scholarly journals On Exact and Approximate Approaches for Stochastic Receptor-Ligand Competition Dynamics—An Ecological Perspective

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1014
Author(s):  
Polly-Anne Jeffrey ◽  
Martín López-García ◽  
Mario Castro ◽  
Grant Lythe ◽  
Carmen Molina-París
Keyword(s):  
Summary Statistics ◽  
Steady State Distribution ◽  
State Distribution ◽  
Cellular Receptors ◽  
Stochastic Description ◽  
The Matrix ◽  
Common Resource ◽  
A Cell ◽  
The Common ◽  
Cellular Medium

Cellular receptors on the cell membrane can bind ligand molecules in the extra-cellular medium to form ligand-bound monomers. These interactions ultimately determine the fate of a cell through the resulting intra-cellular signalling cascades. Often, several receptor types can bind a shared ligand leading to the formation of different monomeric complexes, and in turn to competition for the common ligand. Here, we describe competition between two receptors which bind a common ligand in terms of a bi-variate stochastic process. The stochastic description is important to account for fluctuations in the number of molecules. Our interest is in computing two summary statistics—the steady-state distribution of the number of bound monomers and the time to reach a threshold number of monomers of a given kind. The matrix-analytic approach developed in this manuscript is exact, but becomes impractical as the number of molecules in the system increases. Thus, we present novel approximations which can work under low-to-moderate competition scenarios. Our results apply to systems with a larger number of population species (i.e., receptors) competing for a common resource (i.e., ligands), and to competition systems outside the area of molecular dynamics, such as Mathematical Ecology.

scholarly journals Infinite Series of Singularities in the Correlated Random Matrices Product

2021 ◽  
Vol 9 ◽  
Author(s):  
Ruben Poghosyan ◽  
David B. Saakian
Keyword(s):  
Infinite Series ◽  
Transition Probabilities ◽  
Initial Vector ◽  
Steady State Distribution ◽  
State Distribution ◽  
The Matrix ◽  
Previous Round ◽  
Random Product ◽  
Transition Points ◽  
Product Of Matrices

We consider the product of a large number of two 2 × 2 matrices chosen randomly (with some correlation): at any round there are transition probabilities for the matrix type, depending on the choice at previous round. Previously, a functional equation has been derived to calculate such a random product of matrices. Here, we identify the phase structure of the problem with exact expressions for the transition points separating “localized” and “ergodic” regimes. We demonstrate that the latter regime develops through a formation of an infinite series of singularities in the steady-state distribution of vectors that results from the action of the random product of matrices on an initial vector.

On steady-state queue size distributions of the discrete-time GI/G/1 queue

1996 ◽  
Vol 28 (04) ◽  
pp. 1177-1200 ◽  
Author(s):  
Tao Yang ◽  
M. L. Chaudhry
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Linear Transformation ◽  
State System ◽  
Interarrival Time ◽  
Steady State Distribution ◽  
State Distribution ◽  
The Matrix ◽  
Matrix Geometric Solution ◽  
System Length

In this paper, we present results for the steady-state system length distributions of the discrete-timeGI/G/1 queue. We examine the system at customer arrival epochs (customer departure epochs) and use the residual service time (residual interarrival time) as the supplementary variable. The embedded Markov chain is ofGI/M/1 type if the embedding points are arrival epochs and is ofM/G/1 type if the embedding points are departure epochs. Using the matrix analytic method, we identify the necessary and sufficient condition for both Markov chains to be positive recurrent. For theGI/M/1 type chain, we derive a matrix-geometric solution for its steady-state distribution and for theM/G/1 type chain, we develop a simple linear transformation that relates it to theGI/M/1 type chain and leads to a simple analytic solution for its steady-state distribution. We also show that the steady-state system length distribution at an arbitrary point in time can be obtained by a simple linear transformation of the matrix-geometric solution for theGI/M/1 type chain. A number of applications of the model to communication systems and numerical examples are also discussed.

On steady-state queue size distributions of the discrete-time GI/G/1 queue

1996 ◽  
Vol 28 (4) ◽  
pp. 1177-1200 ◽  
Author(s):  
Tao Yang ◽  
M. L. Chaudhry
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Linear Transformation ◽  
State System ◽  
Interarrival Time ◽  
Steady State Distribution ◽  
State Distribution ◽  
The Matrix ◽  
Matrix Geometric Solution ◽  
System Length

In this paper, we present results for the steady-state system length distributions of the discrete-time GI/G/1 queue. We examine the system at customer arrival epochs (customer departure epochs) and use the residual service time (residual interarrival time) as the supplementary variable. The embedded Markov chain is of GI/M/1 type if the embedding points are arrival epochs and is of M/G/1 type if the embedding points are departure epochs. Using the matrix analytic method, we identify the necessary and sufficient condition for both Markov chains to be positive recurrent. For the GI/M/1 type chain, we derive a matrix-geometric solution for its steady-state distribution and for the M/G/1 type chain, we develop a simple linear transformation that relates it to the GI/M/1 type chain and leads to a simple analytic solution for its steady-state distribution. We also show that the steady-state system length distribution at an arbitrary point in time can be obtained by a simple linear transformation of the matrix-geometric solution for the GI/M/1 type chain. A number of applications of the model to communication systems and numerical examples are also discussed.

Kinetic analysis of mechanism of intestinal Na+-dependent sugar transport

1985 ◽  
Vol 248 (5) ◽  
pp. C498-C509 ◽  
Author(s):  
D. Restrepo ◽  
G. A. Kimmich
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Sugar Transport ◽  
Enzyme Kinetic ◽  
Steady State Distribution ◽  
State Distribution ◽  
Least Squares Fit ◽  
Coupling Stoichiometry ◽  
Rate Limiting ◽  
Kinetics Of

Zero-trans kinetics of Na+-sugar cotransport were investigated. Sugar influx was measured at various sodium and sugar concentrations in K+-loaded cells treated with rotenone and valinomycin. Sugar influx follows Michaelis-Menten kinetics as a function of sugar concentration but not as a function of Na+ concentration. Nine models with 1:1 or 2:1 sodium:sugar stoichiometry were considered. The flux equations for these models were solved assuming steady-state distribution of carrier forms and that translocation across the membrane is rate limiting. Classical enzyme kinetic methods and a least-squares fit of flux equations to the experimental data were used to assess the fit of the different models. Four models can be discarded on this basis. Of the remaining models, we discard two on the basis of the trans sodium dependence and the coupling stoichiometry [G. A. Kimmich and J. Randles, Am. J. Physiol. 247 (Cell Physiol. 16): C74-C82, 1984]. The remaining models are terter ordered mechanisms with sodium debinding first at the trans side. If transfer across the membrane is rate limiting, the binding order can be determined to be sodium:sugar:sodium.

scholarly journals The Evolution of Networks and Local Public Good Provision: A Potential Approach

Games ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 55
Author(s):  
Markus Kinateder ◽  
Luca Paolo Merlino
Keyword(s):  
Public Good ◽  
Nash Equilibria ◽  
Potential Game ◽  
Public Good Provision ◽  
Local Public Good ◽  
Steady State Distribution ◽  
State Distribution ◽  
Long Run ◽  
Split Graphs ◽  
Good Provision

In this paper, we propose a game in which each player decides with whom to establish a costly connection and how much local public good is provided when benefits are shared among neighbors. We show that, when agents are homogeneous, Nash equilibrium networks are nested split graphs. Additionally, we show that the game is a potential game, even when we introduce heterogeneity along several dimensions. Using this result, we introduce stochastic best reply dynamics and show that this admits a unique and stationary steady state distribution expressed in terms of the potential function of the game. Hence, even if the set of Nash equilibria is potentially very large, the long run predictions are sharp.

scholarly journals 3D reconstruction of genomic regions from sparse interaction data

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Julen Mendieta-Esteban ◽  
Marco Di Stefano ◽  
David Castillo ◽  
Irene Farabella ◽  
Marc A Marti-Renom
Keyword(s):  
3D Models ◽  
Genomic Region ◽  
Gene Promoters ◽  
Chromosome Conformation ◽  
The Matrix ◽  
Chromatin Structural ◽  
A Cell ◽  
Similar Accuracy ◽  
Genomic Regions ◽  
Interaction Matrices

Abstract Chromosome conformation capture (3C) technologies measure the interaction frequency between pairs of chromatin regions within the nucleus in a cell or a population of cells. Some of these 3C technologies retrieve interactions involving non-contiguous sets of loci, resulting in sparse interaction matrices. One of such 3C technologies is Promoter Capture Hi-C (pcHi-C) that is tailored to probe only interactions involving gene promoters. As such, pcHi-C provides sparse interaction matrices that are suitable to characterize short- and long-range enhancer–promoter interactions. Here, we introduce a new method to reconstruct the chromatin structural (3D) organization from sparse 3C-based datasets such as pcHi-C. Our method allows for data normalization, detection of significant interactions and reconstruction of the full 3D organization of the genomic region despite of the data sparseness. Specifically, it builds, with as low as the 2–3% of the data from the matrix, reliable 3D models of similar accuracy of those based on dense interaction matrices. Furthermore, the method is sensitive enough to detect cell-type-specific 3D organizational features such as the formation of different networks of active gene communities.

scholarly journals LOCALIZATION OF UROMUCOID IN HUMAN KIDNEY AND IN SECTIONS OF HUMAN KIDNEY STONE WITH THE FLUORESCENT ANTIBODY TECHNIQUE

1965 ◽  
Vol 13 (3) ◽  
pp. 155-160 ◽  
Author(s):  
H. J. KEUTEL
Keyword(s):  
Kidney Stones ◽  
Kidney Stone ◽  
Fluorescent Antibody ◽  
Human Kidney ◽  
Fluorescent Antibody Technique ◽  
Renal Tubules ◽  
Antibody Technique ◽  
The Matrix ◽  
Normal Human ◽  
The Common

Fluorescent labeled antibodies were used for the demonstration of uromucoid. This urine specific mucoprotein is demonstrably present only in the epithelial cells of the proximal segments of the normal human renal tubules and in the matrix of human kidney stones of all the common crystalline compositions.

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