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Cell lineages and the logic of proliferative control.

Lander AD, Gokoffski KK, Wan FY, Nie Q, Calof AL - PLoS Biol. (2009)

Bottom Line: We begin by specifying performance objectives-what, precisely, is being controlled, and to what degree-and go on to calculate how well different types of feedback configurations, feedback sensitivities, and tissue architectures achieve control.Ultimately, we show that many features of the OE-the number of feedback loops, the cellular processes targeted by feedback, even the location of progenitor cells within the tissue-fit with expectations for the best possible control.In so doing, we also show that certain distinctions that are commonly drawn among cells and molecules-such as whether a cell is a stem cell or transit-amplifying cell, or whether a molecule is a growth inhibitor or stimulator-may be the consequences of control, and not a reflection of intrinsic differences in cellular or molecular character.

View Article: PubMed Central - PubMed

Affiliation: Department of Developmental and Cell Biology, University of California, Irvine, Irvine, California, USA. adlander@uci.edu

ABSTRACT
It is widely accepted that the growth and regeneration of tissues and organs is tightly controlled. Although experimental studies are beginning to reveal molecular mechanisms underlying such control, there is still very little known about the control strategies themselves. Here, we consider how secreted negative feedback factors ("chalones") may be used to control the output of multistage cell lineages, as exemplified by the actions of GDF11 and activin in a self-renewing neural tissue, the mammalian olfactory epithelium (OE). We begin by specifying performance objectives-what, precisely, is being controlled, and to what degree-and go on to calculate how well different types of feedback configurations, feedback sensitivities, and tissue architectures achieve control. Ultimately, we show that many features of the OE-the number of feedback loops, the cellular processes targeted by feedback, even the location of progenitor cells within the tissue-fit with expectations for the best possible control. In so doing, we also show that certain distinctions that are commonly drawn among cells and molecules-such as whether a cell is a stem cell or transit-amplifying cell, or whether a molecule is a growth inhibitor or stimulator-may be the consequences of control, and not a reflection of intrinsic differences in cellular or molecular character.

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Lineage Behavior in the Absence of Control(A) Cartoon of an unbranched lineage that begins with a stem cell (type 0), progresses through an arbitrary number of transit-amplifying stages (types 1 to n − 1) and ends with a postmitotic terminal-stage cell (type n). Parameters vi and pi are the rate constants of cell cycle progression and the replication probabilities, respectively, for each stage. Turnover of the terminal-stage cell is represented with a cell-death rate constant, d.(B) Representation of the cell lineage shown in (A), as a system of ordinary differential equations. In these equations, χi(t) stands for the number (or concentration) of cells of type i at time t, with each equation expressing the rate of expansion (or contraction) of each cell type. For all cell types except the first and last, this rate is the sum of two terms: production by cells of the previous lineage stage, and net production (or loss) due to replication (or differentiation) of cells at the same lineage stage. For the first cell type, there is no production from a prior stage, and for the last cell type, loss due to cell death is included.(C) Steady state solution for the output (number of terminal-stage cells) of the general system of equations given in (B). Notice that this output is linearly, or more than linearly, sensitive to every system parameter, with the exception of the vi for i > 0, which do not appear in the solution.
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pbio-1000015-g002: Lineage Behavior in the Absence of Control(A) Cartoon of an unbranched lineage that begins with a stem cell (type 0), progresses through an arbitrary number of transit-amplifying stages (types 1 to n − 1) and ends with a postmitotic terminal-stage cell (type n). Parameters vi and pi are the rate constants of cell cycle progression and the replication probabilities, respectively, for each stage. Turnover of the terminal-stage cell is represented with a cell-death rate constant, d.(B) Representation of the cell lineage shown in (A), as a system of ordinary differential equations. In these equations, χi(t) stands for the number (or concentration) of cells of type i at time t, with each equation expressing the rate of expansion (or contraction) of each cell type. For all cell types except the first and last, this rate is the sum of two terms: production by cells of the previous lineage stage, and net production (or loss) due to replication (or differentiation) of cells at the same lineage stage. For the first cell type, there is no production from a prior stage, and for the last cell type, loss due to cell death is included.(C) Steady state solution for the output (number of terminal-stage cells) of the general system of equations given in (B). Notice that this output is linearly, or more than linearly, sensitive to every system parameter, with the exception of the vi for i > 0, which do not appear in the solution.

Mentions: One way to identify the control needs of a system, and the strategies that may be used to address those needs, is to build models and explore their behavior. Figure 2A is a general representation of an unbranched cell lineage that begins with a pool of stem cells, ends with a postmitotic cell type, and possesses any number of transit-amplifying progenitor stages. If cells at each stage are numerous, and divisions asynchronous, then the behavior of such a system over time can be represented by a system of ordinary differential equations (Figure 2B) with two main classes of parameters. The v-parameters quantify how rapidly cells divide at each lineage stage (in particular, v = ln2/λ, where λ = the duration of a cell cycle). The p-parameters quantify the fraction of the progeny of any lineage stage that remains at the same stage (i.e., 1-p is the fraction that differentiates into cells of the next stage). Thus p may be thought of as an amplification, or replication, probability. As each lineage stage has its own v and p, we use subscripts to distinguish them.


Cell lineages and the logic of proliferative control.

Lander AD, Gokoffski KK, Wan FY, Nie Q, Calof AL - PLoS Biol. (2009)

Lineage Behavior in the Absence of Control(A) Cartoon of an unbranched lineage that begins with a stem cell (type 0), progresses through an arbitrary number of transit-amplifying stages (types 1 to n − 1) and ends with a postmitotic terminal-stage cell (type n). Parameters vi and pi are the rate constants of cell cycle progression and the replication probabilities, respectively, for each stage. Turnover of the terminal-stage cell is represented with a cell-death rate constant, d.(B) Representation of the cell lineage shown in (A), as a system of ordinary differential equations. In these equations, χi(t) stands for the number (or concentration) of cells of type i at time t, with each equation expressing the rate of expansion (or contraction) of each cell type. For all cell types except the first and last, this rate is the sum of two terms: production by cells of the previous lineage stage, and net production (or loss) due to replication (or differentiation) of cells at the same lineage stage. For the first cell type, there is no production from a prior stage, and for the last cell type, loss due to cell death is included.(C) Steady state solution for the output (number of terminal-stage cells) of the general system of equations given in (B). Notice that this output is linearly, or more than linearly, sensitive to every system parameter, with the exception of the vi for i > 0, which do not appear in the solution.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2628408&req=5

pbio-1000015-g002: Lineage Behavior in the Absence of Control(A) Cartoon of an unbranched lineage that begins with a stem cell (type 0), progresses through an arbitrary number of transit-amplifying stages (types 1 to n − 1) and ends with a postmitotic terminal-stage cell (type n). Parameters vi and pi are the rate constants of cell cycle progression and the replication probabilities, respectively, for each stage. Turnover of the terminal-stage cell is represented with a cell-death rate constant, d.(B) Representation of the cell lineage shown in (A), as a system of ordinary differential equations. In these equations, χi(t) stands for the number (or concentration) of cells of type i at time t, with each equation expressing the rate of expansion (or contraction) of each cell type. For all cell types except the first and last, this rate is the sum of two terms: production by cells of the previous lineage stage, and net production (or loss) due to replication (or differentiation) of cells at the same lineage stage. For the first cell type, there is no production from a prior stage, and for the last cell type, loss due to cell death is included.(C) Steady state solution for the output (number of terminal-stage cells) of the general system of equations given in (B). Notice that this output is linearly, or more than linearly, sensitive to every system parameter, with the exception of the vi for i > 0, which do not appear in the solution.
Mentions: One way to identify the control needs of a system, and the strategies that may be used to address those needs, is to build models and explore their behavior. Figure 2A is a general representation of an unbranched cell lineage that begins with a pool of stem cells, ends with a postmitotic cell type, and possesses any number of transit-amplifying progenitor stages. If cells at each stage are numerous, and divisions asynchronous, then the behavior of such a system over time can be represented by a system of ordinary differential equations (Figure 2B) with two main classes of parameters. The v-parameters quantify how rapidly cells divide at each lineage stage (in particular, v = ln2/λ, where λ = the duration of a cell cycle). The p-parameters quantify the fraction of the progeny of any lineage stage that remains at the same stage (i.e., 1-p is the fraction that differentiates into cells of the next stage). Thus p may be thought of as an amplification, or replication, probability. As each lineage stage has its own v and p, we use subscripts to distinguish them.

Bottom Line: We begin by specifying performance objectives-what, precisely, is being controlled, and to what degree-and go on to calculate how well different types of feedback configurations, feedback sensitivities, and tissue architectures achieve control.Ultimately, we show that many features of the OE-the number of feedback loops, the cellular processes targeted by feedback, even the location of progenitor cells within the tissue-fit with expectations for the best possible control.In so doing, we also show that certain distinctions that are commonly drawn among cells and molecules-such as whether a cell is a stem cell or transit-amplifying cell, or whether a molecule is a growth inhibitor or stimulator-may be the consequences of control, and not a reflection of intrinsic differences in cellular or molecular character.

View Article: PubMed Central - PubMed

Affiliation: Department of Developmental and Cell Biology, University of California, Irvine, Irvine, California, USA. adlander@uci.edu

ABSTRACT
It is widely accepted that the growth and regeneration of tissues and organs is tightly controlled. Although experimental studies are beginning to reveal molecular mechanisms underlying such control, there is still very little known about the control strategies themselves. Here, we consider how secreted negative feedback factors ("chalones") may be used to control the output of multistage cell lineages, as exemplified by the actions of GDF11 and activin in a self-renewing neural tissue, the mammalian olfactory epithelium (OE). We begin by specifying performance objectives-what, precisely, is being controlled, and to what degree-and go on to calculate how well different types of feedback configurations, feedback sensitivities, and tissue architectures achieve control. Ultimately, we show that many features of the OE-the number of feedback loops, the cellular processes targeted by feedback, even the location of progenitor cells within the tissue-fit with expectations for the best possible control. In so doing, we also show that certain distinctions that are commonly drawn among cells and molecules-such as whether a cell is a stem cell or transit-amplifying cell, or whether a molecule is a growth inhibitor or stimulator-may be the consequences of control, and not a reflection of intrinsic differences in cellular or molecular character.

Show MeSH
Related in: MedlinePlus