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From bit to it: how a complex metabolic network transforms information into living matter.

Wagner A - BMC Syst Biol (2007)

Bottom Line: For microbes like yeast, natural selection can resolve fitness differences of genetic variants smaller than 10-6, meaning that cells would need to estimate nutrient concentrations to very high accuracy (greater than 22 bits) to ensure optimal growth.I argue that such accuracies are not achievable in practice.The analysis of metabolic networks opens a door to understanding cellular biology from a quantitative, information-theoretic perspective.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Biochemistry, University of Zurich, Building Y27, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland. aw@bioc.uzh.ch

ABSTRACT

Background: Organisms live and die by the amount of information they acquire about their environment. The systems analysis of complex metabolic networks allows us to ask how such information translates into fitness. A metabolic network transforms nutrients into biomass. The better it uses information on available nutrient availability, the faster it will allow a cell to divide.

Results: I here use metabolic flux balance analysis to show that the accuracy I (in bits) with which a yeast cell can sense a limiting nutrient's availability relates logarithmically to fitness as indicated by biomass yield and cell division rate. For microbes like yeast, natural selection can resolve fitness differences of genetic variants smaller than 10-6, meaning that cells would need to estimate nutrient concentrations to very high accuracy (greater than 22 bits) to ensure optimal growth. I argue that such accuracies are not achievable in practice. Natural selection may thus face fundamental limitations in maximizing the information processing capacity of cells.

Conclusion: The analysis of metabolic networks opens a door to understanding cellular biology from a quantitative, information-theoretic perspective.

Show MeSH
Increased glucose information (bits, lower horizontal axis, filled circles) and reduced sensing error (percent, upper horizontal axis, open symbols) cause an increases in fitness (1-s) as estimated through biomass production in the yeast metabolic network via flux balance analysis. The vertical axis shows the selection coefficient s, the difference to the maximal biomass yield at perfectly accurate information. Results are nearly identical for the other four substrates, and are shown for O2 and NH3 in the inset. The dashed horizontal line demarcates a neutral zone, below which (s < 7.33 × 10-8; see text) growth rate increases are selectively neutral.
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Figure 1: Increased glucose information (bits, lower horizontal axis, filled circles) and reduced sensing error (percent, upper horizontal axis, open symbols) cause an increases in fitness (1-s) as estimated through biomass production in the yeast metabolic network via flux balance analysis. The vertical axis shows the selection coefficient s, the difference to the maximal biomass yield at perfectly accurate information. Results are nearly identical for the other four substrates, and are shown for O2 and NH3 in the inset. The dashed horizontal line demarcates a neutral zone, below which (s < 7.33 × 10-8; see text) growth rate increases are selectively neutral.

Mentions: The relationship between information and fitness is best explored for a defined environment, such as a minimal growth medium. The environment I use contains NH3, inorganic phosphate (Pi), sulfate, and glucose as the sole carbon source. Oxygen is available as a terminal electron acceptor. For simplicity, I first focus on a scenario where information about all substrates except glucose is perfectly accurate. I assume that the biomass yield Y per unit time is linearly proportional to a cell's division rate G, a measure of fitness. In other words, Y = cG, c being some constant. I express the effect of incomplete information on biomass yield Y as s = 1-Y/Ymax = 1-G/Gmax, where Ymax and Gmax are the maximally achievable biomass yields and cell division rates, respectively, i.e., the yields and rates for perfectly accurate glucose information. The quantity s can also be thought of as a selection coefficient, as a measure by how far a cell's fitness w = 1-s = G/Gmax is reduced by incomplete information. Figure 1 shows how a cell's fitness depends on the amount of information the cell can acquire about substrate concentration. Specifically, the figure shows that the logarithm of fitness depends linearly on information in bits. The relationship of s and information is especially simple if a binary logarithm is used to scale s, i.e., -log2(s) = IGLC+1. This simple relationship emerges numerically from flux balance analysis, but it also has a straightforward intuitive explanation. If zero bits of information are available for a growth-limiting nutrient, then under the assumptions used here, the cell's "guess" about nutrient concentrations will be randomly distributed in the interval (0, Ni), with an expected value of Ni/2. At this expected value, the division rate of a cell will be half the maximal growth rate, such that s = 1/2. The above relationship between s and I then holds, because -log2(1/2) = 1 = I+1. If one bit of information is available (I = 1), then the cell's measurement will be randomly distributed in the interval (Ni/2, Ni), with an expected value of 3Ni/4, leading to s = 1/4, and -log2(1/4) = 2 = I+1. The same line of reasoning applies to ever increasing values of I. The key assumption in this intuitive explanation is that if one nutrient is growth-limiting, then cell division rate depends linearly on the cell's ability to utilize this nutrient. This is not obvious a priori, because the nutrient's metabolic products may be fed into many different pathways that produce essential biomass components. The distribution of these products among different pathways, and the cell's final resulting division rate, might in principle depend on the concentration of the nutrient and on that of other nutrients. However, flux balance analysis shows that the dependency between nutrient concentration and biomass yield is quite simple and linear.


From bit to it: how a complex metabolic network transforms information into living matter.

Wagner A - BMC Syst Biol (2007)

Increased glucose information (bits, lower horizontal axis, filled circles) and reduced sensing error (percent, upper horizontal axis, open symbols) cause an increases in fitness (1-s) as estimated through biomass production in the yeast metabolic network via flux balance analysis. The vertical axis shows the selection coefficient s, the difference to the maximal biomass yield at perfectly accurate information. Results are nearly identical for the other four substrates, and are shown for O2 and NH3 in the inset. The dashed horizontal line demarcates a neutral zone, below which (s < 7.33 × 10-8; see text) growth rate increases are selectively neutral.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC1994685&req=5

Figure 1: Increased glucose information (bits, lower horizontal axis, filled circles) and reduced sensing error (percent, upper horizontal axis, open symbols) cause an increases in fitness (1-s) as estimated through biomass production in the yeast metabolic network via flux balance analysis. The vertical axis shows the selection coefficient s, the difference to the maximal biomass yield at perfectly accurate information. Results are nearly identical for the other four substrates, and are shown for O2 and NH3 in the inset. The dashed horizontal line demarcates a neutral zone, below which (s < 7.33 × 10-8; see text) growth rate increases are selectively neutral.
Mentions: The relationship between information and fitness is best explored for a defined environment, such as a minimal growth medium. The environment I use contains NH3, inorganic phosphate (Pi), sulfate, and glucose as the sole carbon source. Oxygen is available as a terminal electron acceptor. For simplicity, I first focus on a scenario where information about all substrates except glucose is perfectly accurate. I assume that the biomass yield Y per unit time is linearly proportional to a cell's division rate G, a measure of fitness. In other words, Y = cG, c being some constant. I express the effect of incomplete information on biomass yield Y as s = 1-Y/Ymax = 1-G/Gmax, where Ymax and Gmax are the maximally achievable biomass yields and cell division rates, respectively, i.e., the yields and rates for perfectly accurate glucose information. The quantity s can also be thought of as a selection coefficient, as a measure by how far a cell's fitness w = 1-s = G/Gmax is reduced by incomplete information. Figure 1 shows how a cell's fitness depends on the amount of information the cell can acquire about substrate concentration. Specifically, the figure shows that the logarithm of fitness depends linearly on information in bits. The relationship of s and information is especially simple if a binary logarithm is used to scale s, i.e., -log2(s) = IGLC+1. This simple relationship emerges numerically from flux balance analysis, but it also has a straightforward intuitive explanation. If zero bits of information are available for a growth-limiting nutrient, then under the assumptions used here, the cell's "guess" about nutrient concentrations will be randomly distributed in the interval (0, Ni), with an expected value of Ni/2. At this expected value, the division rate of a cell will be half the maximal growth rate, such that s = 1/2. The above relationship between s and I then holds, because -log2(1/2) = 1 = I+1. If one bit of information is available (I = 1), then the cell's measurement will be randomly distributed in the interval (Ni/2, Ni), with an expected value of 3Ni/4, leading to s = 1/4, and -log2(1/4) = 2 = I+1. The same line of reasoning applies to ever increasing values of I. The key assumption in this intuitive explanation is that if one nutrient is growth-limiting, then cell division rate depends linearly on the cell's ability to utilize this nutrient. This is not obvious a priori, because the nutrient's metabolic products may be fed into many different pathways that produce essential biomass components. The distribution of these products among different pathways, and the cell's final resulting division rate, might in principle depend on the concentration of the nutrient and on that of other nutrients. However, flux balance analysis shows that the dependency between nutrient concentration and biomass yield is quite simple and linear.

Bottom Line: For microbes like yeast, natural selection can resolve fitness differences of genetic variants smaller than 10-6, meaning that cells would need to estimate nutrient concentrations to very high accuracy (greater than 22 bits) to ensure optimal growth.I argue that such accuracies are not achievable in practice.The analysis of metabolic networks opens a door to understanding cellular biology from a quantitative, information-theoretic perspective.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Biochemistry, University of Zurich, Building Y27, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland. aw@bioc.uzh.ch

ABSTRACT

Background: Organisms live and die by the amount of information they acquire about their environment. The systems analysis of complex metabolic networks allows us to ask how such information translates into fitness. A metabolic network transforms nutrients into biomass. The better it uses information on available nutrient availability, the faster it will allow a cell to divide.

Results: I here use metabolic flux balance analysis to show that the accuracy I (in bits) with which a yeast cell can sense a limiting nutrient's availability relates logarithmically to fitness as indicated by biomass yield and cell division rate. For microbes like yeast, natural selection can resolve fitness differences of genetic variants smaller than 10-6, meaning that cells would need to estimate nutrient concentrations to very high accuracy (greater than 22 bits) to ensure optimal growth. I argue that such accuracies are not achievable in practice. Natural selection may thus face fundamental limitations in maximizing the information processing capacity of cells.

Conclusion: The analysis of metabolic networks opens a door to understanding cellular biology from a quantitative, information-theoretic perspective.

Show MeSH