Fitting code and data

Zip file contains code used to produce amino acid model, perform analysis and produce figures, as well as data structures containing fitting information and experimental metadat

Comparison of internal nutrient-dependent regulation of transporter synthesis and activity-dependent transporter downregulation.

<p>For different normalized concentrations of <i>S</i>_<i>ext</i>, the values of <i>n</i> and required to achieve either 0.8 or 0.95 robustness (blue curve and black curve respectively) are plotted. Four different specific normalized <i>S</i>_<i>ext</i> values are represented by the four colored dots. We assumed nutrient uptake per transporter was Michaelian .</p

Homeostasis by activity-dependent transporter downregulation.

<p>The steady-state internal nutrient concentration for a range of external nutrient concentrations is plotted for six different instantiation of the system in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005458#pcbi.1005458.e009" target="_blank">Eq (3)</a>: no transporter regulation (black), flux-based transporter downregulation (red with x's), internal nutrient based repression of transporter synthesis (orange), linear external nutrient based transporter downregulation (blue), flux-based transporter downregulation plus internal nutrient based repression of transporter synthesis (green). This illustrates the criterion from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005458#pcbi.1005458.e010" target="_blank">Eq (4)</a>, which states that the system can only achieve global perfect homeostasis (red and green lines) when flux-based transporter downregulation () is combined with an arbitrary function of the internal nutrient concentration (<i>S</i>_<i>int</i>).</p

Fitting of amino acid composition with one and two-state models can predict population behavior.

<p>(A) Prediction of the number of states in the population for the “grow then mix” (top) and “mix then grow” (bottom) data, based on the fit of the one and two-state models. The gray dashed line indicates the threshold where the log₁₀ of the ratio of <i>f</i>_{<i>one-state</i>} to <i>f</i>_{<i>two-state</i>} is 0.2; a population is predicted to be one-state below this threshold (green) and two-state above this threshold (orange). Color of the points indicates whether the population is actually one- or two-states (green and orange, respectively). (B) Inferred subpopulation size (left) and sugar usage (right) based on fitting of the “grow then mix” data. Bars represent the mean of three replicates, with error bars corresponding to the standard error of the mean. (C) Sugar utilization in the “mix then grow” (co-utilization) experiment determined by fitting the data with a one-state model, compared to its actual sugar usage. Error bars represent the standard error of the mean (<i>n</i> = 3).</p

Modified FiatFlux Code

Modified version of FiatFlux cod

Raw CDF files

CDF files containing raw mass spectrometry data for all samples

A molecular mechanism that can achieve activity-dependent transporter downregulation.

<p>A nutrient molecule (white circle) binds a transporter (a white pair of ovals) to form a nutrient-transporter complex. This complex then undergoes a conformational change. The complex can then either: 1) Uptake—nutrient is released into the cell; the transporter finishes the uptake cycle by returning to its ground state, or 2) Downregulation—the transporter is modified leading directly and/or indirectly to its inactivation. Because uptake and downregulation involve the same molecular species the rates or these two processes are automatically proportional.</p

Regulation by intracellular substrate concentrations.

<p><i>S</i>_<i>int</i> can regulate either (A) transporter synthesis (<i>α</i>_<i>T</i>) or (B) transporter downregulation (<i>γ</i>_<i>T</i>). In both cases, we assume this regulation takes the form of a Hill equation with a 'saturation' constant of (A) <i>K</i>_<i>syn</i> or (B) <i>K</i>_<i>deg</i>. The saturation constant is the equivalent to the standard disassociation constant but represents the concentration where the system is half saturated for its regulatory potential. For (A) and (B) the diagram on the right uses a hill coefficient (<i>n</i>) of 3, (case of <i>n</i> = 1 is in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005458#pcbi.1005458.s001" target="_blank">S1 Appendix</a>, section VII part b, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005458#pcbi.1005458.s002" target="_blank">S1 Fig</a>). Higher <i>n</i> leads to more robustness, but global perfect homeostasis is not achievable by any finite value of <i>n</i>. For both (A) and (B), the saturation constants are normalized by .</p

The difference in sugar utilization between two subpopulations is the major determinant of inference error.

<p>(A) Computational pooling was performed by summing two sets of experimental GC-MS amino acid distributions (GC-MS_A/B) with different ¹²C usage fractions (^<i>12</i><i>C</i>_<i>A/B</i>), weighted by the desired population ratio (<i>P</i>_<i>A</i> and 1-<i>P</i>_<i>A</i>). The minimum population size (min(<i>P</i>_<i>A</i>,(1-<i>P</i>_<i>A</i>))) and difference in ¹²C usage between subpopulations (abs(^<i>12</i><i>C</i>_<i>A</i>-^<i>12</i><i>C</i>_<i>B</i>)) were determined for each computational pool. (B) Inferred subpopulation number based on the log₁₀ <i>f</i>-ratio of the computationally pooled data, with dashed line indicating the 0.2 threshold. Boxes represent the interquartile range with a red line at the median, and outliers >1.5x the interquartile range are shown as a red plus sign. (C) Inference error in subpopulation size (blue) and sugar usage (red) from computationally pooled data that fit best with a two-state model. Boxes represent the interquartile range with a line at the median, and outliers (>1.5x the interquartile range) are shown as a plus sign.</p

Global perfect homeostasis is limited by dilution and basal degradation.

<p><b>(A)</b> Schematic of a system where transporter degradation occurs by two mechanisms: (1) activity-dependent downregulation (rate constant of ) and (2) dilution and basal degradation (rate constant ). <b>(B)</b> Robustness, <i>r</i>, of the system from (A) given different ratios of to . The blue and magenta cross-sections correspond to the blue and magenta curves in (C). <b>(C)</b> In the limit where goes to zero, <i>S</i>_<i>int</i> tracks <i>S</i>_<i>ext</i> (orange). In the limit where goes to zero, the <i>S</i>_<i>int</i> is independent of the <i>S</i>_<i>ext</i> (black). <b>(D)</b> Transporter levels as a function of <i>S</i>_<i>ext</i> for the same four ratios of to as in (C). As , <i>T</i> changes inversely with <i>S</i>_<i>ext</i> which allows the system to achieve homeostasis.</p