scholarly journals A condensate dynamic instability orchestrates oocyte actomyosin cortex activation

2021 ◽  
Author(s):  
Victoria Tianjing Yan ◽  
Arjun Narayanan ◽  
Frank Julicher ◽  
Stephan W Grill
Keyword(s):  
Phase Portrait ◽  
Chemical Reactions ◽  
Dynamic Instability ◽  
Growth Dynamics ◽  
Mass Action ◽  
Cortical Actin ◽  
Mass Action Kinetics ◽  
C Elegans ◽  
Micro Emulsion ◽  
Phase Portrait Analysis

A key event at the onset of development is the activation of a contractile actomyosin cortex during the oocyte-to-embryo transition. We here report on the discovery that in C. elegans oocytes, actomyosin cortex activation is supported by the emergence of thousands of short-lived protein condensates rich in F-actin, N-WASP, and ARP2/3 that form an active micro-emulsion. A phase portrait analysis of the dynamics of individual cortical condensates reveals that condensates initially grow, and then switch to disassembly before dissolving completely. We find that in contrast to condensate growth via diffusion, the growth dynamics of cortical condensates are chemically driven. Remarkably, the associated chemical reactions obey mass action kinetics despite governing both composition and size. We suggest that the resultant condensate dynamic instability suppresses coarsening of the active micro-emulsion, ensures reaction kinetics that are independent of condensate size, and prevents runaway F-actin nucleation during the formation of the first cortical actin meshwork.

scholarly journals Mathematical modeling quantifies ERK-activity in response to inhibition of the BRAFV600E-MEK-ERK cascade

2021 ◽  
Author(s):  
Sara Hamis ◽  
Yury Kapelyukh ◽  
Aileen McLaren ◽  
Colin J. Henderson ◽  
C. Roland Wolf ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Drug Resistance ◽  
Chemical Reactions ◽  
Molecular Mechanisms ◽  
Braf Inhibitor ◽  
Mass Action ◽  
Model Parameters ◽  
Mass Action Kinetics ◽  
Erk Activity

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.

scholarly journals Quantifying ERK activity in response to inhibition of the BRAFV600E-MEK-ERK cascade using mathematical modelling

2021 ◽  
Author(s):  
Sara J. Hamis ◽  
Yury Kapelyukh ◽  
Aileen McLaren ◽  
Colin J. Henderson ◽  
C. Roland Wolf ◽  
...  
Keyword(s):  
Drug Resistance ◽  
Chemical Reactions ◽  
Molecular Mechanisms ◽  
Braf Inhibitor ◽  
Standard Of Care ◽  
Mek Inhibitor ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Erk Activity

Abstract Background Simultaneous 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 mechanism of how vertical inhibition synergistically suppresses intracellular ERK activity, and consequently cell proliferation, are yet to be fully elucidated. Methods We develop a mechanistic mathematical model that describes how the mutant BRAF inhibitor, dabrafenib, and the MEK inhibitor, trametinib, affect BRAFV600E-MEK-ERK signalling. The model is based on a system of chemical reactions that describes cascade signalling dynamics. Using mass action kinetics, the chemical reactions are re-expressed as ordinary differential equations that are parameterised by in vitro data and solved numerically to obtain the temporal evolution of cascade component concentrations. Results The 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. The model elucidates molecular mechanisms of vertical inhibition of the BRAFV600E-MEK-ERK cascade and delineates how elevated BRAF concentrations generate drug resistance to dabrafenib and trametinib. The computational simulations further suggest that elevated ATP levels could be a factor in drug resistance to dabrafenib. Conclusions The model can be used to systematically motivate which dabrafenib–trametinib dose combinations, for treating BRAFV600E-mutated melanoma, warrant experimental investigation.

Non-equilibrium Thermodynamical Principles for Chemical Reactions with Mass-Action Kinetics

2017 ◽  
Vol 77 (4) ◽  
pp. 1562-1585 ◽  
Author(s):  
Alexander Mielke ◽  
Robert I. A. Patterson ◽  
Mark A. Peletier ◽  
D. R. Michiel Renger
Keyword(s):  
Chemical Reactions ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Non Equilibrium

scholarly journals Training an asymmetric signal perceptron through reinforcement in an artificial chemistry

2014 ◽  
Vol 11 (93) ◽  
pp. 20131100 ◽  
Author(s):  
Peter Banda ◽  
Christof Teuscher ◽  
Darko Stefanovic
Keyword(s):  
State Of The Art ◽  
Chemical Species ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Dna Strand Displacement ◽  
Autonomous Adaptation ◽  
Biochemical Systems ◽  
Dna Strand ◽  
Logic Functions ◽  
Application Specific

State-of-the-art biochemical systems for medical applications and chemical computing are application-specific and cannot be reprogrammed or trained once fabricated. The implementation of adaptive biochemical systems that would offer flexibility through programmability and autonomous adaptation faces major challenges because of the large number of required chemical species as well as the timing-sensitive feedback loops required for learning. In this paper, we begin addressing these challenges with a novel chemical perceptron that can solve all 14 linearly separable logic functions. The system performs asymmetric chemical arithmetic, learns through reinforcement and supports both Michaelis–Menten as well as mass-action kinetics. To enable cascading of the chemical perceptrons, we introduce thresholds that amplify the outputs. The simplicity of our model makes an actual wet implementation, in particular by DNA-strand displacement, possible.

Microstructure-dependent dynamic stability analysis of torsional NEMS scanner in van der Waals regime

2016 ◽  
Vol 30 (18) ◽  
pp. 1650109 ◽  
Author(s):  
Javad Abdi ◽  
Maryam Keivani ◽  
Mohamadreza Abadyan
Keyword(s):  
Phase Portrait ◽  
Applied Voltage ◽  
Dynamic Instability ◽  
Equilibrium Points ◽  
Van Der Waals ◽  
Continuum Theory ◽  
Pitchfork Bifurcation ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Microstructure Parameters

The physico-mechanical behavior of nanoscale devices might be microstructure dependent. However, the classical continuum theory cannot correctly predict the microstructure dependency. In this paper, the strain gradient theory is employed to examine the instability characteristics of a nanoscanner with circular geometry. The governing equation of the scanner is derived incorporating the Coulomb and van der Waals (vdW) forces. The influences of applied voltage, squeeze damping and microstructure parameters on the dynamic instability of equilibrium points are studied by plotting the phase portrait and bifurcation diagrams. In the presence of the applied voltage, the phase portrait shows the saddle-node bifurcation while for freestanding scanner a subcritical pitchfork bifurcation is observed. It is concluded that the microstructure parameter enhances the torsional stability.

scholarly journals How is the effectiveness of immune surveillance impacted by the spatial distribution of spreading infections?

2015 ◽  
Vol 370 (1675) ◽  
pp. 20140289 ◽  
Author(s):  
Ulrich D. Kadolsky ◽  
Andrew J. Yates
Keyword(s):  
Spatial Distribution ◽  
Immune Surveillance ◽  
Critical Density ◽  
Search Time ◽  
Handling Time ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Expected Time ◽  
Target Ratio ◽  
Infected Cells

What effect does the spatial distribution of infected cells have on the efficiency of their removal by immune cells, such as cytotoxic T lymphocytes (CTL)? If infected cells spread in clusters, CTL may initially be slow to locate them but subsequently kill more rapidly than in diffuse infections. We address this question using stochastic, spatially explicit models of CTL interacting with different patterns of infection. Rather than the effector : target ratio, we show that the relevant quantity is the ratio of a CTL's expected time to locate its next target (search time) to the average time it spends conjugated with a target that it is killing (handling time). For inefficient (slow) CTL, when the search time is always limiting, the critical density of CTL (that required to control 50% of infections, C * ) is independent of the spatial distribution and derives from simple mass-action kinetics. For more efficient CTL such that handling time becomes limiting, mass-action underestimates C * , and the more clustered an infection the greater is C * . If CTL migrate chemotactically towards targets the converse holds— C * falls, and clustered infections are controlled most efficiently. Real infections are likely to spread patchily; this combined with even weak chemotaxis means that sterilizing immunity may be achieved with substantially lower numbers of CTL than standard models predict.

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