hypothesis that CDC 6 slows down the activation of inactive complexes of CDK 1 and cyclin B upon mitotic entry. Our mathematical model, based on mass action kinetics, provides a possible explanation for the experimental data. We claim that the dynamics of active complexes CDK 1 and cyclin B have a similar nature to diauxic dynamics introduced by Monod in 1949. In mathematical terms we state it as the existence of more than one inflection point of the curve defining the dynamics of the complexes.

Life ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 97
Author(s):  
Andrei K. Garzon Dasgupta ◽  
Alexey A. Martyanov ◽  
Aleksandra A. Filkova ◽  
Mikhail A. Panteleev ◽  
Anastasia N. Sveshnikova

The process of clustering of plasma membrane receptors in response to their agonist is the first step in signal transduction. The rate of the clustering process and the size of the clusters determine further cell responses. Here we aim to demonstrate that a simple 2-differential equation mathematical model is capable of quantitative description of the kinetics of 2D or 3D cluster formation in various processes. Three mathematical models based on mass action kinetics were considered and compared with each other by their ability to describe experimental data on GPVI or CR3 receptor clustering (2D) and albumin or platelet aggregation (3D) in response to activation. The models were able to successfully describe experimental data without losing accuracy after switching between complex and simple models. However, additional restrictions on parameter values are required to match a single set of parameters for the given experimental data. The extended clustering model captured several properties of the kinetics of cluster formation, such as the existence of only three typical steady states for this system: unclustered receptors, receptor dimers, and clusters. Therefore, a simple kinetic mass-action-law-based model could be utilized to adequately describe clustering in response to activation both in 2D and in 3D.


2009 ◽  
Vol 185 (2) ◽  
pp. 193-202 ◽  
Author(s):  
Arne Lindqvist ◽  
Verónica Rodríguez-Bravo ◽  
René H. Medema

The decision to enter mitosis is mediated by a network of proteins that regulate activation of the cyclin B–Cdk1 complex. Within this network, several positive feedback loops can amplify cyclin B–Cdk1 activation to ensure complete commitment to a mitotic state once the decision to enter mitosis has been made. However, evidence is accumulating that several components of the feedback loops are redundant for cyclin B–Cdk1 activation during normal cell division. Nonetheless, defined feedback loops become essential to promote mitotic entry when normal cell cycle progression is perturbed. Recent data has demonstrated that at least three Plk1-dependent feedback loops exist that enhance cyclin B–Cdk1 activation at different levels. In this review, we discuss the role of various feedback loops that regulate cyclin B–Cdk1 activation under different conditions, the timing of their activation, and the possible identity of the elusive trigger that controls mitotic entry in human cells.


Blood ◽  
2012 ◽  
Vol 120 (21) ◽  
pp. 22-22 ◽  
Author(s):  
Joshuaine Toth ◽  
Guanfa Gan ◽  
Joanne van Ryn ◽  
Holly Dursema ◽  
Jennifer Isler ◽  
...  

Abstract Abstract 22 Background: The objective of this study is to determine the pharmacokinetics (PK) and pharmacodynamics (PD) of dabigatran (a small molecule thrombin inhibitor) and its antidote (a humanized Fab against dabigatran) in the monkey and to develop a combined mechanistic mathematical model to describe the data. Methods: There were three groups: control, antidote alone and dabigatran etexilate (DE) + antidote. Rhesus monkeys (n = 2/group) received either 12 mg/kg/day of DE or vehicle orally on Days 1–4, 15–18 and 29–32 with a single IV dose of the antidote administered 90 minutes after DE on Days 4, 18 and 32. Doses of the antidote were 30, 90 or 175 mg/kg, respectively. PK parameters of the antidote and sum dabigatran (dabigatran plus its glucuronides) were determined after measurements of plasma concentrations. Coagulation activity was measured using a diluted thrombin time assay to determine the activity of the unbound sum dabigatran. Results: The PK of the antidote were not affected by dabigatran. Clearance of the antidote was low (0.87 mL/min/kg) and steady-state volume of distribution was small (0.06 L/kg), indicating that the antidote was mostly restricted to plasma. The plasma profile of the antidote was bi-phasic with a short initial phase t1/2 of 0.4 hour (h) and a terminal phase t1/2 of 4.3 h. Immediately after antidote dosing, plasma concentrations of sum dabigatran increased, a consequence of the rapid redistribution of dabigatran and its glucuronides from tissue to plasma due to binding to the antidote. Complete reversal of dabigatran's anticoagulant activity was observed immediately after antidote dosing at all three dose levels, as measured by the diluted thrombin time assay, which indicates that all dabigatran was bound to the antidote. The degree to which this reversal effect was maintained over an extended period (24 h) was dose-dependent. A mechanistic ordinary differential equation model, based on the mass action kinetics for describing the distribution, binding and elimination of dabigatran and its antidote, was developed by combining the PK models for dabigatran and the antidote and adding the binding interaction (1:1 stoichiometry) between the two compounds. The distribution and elimination parameters of the dabigatran-antidote complex were assumed to be the same as those of the antidote, based on similar measured PK parameters of the antidote with and without dabigatran in the monkey. The combined PK/PD model of dabigatran and antidote was able to describe the in vivo PK/PD data observed in monkeys. Conclusion: The dabigatran-specific antidote successfully reversed the anticoagulant activity of dabigatran in the monkey in a dose-dependent manner, and our combined mathematical model accurately describes monkey PK/PD data of sum dabigatran and its antidote. Insights gained from this model will be used to guide model development for clinical trials. Disclosures: Toth: Boehringer Ingelheim: Employment. Gan:Boehringer Ingelheim: Employment. van Ryn:Boehringer Ingelheim: Employment. Dursema:Boehringer Ingelheim: Employment. Isler:Boehringer Ingelheim: Employment. Coble:Boehringer Ingelheim: Employment. Burke:Boehringer Ingelheim: Employment. Lalovic:Boehringer Ingelheim: Employment. Olson:Boehringer Ingelheim: Employment.


2021 ◽  
Author(s):  
Fabian Froehlich ◽  
Peter Karl Sorger

Motivation: Because they effectively represent mass action kinetics, ordinary differential equation models are widely used to describe biochemical processes. Optimization-based calibration of these models on experimental data can be challenging, even for low-dimensional problems. However, reliable model calibration is a prerequisite for many subsequent analysis steps, including uncertainty analysis, model selection and biological interpretation. Although multiple hypothesis have been advanced to explain why optimization based calibration of biochemical models is challenging, there are few comprehensive studies that test these hypothesis and tools for performing such studies are also lacking. Results: We implemented an established trust-region method as a modular python framework (fides) to enable structured comparison of different approaches to ODE model calibration involving Hessian approximation schemes and trust-region subproblem solvers. We evaluate fides on a set of benchmark problems that include experimental data. We find a high variability in optimizer performance among different implementations of the same algorithm, with fides performing more reliably that other implementations investigated. Our investigation of possible sources of poor optimizer performance identify shortcomings in the widely used Gauss-Newton approximation. We address these shortcomings by proposing a novel hybrid Hessian approximation scheme that enhances optimizer performance.


2021 ◽  
Author(s):  
Sara Hamis ◽  
Yury Kapelyukh ◽  
Aileen McLaren ◽  
Colin J. Henderson ◽  
C. Roland Wolf ◽  
...  

AbstractSimultaneous inhibition of multiple components of the BRAF-MEK-ERK cascade (vertical inhibition) has become a standard of care for treating BRAF-mutant melanoma. However, the molecular mechanisms of how vertical inhibition synergistically suppress intracellular ERK activity, and as a consequence cell proliferation, are yet to be fully elucidated.In this study, we develop a mechanistic mathematical model that describes how the mutant BRAF-inhibitor, dabrafenib, and the MEK-inhibitor, trametinib, affect signaling through the BRAFV600E-MEK-ERK cascade. We formulate a system of chemical reactions that describes cascade signaling dynamics and, using mass action kinetics, the chemical reactions are re-expressed as ordinary differential equations. Using model parameters obtained from in vitro data available in the literature, these equations are solved numerically to obtain the temporal evolution of the concentrations of the components in the signaling cascade.Our mathematical model provides a quantitative method to compute how dabrafenib and trametinib can be used in combination to synergistically inhibit ERK activity in BRAFV600E mutant melanoma cells. This work elucidates molecular mechanisms of vertical inhibition of the BRAFV600E-MEK-ERK cascade and delineates how elevated cellular BRAF concentrations generate drug resistance to dabrafenib and trametinib. In addition, the computational simulations suggest that elevated ATP levels could be a factor in drug resistance to dabrafenib. The mathematical model that is developed in this study will have generic application in the improved design of anticancer combination therapies that target BRAF-MEK-ERK pathways.


2000 ◽  
Author(s):  
Gideon Grafi ◽  
Brian Larkins

The focus of this research project is to investigate the role of endoreduplication in maize endosperm development and the extent to which this process contributes to high levels of starch and storage protein synthesis. Although endoreduplication has been widely observed in many cells and tissues, especially those with high levels of metabolic activity, the molecular mechanisms through which the cell cycle is altered to produce consecutive cycles of S-phase without an intervening M-phase are unknown. Our previous research has shown that changes in the expression of several cell cycle regulatory genes coincide with the onset of endoreduplication. During this process, there is a sharp reduction in the activity of the mitotic cyclin-dependent kinase (CDK) and activation of the S-phase CDK. It appears the M-phase CDK is stable, but its activity is blocked by a proteinaceous inhibitor. Coincidentally, the S-phase checkpoint protein, retinoblastoma (ZmRb), becomes phosphorylated, presumably releasing an E2F-type transcriptional regulator which promotes the expression of genes responsible for DNA synthesis. To investigate the role of these cell cycle proteins in endoreduplication, we have created transgenic maize plants that express various genes in an endosperm-specific manner using a storage protein (g-zein) promoter. During the first year of the grant, we constructed point mutations of the maize M-phase kinase, p34cdc2. One alteration replaced aspartic acid at position 146 with asparagine (p3630-CdcD146N), while another changed threonine 161 to alanine (p3630-CdcT161A). These mutations abolish the activity of the CDK. We hypothesized that expression of the mutant forms of p34cdc2 in endoreduplicating endosperm, compared to a control p34cdc2, would lead to extra cycles of DNA synthesis. We also fused the gene encoding the regulatory subunit of the M- phase kinase, cyclin B, under the g-zein promoter. Normally, cyclin B is expected to be destroyed prior to the onset of endoreduplication. By producing high levels of this protein in developing endosperm, we hypothesized that the M-phase would be extended, potentially reducing the number of cycles of endoreduplication. Finally, we genetically engineered the wheat dwarf virus RepA protein for endosperm-specific expression. RepA binds to the maize retinoblastoma protein and presumably releases E2F-like transcription factors that activate DNA synthesis. We anticipated that inactivation of ZmRb by RepA would lead to additional cycles of DNA synthesis.


2018 ◽  
Vol 15 (142) ◽  
pp. 20170965 ◽  
Author(s):  
Stefano Magni ◽  
Antonella Succurro ◽  
Alexander Skupin ◽  
Oliver Ebenhöh

Global warming exposes plants to severe heat stress, with consequent crop yield reduction. Organisms exposed to high temperature stresses typically protect themselves with a heat shock response (HSR), where accumulation of unfolded proteins initiates the synthesis of heat shock proteins through the heat shock transcription factor HSF1. While the molecular mechanisms are qualitatively well characterized, our quantitative understanding of the underlying dynamics is still very limited. Here, we study the dynamics of HSR in the photosynthetic model organism Chlamydomonas reinhardtii with a data-driven mathematical model of HSR. We based our dynamical model mostly on mass action kinetics, with a few nonlinear terms. The model was parametrized and validated by several independent datasets obtained from the literature. We demonstrate that HSR quantitatively and significantly differs if an increase in temperature of the same magnitude occurs abruptly, as often applied under laboratory conditions, or gradually, which would rather be expected under natural conditions. In contrast to rapid temperature increases, under gradual changes only negligible amounts of misfolded proteins accumulate, indicating that the HSR of C. reinhardtii efficiently avoids the accumulation of misfolded proteins under conditions most likely to prevail in nature. The mathematical model we developed is a flexible tool to simulate the HSR to different conditions and complements the current experimental approaches.


2013 ◽  
Vol 3 (1) ◽  
pp. 1-10 ◽  

Pump-and-treat (P&T) is one of the most common methods for remediation of groundwater contaminated by hazardous wastes. However, this method suffers from serious disadvantages, due a series of subsurface processes. Using experimental data and mathematical model simulations, the role of sorption/ desorption and dissolution of non-aqueous phase liquids on the effectiveness of P&T remediation was examined. The results showed that the remediation of groundwater depends directly on the physical/ chemical properties of the contaminants and the hydrogeology of the site. With the exception of water-soluble contaminants occupying relatively small parts of relatively homogeneous and water-permeable geologic media, the remediation of groundwater contaminated by hazardous waste using P&T is, for all practical purposes, impossible and prohibitively expensive.


2013 ◽  
Vol 330 ◽  
pp. 687-692 ◽  
Author(s):  
Jean Louis Canaletti ◽  
Christian Cristofari ◽  
Gilles Notton

The work described in this paper concerns a part of the modelling of a standalone air solar collector producing low temperature heat. The main role of the system is to avoid freezing temperatures and to reduce humidity in a room or in an unoccupied home during a long time, with only solar radiation. In view to dispose an essential sizing tool for this solar collector, we developed a mathematical model based on energy balance equations and on the characteristics of the system. This model allows simulation of the aerolic and thermal behaviour of the solar collector. It was validated using experimental data collected by telemetry in six operating sites. We present here the behaviour model of the ventilation unit part.


2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Jacek Z. Kubiak ◽  
Mohammed El Dika

Cyclin-Dependent Kinase 1 (CDK1) is the major M-phase kinase known also as the M-phase Promoting Factor or MPF. Studies performed during the last decade have shown many details of how CDK1 is regulated and also how it regulates the cell cycle progression. Xenopus laevis cell-free extracts were widely used to elucidate the details and to obtain a global view of the role of CDK1 in M-phase control. CDK1 inactivation upon M-phase exit is a primordial process leading to the M-phase/interphase transition during the cell cycle. Here we discuss two closely related aspects of CDK1 regulation in Xenopus laevis cell-free extracts: firstly, how CDK1 becomes inactivated and secondly, how other actors, like kinases and phosphatases network and/or specific inhibitors, cooperate with CDK1 inactivation to assure timely exit from the M-phase.


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