Identifying Multiple Potential Metabolic Cycles in Time-Series from Biolog Experiments

<div><p>Biolog Phenotype Microarray (PM) is a technology allowing simultaneous screening of the metabolic behaviour of bacteria under a large number of different conditions. Bacteria may often undergo several cycles of metabolic activity during a Biolog experiment. We introduce a novel algorithm to identify these metabolic cycles in PM experimental data, thus increasing the potential of PM technology in microbiology. Our method is based on a statistical decomposition of the time-series measurements into a set of growth models. We show that the method is robust to measurement noise and captures accurately the biologically relevant signals from the data. Our implementation is made freely available as a part of an R package for PM data analysis and can be found at <a href="http://www.helsinki.fi/bsg/software/Biolog_Decomposition" target="_blank">www.helsinki.fi/bsg/software/Biolog_Decomposition</a>.</p></div

Example of the distance measure.

<p>The similarity was computed using the data and decomposition presented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0162276#pone.0162276.g005" target="_blank">Fig 5</a>. Dark colour indicates less similar signals. Panel A—the Euclidean distance between the raw signals was used. Panel B—the similarity between signals is estimated as the similarity between their decompositions. To compute the distance we used <i>δ</i>_(<i>max</i>) = 3, <i>δ</i>_{(<i>size</i>)} = 100 and <i>δ</i>_{(<i>center</i>)} = 30.</p

Sensitivity test.

<p>Sensitivity test.</p

Example of the component decomposition.

<p>The signals of <i>E. coli</i> strains IMT17887, PCV17887 and T17887 (three replicates each) on plate PM1 and substrate A08 (L-Proline). The black lines show the analysed raw signal (not to scale). Colour corresponds to the type of the components. Raw signals and their decompositions are similar among replicates of the same strain. The algorithm parameters were set as following: blur strength <i>b</i> = 0.5, <i>δ</i> = 20, correlation weight <i>γ</i> = 2.</p

Decomposition of a single mock-up signal with different noise <i>λ</i> and smoothing coefficient <i>b</i>.

<p>Each subplot presents 10 decompositions superimposed one on the top of each other. The colour represents the number of components in the decomposition: blue for one, red for two, cyan for three or more. Gray lines show the correct decomposition smoothed with a corresponding coefficient <i>b</i>. Other parameters were fixed to the values <i>δ</i> = 20 and <i>γ</i> = 2.</p

Decomposition of a Biolog signal.

<p>During the pre-processing raw signal is converted to the target signal. During the initial decomposition three components (putative cycles of metabolic activity) are revealed: two Gaussian sequences and a slope sequence. During the calibration these components are refined: the first component changes its type to a brick sequence, the second and the third are slightly adjusted.</p

Basic components.

<p>The function used as components, smoothed functions and the type of growth represented by these components.</p

Kinetics of accumulation of the colour production may represent metabolic cycles in bacteria.

<p>Panel A—colour production of three replicates of the bacterial <i>E. coli</i> strain IMT17887 during growth on plate PM1 in the substrates H03 (Tyramine), B03 (Glycerol) and A03 (N-Acetyl-D Glucosamine). Panel B—lagged difference <i>L</i> of the colouration of these signals. Panels C—growth rate <i>S</i> (smoothed lagged difference of the colouration) of these signals. The smoothing coefficient is set to <i>b</i> = 0.5.</p

Infection assays of <i>S</i>. Typhimurium 4/74 parental and mutant strains in epithelial cells and macrophages.

<p>The charts show the percentage attenuation in mIC_c12, HeLa, THP-1A and RAW 264.7 cells for the following mutant strains relative to the parent strain. (A) Δ<i>pfkAB</i>, Δ<i>ptsG</i>Δ<i>manXYZ</i>Δ<i>glk</i>. (B) Δ<i>sucCD</i>, Δ<i>mdh</i>, Δ<i>gltA</i>, <i>ΔsucCD</i>, Δ<i>sdhCDAB</i> (mIC_c12, HeLa infections not determined for latter strain). Error bars represent the standard deviation from at least three independent biological replicates performed on separate days and significant differences between parental strain 4/74 and the mutant strains are indicated by asterisks, as follows: no asterisk, <i>P</i> > 0.05; *, <i>P</i> < 0.05; **, <i>P</i> < 0.01; and ***, <i>P</i> < 0.001. Replicate data and statistical analysis is from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150687#pone.0150687.s005" target="_blank">S2 Table</a>.</p

Exometabolite concentrations of acetate, lactate and formate produced by <i>S</i>. Typhimurium within macrophages and epithelial cells.

<p>Concentrations of acetate lactate and formate are shown for all host cell lines for the <i>S</i>. Typhimurium parent strain (4/74) or Δ<i>pta</i>Δ<i>ackA</i> strain as indicated. The data was corrected for exometabolite production by uninfected host cells. Error bars represent the standard deviation from at least three independent biological replicates performed on separate days and significant differences between infected and uninfected medium is indicated by asterisks, as follows: no asterisk, <i>P</i> > 0.05; *, <i>P</i> < 0.05; **, <i>P</i> < 0.01; and ***, <i>P</i> < 0.001. The data is presented as average concentrations of exometabolite produced per bacterial cell, per hour.</p