scholarly journals Equilibrium probability distribution for number of bound receptor-ligand complexes

2021 ◽  
Vol 89 (1) ◽  
pp. 41-50
Author(s):  
Tuhin Chakrabortty ◽  
Manoj M. Varma
Keyword(s):  
Probability Distribution ◽  
Receptor Ligand ◽  
Equilibrium Probability

Analysis of a non-preemptive priority multiserver queue

1988 ◽  
Vol 20 (04) ◽  
pp. 852-879 ◽  
Author(s):  
H. R. Gail ◽  
S. L. Hantler ◽  
B. A. Taylor
Keyword(s):  
Probability Distribution ◽  
Queueing System ◽  
Waiting Times ◽  
Complex Variables ◽  
Arrival Process ◽  
Preemptive Priority ◽  
Multiple Servers ◽  
The Mean ◽  
Equilibrium Probability ◽  
Number Of Customers

We consider a non-preemptive priority head of the line queueing system with multiple servers and two classes of customers. The arrival process for each class is Poisson, and the service times are exponentially distributed with different means. A Markovian state description consists of the number of customers of each class in service and in the queue. We solve a matrix equation to obtain the generating function of the equilibrium probability distribution by analyzing singularities of the equation coefficients, which are meromorphic matrices of two complex variables. We then obtain the mean waiting times for each class.

Analysis of a non-preemptive priority multiserver queue

1988 ◽  
Vol 20 (4) ◽  
pp. 852-879 ◽  
Author(s):  
H. R. Gail ◽  
S. L. Hantler ◽  
B. A. Taylor
Keyword(s):  
Probability Distribution ◽  
Queueing System ◽  
Waiting Times ◽  
Complex Variables ◽  
Arrival Process ◽  
Preemptive Priority ◽  
Multiple Servers ◽  
The Mean ◽  
Equilibrium Probability ◽  
Number Of Customers

We consider a non-preemptive priority head of the line queueing system with multiple servers and two classes of customers. The arrival process for each class is Poisson, and the service times are exponentially distributed with different means. A Markovian state description consists of the number of customers of each class in service and in the queue. We solve a matrix equation to obtain the generating function of the equilibrium probability distribution by analyzing singularities of the equation coefficients, which are meromorphic matrices of two complex variables. We then obtain the mean waiting times for each class.

scholarly journals Three-dimensional Monte Carlo simulations of the dynamics of macromolecular particles in solutions flowing in mesopores

2010 ◽  
Vol 8 (5) ◽  
pp. 1009-1013 ◽  
Author(s):  
Ali Atwi ◽  
Antoine Khater ◽  
Abbas Hijazi
Keyword(s):  
Monte Carlo ◽  
Probability Distribution ◽  
Numerical Simulations ◽  
Solid Surface ◽  
Dynamic Equilibrium ◽  
Three Dimensional ◽  
Distribution Functions ◽  
Depletion Layer ◽  
Probability Distribution Functions ◽  
Equilibrium Probability

AbstractNumerical simulations are developed to calculate the dynamic equilibrium probability distribution functions (PDF) for macromolecular rod-like particles suspended in a fluid under hydrodynamic flow inside mesopores. The simulations take into account the effects of Brownian and hydrodynamic forces acting on the particles, as well as diffusive collisions of the particles with the solid surface boundaries. An algorithm is developed for this purpose based on Jeffery’s equations for the dynamics of ellipsoidal objects in bulk fluids, and on a mechanism of restitution for the diffusive collisions. The results are presented with a focus on the depletion layer next to two types of solid boundaries, ideally flat and rough. They demonstrate the significance of numerical simulations in 3D compared to previous results based on a 2D approach. In particular, we are able to obtain a complete topography for the PDFs segmented as a hierarchy in the depletion layer.

scholarly journals Quantifying the phosphorylation timescales of receptor–ligand complexes: a Markovian matrix-analytic approach

Open Biology ◽  
2018 ◽  
Vol 8 (9) ◽  
pp. 180126 ◽  
Author(s):  
M. López-García ◽  
M. Nowicka ◽  
C. Bendtsen ◽  
G. Lythe ◽  
S. Ponnambalam ◽  
...  
Keyword(s):  
Vascular Endothelial Growth Factor ◽  
Steady State ◽  
Growth Factor ◽  
Probability Distribution ◽  
State Probability ◽  
Vascular Endothelial ◽  
Steady State Probability ◽  
Receptor Ligand ◽  
Receptor Signalling ◽  
Endothelial Growth Factor

Cells interact with the extracellular environment by means of receptor molecules on their surface. Receptors can bind different ligands, leading to the formation of receptor–ligand complexes. For a subset of receptors, called receptor tyrosine kinases, binding to ligand enables sequential phosphorylation of intra-cellular residues, which initiates a signalling cascade that regulates cellular function and fate. Most mathematical modelling approaches employed to analyse receptor signalling are deterministic, especially when studying scenarios of high ligand concentration or large receptor numbers. There exist, however, biological scenarios where low copy numbers of ligands and/or receptors need to be considered, or where signalling by a few bound receptor–ligand complexes is enough to initiate a cellular response. Under these conditions stochastic approaches are appropriate, and in fact, different attempts have been made in the literature to measure the timescales of receptor signalling initiation in receptor–ligand systems. However, these approaches have made use of numerical simulations or approximations, such as moment-closure techniques. In this paper, we study, from an analytical perspective, the stochastic times to reach a given signalling threshold for two receptor–ligand models. We identify this time as an extinction time for a conveniently defined auxiliary absorbing continuous time Markov process, since receptor–ligand association/dissociation events can be analysed in terms of quasi-birth-and-death processes. We implement algorithmic techniques to compute the different order moments of this time, as well as the steady-state probability distribution of the system. A novel feature of the approach introduced here is that it allows one to quantify the role played by each kinetic rate in the timescales of signal initiation, and in the steady-state probability distribution of the system. Finally, we illustrate our approach by carrying out numerical studies for the vascular endothelial growth factor and one of its receptors, the vascular endothelial growth factor receptor of human endothelial cells.

scholarly journals DIRECTED RANDOM MARKETS: CONNECTIVITY DETERMINES MONEY

2013 ◽  
Vol 24 (01) ◽  
pp. 1250088 ◽  
Author(s):  
ISMAEL MARTÍNEZ-MARTÍNEZ ◽  
RICARDO LÓPEZ-RUIZ
Keyword(s):  
Probability Distribution ◽  
Economic System ◽  
Probability Distributions ◽  
Economic Agent ◽  
Statistical Equilibrium ◽  
Stationary Probability ◽  
New Family ◽  
Underlying Network ◽  
The Mean ◽  
Equilibrium Probability

Boltzmann–Gibbs (BG) distribution arises as the statistical equilibrium probability distribution of money among the agents of a closed economic system where random and undirected exchanges are allowed. When considering a model with uniform savings in the exchanges, the final distribution is close to the gamma family. In this paper, we implement these exchange rules on networks and we find that these stationary probability distributions are robust and they are not affected by the topology of the underlying network. We introduce a new family of interactions: random but directed ones. In this case, it is found the topology to be determinant and the mean money per economic agent is related to the degree of the node representing the agent in the network. The relation between the mean money per economic agent and its degree is shown to be linear.

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