scholarly journals A Host-Parasite Model for a Two-Type Cell Population

2013 ◽  
Vol 45 (03) ◽  
pp. 719-741 ◽  
Author(s):  
Gerold Alsmeyer ◽  
Sören Gröttrup
Keyword(s):  
B Cell ◽  
Random Environment ◽  
Branching Process ◽  
Relative Proportion ◽  
Single Type ◽  
Type Model ◽  
Daughter Cells ◽  
A Cell ◽  
Host Parasite ◽  
A And B Cells

We consider a host-parasite model for a population of cells that can be of two types, A or B, and exhibits unilateral reproduction: while a B-cell always splits into two cells of the same type, the two daughter cells of an A-cell can be of any type. The random mechanism that describes how parasites within a cell multiply and are then shared into the daughter cells is allowed to depend on the hosting mother cell as well as its daughter cells. Focusing on the subpopulation of A-cells and its parasites, our model differs from the single-type model recently studied by Bansaye (2008) in that the sharing mechanism may be biased towards one of the two types. Our main results are concerned with the nonextinctive case and provide information on the behavior, as n → ∞, of the number of A-parasites in generation n and the relative proportion of A- and B-cells in this generation which host a given number of parasites. As in Bansaye (2008), proofs will make use of a so-called random cell line which, when conditioned to be of type A, behaves like a branching process in a random environment.

scholarly journals A Host-Parasite Model for a Two-Type Cell Population

2013 ◽  
Vol 45 (3) ◽  
pp. 719-741
Author(s):  
Gerold Alsmeyer ◽  
Sören Gröttrup
Keyword(s):  
B Cell ◽  
Random Environment ◽  
Branching Process ◽  
Relative Proportion ◽  
Single Type ◽  
Type Model ◽  
Daughter Cells ◽  
A Cell ◽  
Host Parasite ◽  
A And B Cells

We consider a host-parasite model for a population of cells that can be of two types, A or B, and exhibits unilateral reproduction: while a B-cell always splits into two cells of the same type, the two daughter cells of an A-cell can be of any type. The random mechanism that describes how parasites within a cell multiply and are then shared into the daughter cells is allowed to depend on the hosting mother cell as well as its daughter cells. Focusing on the subpopulation of A-cells and its parasites, our model differs from the single-type model recently studied by Bansaye (2008) in that the sharing mechanism may be biased towards one of the two types. Our main results are concerned with the nonextinctive case and provide information on the behavior, as n → ∞, of the number of A-parasites in generation n and the relative proportion of A- and B-cells in this generation which host a given number of parasites. As in Bansaye (2008), proofs will make use of a so-called random cell line which, when conditioned to be of type A, behaves like a branching process in a random environment.

The expected population size in a cell-size-dependent branching process

1981 ◽  
Vol 18 (01) ◽  
pp. 65-75 ◽  
Author(s):  
Aidan Sudbury
Keyword(s):  
Cell Size ◽  
Exponential Growth ◽  
Branching Process ◽  
Expected Number ◽  
Size Dependent ◽  
Daughter Cells ◽  
Rate Of Increase ◽  
A Cell ◽  
Dependent Growth ◽  
Number Of Cells

In cell-size-dependent growth the probabilistic rate of division of a cell into daughter-cells and the rate of increase of its size depend on its size. In this paper the expected number of cells in the population at time t is calculated for a variety of models, and it is shown that population growths slower and faster than exponential are both possible. When the cell sizes are bounded conditions are given for exponential growth.

scholarly journals Cell contamination and branching processes in a random environment with immigration

2009 ◽  
Vol 41 (4) ◽  
pp. 1059-1081 ◽  
Author(s):  
Vincent Bansaye
Keyword(s):  
Random Environment ◽  
Law Of Large Numbers ◽  
Branching Processes ◽  
Convergence In Distribution ◽  
Daughter Cells ◽  
State Dependent ◽  
Branching Model ◽  
Large Numbers ◽  
Dividing Cells ◽  
A Cell

We consider a branching model for a population of dividing cells infected by parasites. Each cell receives parasites by inheritance from its mother cell and independent contamination from outside the cell population. Parasites multiply randomly inside the cell and are shared randomly between the two daughter cells when the cell divides. The law governing the number of parasites which contaminate a given cell depends only on whether the cell is already infected or not. We first determine the asymptotic behavior of branching processes in a random environment with state-dependent immigration, which gives the convergence in distribution of the number of parasites in a cell line. We then derive a law of large numbers for the asymptotic proportions of cells with a given number of parasites. The main tools are branching processes in a random environment and laws of large numbers for a Markov tree.

scholarly journals A note on the multitype measure branching process

1992 ◽  
Vol 24 (2) ◽  
pp. 496-498 ◽  
Author(s):  
Zeng-Hu Li
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Single Type ◽  
Type Model

The existence of a class of multitype measure branching processes is deduced from a single-type model introduced by Li [8], which extends the work of Gorostiza and Lopez-Mimbela [5] and shows that the study of a multitype process can sometimes be reduced to that of a single-type one.

scholarly journals A note on the multitype measure branching process

1992 ◽  
Vol 24 (02) ◽  
pp. 496-498 ◽  
Author(s):  
Zeng-Hu Li
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Single Type ◽  
Type Model

The existence of a class of multitype measure branching processes is deduced from a single-type model introduced by Li [8], which extends the work of Gorostiza and Lopez-Mimbela [5] and shows that the study of a multitype process can sometimes be reduced to that of a single-type one.

scholarly journals Cell contamination and branching processes in a random environment with immigration

2009 ◽  
Vol 41 (04) ◽  
pp. 1059-1081
Author(s):  
Vincent Bansaye
Keyword(s):  
Random Environment ◽  
Law Of Large Numbers ◽  
Branching Processes ◽  
Convergence In Distribution ◽  
Daughter Cells ◽  
State Dependent ◽  
Branching Model ◽  
Large Numbers ◽  
Dividing Cells ◽  
A Cell

We consider a branching model for a population of dividing cells infected by parasites. Each cell receives parasites by inheritance from its mother cell and independent contamination from outside the cell population. Parasites multiply randomly inside the cell and are shared randomly between the two daughter cells when the cell divides. The law governing the number of parasites which contaminate a given cell depends only on whether the cell is already infected or not. We first determine the asymptotic behavior of branching processes in a random environment with state-dependent immigration, which gives the convergence in distribution of the number of parasites in a cell line. We then derive a law of large numbers for the asymptotic proportions of cells with a given number of parasites. The main tools are branching processes in a random environment and laws of large numbers for a Markov tree.

The expected population size in a cell-size-dependent branching process

1981 ◽  
Vol 18 (1) ◽  
pp. 65-75 ◽  
Author(s):  
Aidan Sudbury
Keyword(s):  
Cell Size ◽  
Exponential Growth ◽  
Branching Process ◽  
Expected Number ◽  
Size Dependent ◽  
Daughter Cells ◽  
Rate Of Increase ◽  
A Cell ◽  
Dependent Growth ◽  
Number Of Cells

In cell-size-dependent growth the probabilistic rate of division of a cell into daughter-cells and the rate of increase of its size depend on its size. In this paper the expected number of cells in the population at time t is calculated for a variety of models, and it is shown that population growths slower and faster than exponential are both possible. When the cell sizes are bounded conditions are given for exponential growth.

The locomotory behaviour of small groups of fibroblasts

1965 ◽  
Vol 162 (988) ◽  
pp. 289-302 ◽  
Keyword(s):  
Small Groups ◽  
Control Groups ◽  
Isolated Cells ◽  
Daughter Cells ◽  
A Cell ◽  
Locomotory Behaviour ◽  
Chick Embryo Heart ◽  
Embryo Heart ◽  
Random Nature ◽  
Chemotactic Gradient

Small groups of two to four fibroblasts at the periphery of outgrowths from cultured explants of chick embryo heart were isolated from their neighbours by sweeping away the nearby cells. The groups and the explants were left attached to the glass substrate, undisturbed. The behaviour of the isolated cells was photographically recorded during about 8 h of further culture. The cells of these groups dispersed, though not as a rule so far as to lose all mutual contacts, the dispersal being counterbalanced by the addition of new cells through mitosis. The accompanying changes in speed of locomotion, and the non-random nature of the spreading, are interpreted in terms of the effects of contacts between the cells. During the first four hours after isolation, but not thereafter, the cells of the groups on the average moved slowly away from the explant. Control groups in an intact outgrowth moved away faster and with no diminution of speed during the period of observation. The movement of the isolated groups can be partly accounted for by the tendency of cells to conserve for a time the direction of their movement before isolation; and by a strong reluctance of the isolated cells to move across the area, from which cells had been scraped away, that lay between the group and the explant. A new outgrowth of the residual sheet of cells still connected to the explant, however, advanced across this area, approaching and in most cases overhauling the isolated group. It is concluded that a chemotactic gradient around the explant is unlikely to play any significant part in the outward movement of fibroblasts from an explant in tissue culture. The cells of the isolated groups underwent an outburst of mitosis about 3 h after isolation. Mitoses in these relatively free cells are oriented in relation to the polarity of the cell before division. Locomotion of the daughter-cells tends to be faster than usual for at least 2 h after a cell divides.

scholarly journals Selection of a Nuclease-Resistant RNA Aptamer Targeting CD19

Cancers ◽  
2021 ◽  
Vol 13 (20) ◽  
pp. 5220
Author(s):  
Carla L. Esposito ◽  
Katrien Van Roosbroeck ◽  
Gianluca Santamaria ◽  
Deborah Rotoli ◽  
Annamaria Sandomenico ◽  
...  
Keyword(s):  
B Cell ◽  
Binding Activity ◽  
Rna Aptamer ◽  
Transmembrane Glycoprotein ◽  
B Cell Malignancy ◽  
A Cell ◽  
Enrichment Protocol ◽  
Interesting Class ◽  
Exponential Enrichment ◽  
Cluster Of Differentiation

The transmembrane glycoprotein cluster of differentiation 19 (CD19) is a B cell–specific surface marker, expressed on the majority of neoplastic B cells, and has recently emerged as a very attractive biomarker and therapeutic target for B-cell malignancies. The development of safe and effective ligands for CD19 has become an important need for the development of targeted conventional and immunotherapies. In this regard, aptamers represent a very interesting class of molecules. Additionally referred to as ‘chemical antibodies’, they show many advantages as therapeutics, including low toxicity and immunogenicity. Here, we isolated a nuclease-resistant RNA aptamer binding to the human CD19 glycoprotein. In order to develop an aptamer also useful as a carrier for secondary reagents, we adopted a cell-based SELEX (Systematic Evolution of Ligands by EXponential Enrichment) protocol adapted to isolate aptamers able to internalise upon binding to their cell surface target. We describe a 2′-fluoro pyrimidine modified aptamer, named B85.T2, which specifically binds to CD19 and shows an exquisite stability in human serum. The aptamer showed an estimated dissociation constant (KD) of 49.9 ± 13 nM on purified human recombinant CD19 (rhCD19) glycoprotein, a good binding activity on human B-cell chronic lymphocytic leukaemia cells expressing CD19, and also an effective and rapid cell internalisation, thus representing a promising molecule for CD19 targeting, as well as for the development of new B-cell malignancy-targeted therapies.

scholarly journals A Stochastic Model for Virus Growth in a Cell Population

2014 ◽  
Vol 51 (3) ◽  
pp. 599-612 ◽  
Author(s):  
J. E. Björnberg ◽  
T. Britton ◽  
E. I. Broman ◽  
E. Natan
Keyword(s):  
Stochastic Model ◽  
Host Cell ◽  
Cell Population ◽  
Branching Process ◽  
Virus Population ◽  
Virus Growth ◽  
Optimal Balance ◽  
Large Numbers ◽  
A Cell

In this work we introduce a stochastic model for the spread of a virus in a cell population where the virus has two ways of spreading: either by allowing its host cell to live and duplicate, or by multiplying in large numbers within the host cell, causing the host cell to burst and thereby let the virus enter new uninfected cells. The model is a kind of interacting Markov branching process. We focus in particular on the probability that the virus population survives and how this depends on a certain parameter λ which quantifies the ‘aggressiveness’ of the virus. Our main goal is to determine the optimal balance between aggressive growth and long-term success. Our analysis shows that the optimal strategy of the virus (in terms of survival) is obtained when the virus has no effect on the host cell's life cycle, corresponding to λ = 0. This is in agreement with experimental data about real viruses.

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