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      Fast Bayesian parameter estimation for stochastic logistic growth models

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          Abstract

          The transition density of a stochastic, logistic population growth model with multiplicative intrinsic noise is analytically intractable. Inferring model parameter values by fitting such stochastic differential equation (SDE) models to data therefore requires relatively slow numerical simulation. Where such simulation is prohibitively slow, an alternative is to use model approximations which do have an analytically tractable transition density, enabling fast inference. We introduce two such approximations, with either multiplicative or additive intrinsic noise, each derived from the linear noise approximation (LNA) of a logistic growth SDE. After Bayesian inference we find that our fast LNA models, using Kalman filter recursion for computation of marginal likelihoods, give similar posterior distributions to slow, arbitrarily exact models. We also demonstrate that simulations from our LNA models better describe the characteristics of the stochastic logistic growth models than a related approach. Finally, we demonstrate that our LNA model with additive intrinsic noise and measurement error best describes an example set of longitudinal observations of microbial population size taken from a typical, genome-wide screening experiment.

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          Stochastic modelling for quantitative description of heterogeneous biological systems.

          Two related developments are currently changing traditional approaches to computational systems biology modelling. First, stochastic models are being used increasingly in preference to deterministic models to describe biochemical network dynamics at the single-cell level. Second, sophisticated statistical methods and algorithms are being used to fit both deterministic and stochastic models to time course and other experimental data. Both frameworks are needed to adequately describe observed noise, variability and heterogeneity of biological systems over a range of scales of biological organization.
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            Bayesian inference for stochastic kinetic models using a diffusion approximation.

            This article is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white noise term models stochastic behavior and the model is identified using equispaced time course data. The estimation framework involves the introduction of m- 1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters. The methodology is applied to the estimation of parameters in a prokaryotic autoregulatory gene network.
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              Quantitative Fitness Analysis Shows That NMD Proteins and Many Other Protein Complexes Suppress or Enhance Distinct Telomere Cap Defects

              Introduction Linear chromosome ends must be protected from the DNA damage response machinery and from shortening of chromosome ends during DNA replication [1], [2]. Chromosome ends therefore adopt specialized structures called telomeres, distinct from double-stranded DNA breaks elsewhere in the genome. Telomeric DNA is protected, or capped and replicated by a large number of different DNA-binding proteins in all eukaryotic cell types [2], [3]. In budding yeast, numerous proteins contribute to telomere capping and amongst these are two critical protein complexes, the Yku70/Yku80 (Ku) heterodimer and the Cdc13/Stn1/Ten1 (CST) heterotrimeric complex [4]. Orthologous protein complexes play roles at telomeres in other eukaryotic cell types suggesting that understanding the function of the Ku and CST protein complexes in budding yeast will be generally informative about key aspects of eukaryotic telomere structure and function. In budding yeast Yku70 is a non-essential protein that has multiple roles in DNA repair and at telomeres, being involved in the non-homologous end-joining (NHEJ) DNA repair pathway, in the protection of telomeres and the recruitment of telomerase. The mammalian orthologue, Ku70, has similar properties [5]. In budding yeast, deletion of the YKU70 gene (yku70Δ) results in short telomeres and temperature sensitivity [6]. At high temperatures, cells lacking Yku70 accumulate ssDNA at telomeres, which activates the DNA damage response and leads to cell-cycle arrest [7], [8], [9]. Cdc13 is a constituent of the essential budding yeast Cdc13-Stn1-Ten1 (CST) protein complex which is analogous to the CST complex found recently in mammalian, plant and fission yeast cells [10], [11]. Cdc13 binds to ssDNA overhangs at telomeres and functions in telomerase recruitment and telomere capping [12], [13], [14]. Acute inactivation of Cdc13 by the temperature sensitive cdc13-1 allele induces ssDNA generation at telomeres and rapid, potent checkpoint-dependent cell cycle arrest [14]. cdc13-1 or yku70Δ mutations each cause temperature dependent disruption of telomere capping that is accompanied by ssDNA production, cell-cycle arrest and cell death [7], [15]. Interestingly, the poor growth imparted by each mutation can be suppressed by deletion of EXO1, removing the Exo1 nuclease that contributes to ssDNA production when either Cdc13 or Yku70 is defective [7]. However, cdc13-1 and yku70Δ mutations show a synthetic poor growth interaction [8] and different checkpoint pathways are activated by each mutation [7]. These latter observations, along with numerous others, show that CST and Ku complexes perform distinct roles capping budding yeast telomeres and that further clarification of their functions at the telomere is important to help understand how eukaryotic telomeres function. Many insights into the telomere cap and the DNA damage responses induced when capping is defective were first identified as genetic interactions. For example all DNA damage checkpoint mutations suppress the temperature sensitive growth of cdc13-1 mutants [16], but only a subset of these suppress the temperature sensitive growth of yku70Δ mutants [7]. We reasoned that the roles of Cdc13 and Yku70 at telomeres could be further understood by quantitative, systematic analysis of genetic interactions between telomere capping mutations and a genome-wide collection of gene deletions. We used standard synthetic genetic array (SGA) approaches to combine the systematic gene deletion collection with cdc13-1 and yku70Δ mutations [17], [18]. After this, strain fitnesses were measured at a number of temperatures by quantitative fitness analysis (QFA). For QFA, liquid cultures were spotted onto solid agar plates and culture growth was followed by time course photography. Images were processed and fitted to a logistic growth model to allow an accurate estimation of growth parameters, such as doubling time. In other high-throughput experiments such as SGA or EMAP approaches, culture fitness is determined from colony size [17], [18], [19]. In QFA, analysis of growth curves of cultures grown on solid agar plates allows us to measure fitness more precisely. Through QFA we identify hundreds of gene deletions, in numerous different classes, showing genetic interactions with cdc13-1, yku70Δ or both. One particularly striking example of the type of genetic interactions we measured by QFA is between deletions affecting nonsense mediated RNA decay pathways (upf1Δ, upf2Δ, upf3Δ), cdc13-1 and yku70Δ. Additional experiments show that disabling nonsense mediated mRNA decay pathways, using upf2Δ as an example, suppresses the cdc13-1 defect but enhances the yku70Δ defect by increasing the levels of the telomere capping protein Stn1. QFA is generally applicable and will be useful for understanding other aspects of yeast cell biology or studying other microorganisms. Results QFA identifies gene deletions that interact with cdc13-1 and yku70Δ To systematically examine genetic interactions between a genome-wide collection of gene deletion strains (yfgΔ, your favorite gene deletion, to indicate any of ∼4200 viable systematic gene deletions) and mutations causing telomere capping defects we crossed the knockout library to cdc13-1 or yku70Δ mutations, each affecting the telomere, or to a neutral control query mutation (ura3Δ) using SGA methodology [17], [18]. Since both cdc13-1 and yku70Δ mutations cause temperature sensitive defects, we generated all double mutants at low, permissive temperatures before measuring the growth of double mutants at a number of semi-permissive or non-permissive temperatures. We cultured yku70Δ yfgΔ strains at 23°C, 30°C, 37°C and 37.5°C, cdc13-1 yfgΔ strains at 20°C, 27°C and 36°C and ura3Δ yfgΔ strains at 20°C, 27°C and 37°C and measured fitness. Double mutant fitness was measured after spotting of dilute liquid cultures onto solid agar. We estimate approximately 100 separate cells were placed in each of 384 spots on each agar plate. Fitness of thousands of individual cultures, each derived from spotted cells, was deduced by time course photography of agar plates followed by image processing, data analysis, fitting of growth measurements to a logistic model and determination of quantitative growth parameters (Figure 1) [20], [21], [22]. We fitted logistic growth model parameters to growth curves allowing us to estimate maximum doubling rate (MDR, population doublings/day) and maximum doubling potential (MDP, population doublings) of approximately 12,000 different yeast genotypes (e.g. cdc13-1 yfg1Δ, yku70Δ yfg1Δ, etc.) at several temperatures. At least eight independent biological replicates for each strain at each temperature were cultured and repeatedly photographed, capturing more than 4 million images in total. To rank fitness we assigned equal importance to maximum doubling rate and maximum doubling potential and defined strain fitness as the product of the MDR and MDP values (Fitness, F, population doublings2/day). Other measures of fitness can be derived from the sets of logistic parameters available from Text S1. 10.1371/journal.pgen.1001362.g001 Figure 1 Cell fitness determination from growth on agar plates for quantitative fitness analysis (QFA). A) Time course images of eight independent upf2Δ ura3Δ, yku70Δ ura3Δ and upf2Δ yku70Δ strains at the indicated temperatures; B) Cell density of individual replicate cultures was determined after image-analysis. The logistic growth model is fitted to each culture density time-series. The same data are plotted on linear or logarithmic scales on left and right respectively. C) Average values for Maximum Doubling Rate, Maximum Doubling Potential and Fitness (MDR, MDP and F respectively; see Text S1, experimental procedures), determined from the fitted curves. Data for yku70Δ ura3Δ is presented here to illustrate epistasis between yku70Δ and upf3Δ, however this is not how epistasis was calculated (see Figure 2 and Text S1, experimental procedures). Figure 1A shows approximately 170 example images, corresponding to eight independent time courses for each of three pair-wise combinations of yku70Δ, ura3Δ and upf2Δ mutations. These example images clearly show, qualitatively, that upf2Δ yku70Δ strains grow less well than yku70Δ ura3Δ strains, which in turn grow less well than upf2Δ ura3Δ strains at 37°C. These fitness measures are consistent with numerous earlier studies, showing that yku70Δ mutants do not grow well at high temperatures, but also demonstrate a novel observation, that the upf2Δ mutation enhances the yku70Δ defect and this is further investigated below. Images like those in Figure 1A were processed, quantified, plotted and logistic growth curves fitted to the data (Figure 1B). We applied QFA to all genotypes at each temperature, as the three examples in Figure 1C illustrate. QFA of telomere capping mutants QFA of cdc13-1 yfgΔ, yku70Δ yfgΔ and ura3Δ yfgΔ double mutant libraries was performed at a number of temperatures and therefore a variety of informative comparisons were possible. For example to help identify gene deletions that suppress or enhance the yku70Δ temperature dependent growth defect it is useful to compare the fitness of yku70Δ yfgΔ cells incubated at 37.5°C, with that of control, ura3Δ yfgΔ, cells incubated at 37°C. In Figure 2, genes which, when deleted, suppress the yku70Δ phenotype at 37.5°C will be positioned above the linear regression line and enhancers of yku70Δ defects below the line. yfgΔ mutations that result in low fitness when combined with the neutral ura3Δ mutation will be found on the left and those with high fitness on the right of the x-axis. 10.1371/journal.pgen.1001362.g002 Figure 2 Fitness of yku70Δ strains at high temperature. The yeast genome knock out collection was crossed to the yku70Δ mutation, or as a control to the ura3Δ mutation. 8 replicate crosses were performed and for each, the fitness of all double mutant cultures measured as in Figure 1. Growth of yku70Δ yfgΔ (“your favourite gene deletion”) double mutants was measured at 37.5°C and ura3Δ yfgΔ strains at 37°C. Gene deletions that significantly enhance (green) or suppress (red) the yku70Δ defect, in comparison with the ura3Δ mutation are indicated. Those marked by open circles have p-values 0.5). 10.1371/journal.pgen.1001362.t001 Table 1 Percentage of deletions suppressing or enhancing query mutation fitness defects in specific QFA screens. Suppressors (%) Enhancers (%) GIS≥0 GIS≥0.5 GIS≤0 GIS≤−0.5 cdc13-1 20°C 1.65 0.07 2.06 0.22 cdc13-1 27°C 10.11 4.85 7.15 2.60 cdc13-1 36°C 0.53 0.53 0.00 0.00 yku70Δ 23°C 1.46 0.07 3.76 0.61 yku70Δ 30°C 0.61 0.05 4.07 0.73 yku70Δ 37°C 0.92 0.12 7.93 2.52 yku70Δ 37.5°C 3.42 0.12 13.19 5.14 We examined the effects of 4,120 gene deletions, ignoring deletions that were technically problematic (e.g. displayed linkage with query mutation, affected uracil, leucine or histidine biosynthesis). The table above shows percentages classified as significant suppressors (FDR corrected q-value 25000 after 6 days at 36°C (provided this included no more than 3 repeats for a single gene deletion) were stripped out. In each SGA experiment, a small number of strains were missing from the starting mutant array (due to mis-pinning, strains being lost, replaced etc.). These experiment-specific missing strains; together with genes affecting selection during SGA; and experiment-specific genes situated within 20 kb of SGA markers; were removed from analysis. Photography Solid agar plates were photographed on an spImager (S&P Robotics Inc., Toronto, Canada). The integrated camera (Canon EOS 40D) was used in manual mode with a pre-set manual focus. Manual settings were as follows: exposure, 0.25 s; aperture, F10; white balance, 3700 K; ISO100; image size, large; image quality, fine; image type, .jpg. Using the spImager software, the plate barcode number and a time stamp (date in year, month, day and time in hour, minute, second) were incorporated as the image name (e.g. DLY00000516-2008-12-24_23-59-59.jpg). Image analysis The image analysis tool Colonyzer [21] was used to quantify cell density from captured photographs. Colonyzer corrects for lighting gradients, removing spatial bias from density estimates. It is designed to detect cultures with extremely low cell densities, allowing it to capture a wide range of culture densities after dilute spotting on agar. Colonyzer is available under GPL at http://research.ncl.ac.uk/colonyzer. 384 spot versus 1,536 colony sensitivity We directly compared QFA of pinned 1536- colony format versus spotted 384- culture format and found that the range of normalized 384 spot fitness is approximately 4 times that estimated from 1,536 colony growth curves (Lawless et al., in prep). We also find that 384 spot fitness estimates adequately captures the strong temperature dependent growth of cdc13-1 mutants, whereas 1536-format growth estimates do not, and that analysis of growth in 384 spot format captures a much higher dynamic range of cell densities than 1536 colony format (approx 1,000 versus 20 fold, see Fig. 2, Lawless et al, 2010). For these reasons we chose to perform QFA of telomere capping mutants arrayed as 384 spotted cultures. Sample tracking and data storage Strain array positions on a 384-spot layout (plate, row, column) were defined in a comma-separated text file and tracked using bar-codes reported in robot log-files. Data was stored in a Robot Object Database (ROD) as described previously [20]. Screen data is exported from ROD in tab delimited format (Table S7) ready for modeling and statistical analysis (see below). Modeling of fitness Culture density (G) was estimated from captured photographs using the Integrated Optical Density (IOD or Trimmed Area; Table S7) measure of cell density provided by the image-analysis tool Colonyzer (Lawless et al 2010). Observed density time series were summarised with the logistic population model, which is an ODE describing self-limiting population growth. It has an analytical solution G (t): Modelled inoculum density (G0 , AU) was fixed (at 43 AU in this case), assuming that all liquid cultures reached the same density in stationary phase before water dilution and inoculation onto agar. Logistic parameter values r (growth rate, d−1) and K (carrying capacity, AU) were inferred by least squares fit to observations, using optimization routines in the SciPy Python library (code available from http://sourceforge.net/projects/colonyzer/). For least-squares minimisation, initial guesses for K were the maximum observed cell density for that culture. For r, we constructed initial guesses by observing that G'(t) is at a maximum when t = t* : Linearly interpolating between cell density observations we estimated the time of greatest rate of change of density. We then estimated r as: A quantitative measure of fitness was then constructed from the optimal parameters. The particular measure we used was the product of the maximal doubling rate (MDR, doublings.d−1), which is the inverse of the doubling time and the maximal doubling potential (MDP, doublings). These phenotypes were quantified using logistic model parameter estimates as follows. We estimate the minimum doubling time T which the cell population takes to reach a density of 2G0 (assuming that the culture is in exponential phase immediately after inoculation): MDP is the number of divisions the culture is observed to undergo. Considering cell growth as a geometric progression: These two phenotypes provide different information about the nature of population fitness and both of them are important, reflecting the rate of growth (MDR) and the capacity of the mutant to divide (MDP) under given experimental conditions. Our chosen measure of fitness (F = MDR×MDP) places equal importance on these two phenotypes. Quantifying genetic interaction To estimate GIS, F is obtained for a particular temperature for both the QFA screen of interest and a second QFA screen using a control query mutation, ura3Δ, which is assumed to be neutral under the experimental conditions, approximating wild-type fitness. Experimental and control strain fitnesses are analysed for evidence of epistatic interactions contradicting a multiplicative model of genetic independence [49] (used due to the ratio scale of the phenotype). We denote the fitness of the query (or background) mutation Fxyz , that of a typical deletion from the yeast knockout library FyfgΔ and double mutant fitnesses as Fxyz yfgΔ . Genetic independence therefore implies: and re-arranging gives: where M = Fxyz /Fura3Δ is a constant independent of the particular knockout, yfgΔ. Thus, after normalising fitnesses ( ) so that the means across all knockouts for both the experimental (QFA, xyz yfgΔ) and control (cQFA, ura3Δ yfgΔ) mutation strains are equal to 1, evidence that is significantly different from is evidence of genetic interaction. Thus for each knockout a model is fitted of the form: where i = 1,2, j = 1,..,ni is the j th normalised fitness for treatment i (cQFA = 1, QFA = 2), µ is the mean fitness for the knockout in the control QFA, γ 1 = 0, γ 2 represents genetic interaction and ε ij is (normal, iid) random error. Typically ni is 8 (4 replicates each of SGAv2p15 and SGAv3), but is sometimes a larger multiple of 8 for strains that are repeated in the libraries (e.g. those on plate 15). The model is fitted in R using the lmList command. For each knockout the fitted value of γ 2 is recorded as an estimated measure of the strength of genetic interaction (with the sign indicating suppression or enhancement) and the corresponding p-value is used as a measure of statistical significance of the effect. The p-value is corrected using the R function p.adjust to give a FDR-corrected q-value, and it is this q-value which is thresholded to give the lists of statistically significant genetically interacting strains (see Figure 2). The R code used for the statistical analysis of data from ROD and Colonyzer is available from the authors on request and sample logistic analysis output is presented in Table S8. Stringent lists of genetic interactors for each query mutation and growth condition (Tables S1, S2, S3, S4, S5, S6) were compiled by imposing a 5% FDR cutoff and arbitrarily removing genes with −0.5 0.5. Supplementary information data files website Raw output data and hyperlinked supplementary tables, together with detailed legends for interpretation of data files are available from: http://research.ncl.ac.uk/colonyzer/AddinallQFA/ Supporting Information Figure S1 Fitness plots for cdc13-1 versus ura3Δ strains at 20°C and 27°C and for ura3Δ strains at 20°C versus 37°C. A] Fitness plot showing cdc13-1 at 20°C, compared with QFA for ura3Δ at 20°C. B] Fitness plot showing QFA for of cdc13-1 at 27°C compared with QFA for ura3Δ at 27°C. Note that SPE1, SPE2 and SPE3 (blue text and symbols) have poor fitness in both conditions but fall above the line of equal growth, hence double mutants with cdc13-1 grow better than the single deletion strains. Note the tight clustering of the members of the MRX complex: MRE11, RAD50 and XRS2 (blue squares) C] Temperature sensitivity analysis of ura3Δ strains comparing fitnesses of ura3Δ mutations at 37°C with those at 20°C. A list of stringent temperature sensitive deletion mutations taken from this analysis are presented in Table S9. Figure annotations are as for Figure 2. (1.27 MB TIF) Click here for additional data file. Figure S2 W303 Spot tests. Strains shown in Figure 4 were incubated at the additional temperatures shown. (2.28 MB TIF) Click here for additional data file. Figure S3 Genetic interaction strength (GIS) analysis of ribosomal and telomere length maintenance genes. A] Large ribosomal subunit genes [26] (blue) and small ribosomal subunit genes [26] (red) are indicated. B] Contour lines represent the density of large (blue) and small (red) ribosomal subunit genes and all other genes (white). Density was estimated using the kde2d function in the R package MASS (bandwidth  =  0.6). Crosses represent the mean location for genes in each group. See also Figure S3. C] Genes identified as affecting telomere length maintenance [24]–[26] are indicated. Colour represents telomere length, ranging from blue (short telomeres) to red (long telomeres). White indicates telomere length was either wild-type or not measured [24]. D] Genes that were previously identified [20] as suppressors of cdc13-1 (red) are indicated. (2.22 MB TIF) Click here for additional data file. Figure S4 Effects of over-expression of STN1 or Nonsense Mediated Decay genes on telomere capping mutants. A] Spot tests of yku70Δ (4413) or cdc13-1 (1195) mutants over-expressing STN1 using the centromeric vector pVL1045 and the 2 µ vector pVL1066. The empty centromeric vector Ycplac111 or the 2 µ vector YEplac181 were used as controls. Strains were grown on selective media at the temperatures indicated. B] Spot tests of strains on YEPD at the temperatures indicated. Strains were 2787, 4557, 6656, 4765, 6976, 6808, 5007, 6974, 6975, 6810, 5107, 6867 and 6868. (1.07 MB TIF) Click here for additional data file. Table S1 List of suppressors and enhancers of yku70Δ defect at 23°C. A list of genes which, when deleted, result in suppression or enhancement of the yku70Δ phenotype at 23°C. Only included are gene deletions which passed a 5% FDR cutoff and had a GIS of greater than 0.5 (+ or −) in magnitude. http://research.ncl.ac.uk/colonyzer/AddinallQFA/S1_yku70_23.html. See http://research.ncl.ac.uk/colonyzer/AddinallQFA for a list of all significant interactors, a GIS plot showing interactors and raw data. (0.01 MB HTML) Click here for additional data file. Table S2 List of suppressors and enhancers of yku70Δ defect at 30°C. A list of genes which, when deleted, result in suppression or enhancement of the yku70Δ phenotype at 30°C. Only included are gene deletions which passed a 5% FDR cutoff and had a GIS of greater than 0.5 (+ or −) in magnitude. http://research.ncl.ac.uk/colonyzer/AddinallQFA/S2_yku70_30.html. See http://research.ncl.ac.uk/colonyzer/AddinallQFA for a list of all significant interactors, a GIS plot showing interactors and raw data. (0.02 MB HTML) Click here for additional data file. Table S3 List of suppressors and enhancers of yku70Δ defect at 37°C. A list of genes which, when deleted, result in suppression or enhancement of the yku70Δ phenotype at 37°C. Only included are gene deletions which passed a 5% FDR cutoff and had a GIS of greater than 0.5 (+ or −) in magnitude. http://research.ncl.ac.uk/colonyzer/AddinallQFA/S3_yku70_37.html. See http://research.ncl.ac.uk/colonyzer/AddinallQFA for a list of all significant interactors, a GIS plot showing interactors and raw data. (0.05 MB HTML) Click here for additional data file. Table S4 List of suppressors and enhancers of yku70Δ defect at 37.5°C. A list of genes which, when deleted, result in suppression or enhancement of the yku70Δ phenotype at 37.5°C. Only included are gene deletions which passed a 5% FDR cutoff and had a GIS of greater than 0.5 (+ or −) in magnitude. http://research.ncl.ac.uk/colonyzer/AddinallQFA/S4_yku70_375.html. See http://research.ncl.ac.uk/colonyzer/AddinallQFA for a list of all significant interactors, a GIS plot showing interactors and raw data. (0.10 MB HTML) Click here for additional data file. Table S5 List of suppressors and enhancers of cdc13-1 defect at 20°C. A list of genes which, when deleted, result in suppression or enhancement of the cdc13-1 phenotype at 20°C. Only included are gene deletions which passed a 5% FDR cutoff and had a GIS of greater than 0.5 (+ or −) in magnitude. http://research.ncl.ac.uk/colonyzer/AddinallQFA/S5_cdc131_20.html. See http://research.ncl.ac.uk/colonyzer/AddinallQFA for a list of all significant interactors, a GIS plot showing interactors and raw data. (0.01 MB HTML) Click here for additional data file. Table S6 List of suppressors and enhancers of cdc13-1 defect at 27°C. A list of genes which, when deleted, result in suppression or enhancement of the cdc13-1 phenotype at 27°C. Only included are gene deletions which passed a 5% FDR cutoff and had a GIS of greater than 0.5 (+ or −) in magnitude. http://research.ncl.ac.uk/colonyzer/AddinallQFA/S6_cdc131_27.html. See http://research.ncl.ac.uk/colonyzer/AddinallQFA for a list of all significant interactors, a GIS plot showing interactors and raw data. (0.14 MB HTML) Click here for additional data file. Table S7 ROD output. Robot log files, metadata and image analysis data are stored in the ROD database, then exported in this format for further analysis. These are text files compressed in. zip format: http://research.ncl.ac.uk/colonyzer/AddinallQFA/RODOutput.zip. See http://research.ncl.ac.uk/colonyzer/AddinallQFA for detailed description of column contents. (131.84 MB ZIP) Click here for additional data file. Table S8 Logistic data file. ROD output data is subjected to logistic modelling and exported in this format for further analysis. These are text files compressed in .zip format: http://research.ncl.ac.uk/colonyzer/AddinallQFA/Logistic.zip. See http://research.ncl.ac.uk/colonyzer/AddinallQFA for detailed description of column contents. (30.13 MB ZIP) Click here for additional data file. Table S9 List of suppressors and enhancers of temperature-induced fitness defect at 37°C. A list of genes which, when deleted, result in significantly better or worse growth at 37°C compared to 20°C. Only included are gene deletions which passed a 5% FDR cutoff and had a GIS of greater than 0.5 (+ or −) in magnitude. http://research.ncl.ac.uk/colonyzer/AddinallQFA/S9_cSGA_37_20.html. See http://research.ncl.ac.uk/colonyzer/AddinallQFA for a list of all significant interactors, a GIS plot of these data and raw data. (0.09 MB HTML) Click here for additional data file. Text S1 Supplemental experimental procedures, strains and strain collections list, supplemental references. (0.12 MB PDF) Click here for additional data file.
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                Author and article information

                Contributors
                Journal
                Biosystems
                BioSystems
                Bio Systems
                Elsevier Science Ireland
                0303-2647
                1872-8324
                1 August 2014
                August 2014
                : 122
                : 55-72
                Affiliations
                Newcastle University, UK
                Author notes
                [* ]Corresponding author. Tel.: +44 01912087320 conor.lawless@ 123456ncl.ac.uk
                Article
                S0303-2647(14)00066-5
                10.1016/j.biosystems.2014.05.002
                4169184
                24906175
                © 2014 The Authors
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