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Biological systems from an engineer's point of view.

Reeves GT, Fraser SE - PLoS Biol. (2009)

View Article: PubMed Central - PubMed

Affiliation: Biological Imaging Center, Beckman Institute, Division of Biology, California Institute of Technology, Pasadena, California, USA.

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Mathematical modeling of the processes that pattern embryonic development (often called biological pattern formation) has a long and rich history... If the decay constant, μ, is increased, the solid line shown in Figure 1C shifts to the dotted line... Correspondingly, the steady state value of c decreases to the open circle... Engineered systems were designed with a particular purpose in mind, so it would be helpful to ask, “What is/are the purpose(s) of this biological system?” Lander has called these purposes “performance objectives,” and determining what they are for a particular biological system is especially important in light of design trade-offs, and furthermore will provide clues to a system's molecular behavior... To demonstrate, let us return our simple example in Figure 1... We had originally assumed the removal rate of the enzyme was first-order, partially due to a dilution effect: enzyme concentration decreases as the cell grows in volume... In this issue of PLoS Biology, Lander and colleagues illustrate the utility of taking an engineer's perspective in the context of the olfactory neuron cell lineage in the mammalian olfactory epithelium (OE)... Thus, as the tissue grows, inhibitor concentration increases, slowly stalling and eventually ceasing cell division... Any loss of tissue results in a decrease in inhibitor concentration, leading to a proliferative phase for the stem and precursor cells to replace the lost tissue... In further analysis, Lander et al. focus on several experimentally observed performance objectives—including rapid regeneration after injury, low progenitor load (stem plus precursor cells make up less than 10% of the OE), and robustness of the steady state—and ask whether feedback loops could be designed to simultaneously meet these objectives... On the other hand, some readers would be skeptical of results that so heavily focus on the mathematics... This is not an unfounded skepticism, as evinced by numerous mathematical models in biology that have failed to accurately describe experimental systems... The authors begin with very general arguments from physics and mathematics, which correctly describe the overall behavior of a cell lineage without feedback, and have no need to model further detail... Indeed, a more detailed model would necessarily behave in a qualitatively similar fashion, but would muddy the water on the conclusions... Their model is sufficient to show that feedback is vital to the stability and robustness of any such lineage.

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Example of a Dynamical System(A) Reaction schematic of an enzyme, E, catalyzing the conversion of substrate, S, to product, P. The final product acts as a catabolite to promote the expression of enzyme.(B) ODE describing the change in time of enzyme concentration, c. The first term is the production term, rp(c), and the second term is degradation, r d(c).(C) Graphical representation of r p(c) and rd(c). At steady state, these two processes will balance, and the concentration of enzyme will become constant in time, with a value corresponding to the intersection of these two curves. Increasing the degradation constant μ (depicted by shift from solid line to dashed line) changes the steady state value of c (from closed circle to open circle). The sensitivity of this steady state value of c to such changes in parameters can be quantified by the sensitivity coefficient.
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pbio-1000021-g001: Example of a Dynamical System(A) Reaction schematic of an enzyme, E, catalyzing the conversion of substrate, S, to product, P. The final product acts as a catabolite to promote the expression of enzyme.(B) ODE describing the change in time of enzyme concentration, c. The first term is the production term, rp(c), and the second term is degradation, r d(c).(C) Graphical representation of r p(c) and rd(c). At steady state, these two processes will balance, and the concentration of enzyme will become constant in time, with a value corresponding to the intersection of these two curves. Increasing the degradation constant μ (depicted by shift from solid line to dashed line) changes the steady state value of c (from closed circle to open circle). The sensitivity of this steady state value of c to such changes in parameters can be quantified by the sensitivity coefficient.

Mentions: The first step in analysis is to determine the steady-state solution (the enzyme concentration that allows for the balance between the rates of production and degradation; see example in Figure 1). This is achieved by setting dc/dt = 0 (implying that concentration no longer changes in time) and solving the remaining algebraic equation.


Biological systems from an engineer's point of view.

Reeves GT, Fraser SE - PLoS Biol. (2009)

Example of a Dynamical System(A) Reaction schematic of an enzyme, E, catalyzing the conversion of substrate, S, to product, P. The final product acts as a catabolite to promote the expression of enzyme.(B) ODE describing the change in time of enzyme concentration, c. The first term is the production term, rp(c), and the second term is degradation, r d(c).(C) Graphical representation of r p(c) and rd(c). At steady state, these two processes will balance, and the concentration of enzyme will become constant in time, with a value corresponding to the intersection of these two curves. Increasing the degradation constant μ (depicted by shift from solid line to dashed line) changes the steady state value of c (from closed circle to open circle). The sensitivity of this steady state value of c to such changes in parameters can be quantified by the sensitivity coefficient.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2628404&req=5

pbio-1000021-g001: Example of a Dynamical System(A) Reaction schematic of an enzyme, E, catalyzing the conversion of substrate, S, to product, P. The final product acts as a catabolite to promote the expression of enzyme.(B) ODE describing the change in time of enzyme concentration, c. The first term is the production term, rp(c), and the second term is degradation, r d(c).(C) Graphical representation of r p(c) and rd(c). At steady state, these two processes will balance, and the concentration of enzyme will become constant in time, with a value corresponding to the intersection of these two curves. Increasing the degradation constant μ (depicted by shift from solid line to dashed line) changes the steady state value of c (from closed circle to open circle). The sensitivity of this steady state value of c to such changes in parameters can be quantified by the sensitivity coefficient.
Mentions: The first step in analysis is to determine the steady-state solution (the enzyme concentration that allows for the balance between the rates of production and degradation; see example in Figure 1). This is achieved by setting dc/dt = 0 (implying that concentration no longer changes in time) and solving the remaining algebraic equation.

View Article: PubMed Central - PubMed

Affiliation: Biological Imaging Center, Beckman Institute, Division of Biology, California Institute of Technology, Pasadena, California, USA.

AUTOMATICALLY GENERATED EXCERPT
Please rate it.

Mathematical modeling of the processes that pattern embryonic development (often called biological pattern formation) has a long and rich history... If the decay constant, μ, is increased, the solid line shown in Figure 1C shifts to the dotted line... Correspondingly, the steady state value of c decreases to the open circle... Engineered systems were designed with a particular purpose in mind, so it would be helpful to ask, “What is/are the purpose(s) of this biological system?” Lander has called these purposes “performance objectives,” and determining what they are for a particular biological system is especially important in light of design trade-offs, and furthermore will provide clues to a system's molecular behavior... To demonstrate, let us return our simple example in Figure 1... We had originally assumed the removal rate of the enzyme was first-order, partially due to a dilution effect: enzyme concentration decreases as the cell grows in volume... In this issue of PLoS Biology, Lander and colleagues illustrate the utility of taking an engineer's perspective in the context of the olfactory neuron cell lineage in the mammalian olfactory epithelium (OE)... Thus, as the tissue grows, inhibitor concentration increases, slowly stalling and eventually ceasing cell division... Any loss of tissue results in a decrease in inhibitor concentration, leading to a proliferative phase for the stem and precursor cells to replace the lost tissue... In further analysis, Lander et al. focus on several experimentally observed performance objectives—including rapid regeneration after injury, low progenitor load (stem plus precursor cells make up less than 10% of the OE), and robustness of the steady state—and ask whether feedback loops could be designed to simultaneously meet these objectives... On the other hand, some readers would be skeptical of results that so heavily focus on the mathematics... This is not an unfounded skepticism, as evinced by numerous mathematical models in biology that have failed to accurately describe experimental systems... The authors begin with very general arguments from physics and mathematics, which correctly describe the overall behavior of a cell lineage without feedback, and have no need to model further detail... Indeed, a more detailed model would necessarily behave in a qualitatively similar fashion, but would muddy the water on the conclusions... Their model is sufficient to show that feedback is vital to the stability and robustness of any such lineage.

Show MeSH