Phenotypic signatures arising from unbalanced bacterial growth

Abstract

Fluctuations in the growth rate of a bacterial culture during unbalanced growth are generally considered undesirable in quantitative studies of bacterial physiology. Under well-controlled experimental conditions, however, these fluctuations are not random but instead reflect the interplay between intra-cellular networks underlying bacterial growth and the growth environment. Therefore, these fluctuations could be considered quantitative phenotypes of the bacteria under a specific growth condition. Here, we present a method to identify "phenotypic signatures" by time-frequency analysis of unbalanced growth curves measured with high temporal resolution. The signatures are then applied to differentiate amongst different bacterial strains or the same strain under different growth conditions, and to identify the essential architecture of the gene network underlying the observed growth dynamics. Our method has implications for both basic understanding of bacterial physiology and for the classification of bacterial strains.

Figure 1. The analysis of unbalanced growth dynamics using wavelet transform.

Unbalanced growth dynamics arise due to coupling between bacterial physiology and the growth environment (left panel). Such fluctuations are typically neglected in quantitative studies of bacterial growth but could be exploited as phenotype signatures using wavelet transform (middle panel). The signatures could be used to distinguish bacterial strains and infer growth models (right panel).

Figure 2. Unbalanced growth environments improve the identification of simple models.

A. The difference of correctly estimated parameters between cell-coupled (k_unbalanced) and constant signals (k_balanced). Cell-coupled signals gave rise to overall higher parameter identifiability than constant signals. We created 500 models with random edges between three nodes (left panel, P, Q, R). We then compared parameter identifiability by using time series of N, Q, and R (right panel). Positive values indicate higher identifiability of parameters using cell-coupled signals. Negative values indicate higher identifiability using constant signals. The red line indicates time series of a constant input signal. The blue line represents time series of a cell-coupled signal. B. Histograms of the accuracy of estimated models using either constant or cell-coupled signals. Models estimated using cell-coupled signals (red bars) have a higher accuracy as compared to models estimated using constant signals (grey bars). Each histogram was calculated using 500 models.

Figure 3. Unbalanced growth environments give rise to rich perturbations.

A. A typical growth curve of MG1655z1 bacterial strain. Grey crosses represent original data. The black line represents the denoised growth curve using the “wden” function in Matlab with a Daubechies (db4) wavelet, a soft universal threshold and no rescaling. B. Wavelet transform of the raw growth curve (a) using a Daubechies (db4) wavelet. The heat map shows the amplitudes at each specific period and time-point. The black box indicates the range of periods that did not generate tight clusters of bacterial strains (Figure S2C). C. Classification of bacterial strains using the corresponding wavelet transforms. All bacterial strains were classified correctly. mg = MG1655z1, dpro = DH5αPro, pao = PAO1, mds = MDS42, bpro = BL21Pro, etec = ETEC, jm109 = JM109, top 10 = Top10. All data was classified using the standard hierarchical clustering algorithm in Matlab with the average Euclidean distance as the metric. D. Classification of bacterial strains using the raw growth curves. One strain was classified incorrectly, as indicated by the red arrow.

Figure 4. Analysis of bacteriophage lambda infection dynamics.

Classification of bacterial knockout strains using unbalanced growth dynamics perturbed by the infection of bacteriophage lambda. Wild type K12 strains were classified into one tight cluster (left panel). Furthermore, two clusters associated with either lipopolysaccharide synthesis or LamB regulation were identified by distinct clusters. Each distinct cluster is represented by the same color in the tree. The right panel shows the corresponding phenotypic signatures of each strain.

Figure 5. Reverse engineering of a growth model using the wavelet transform.

A. The flowchart of a swarm algorithm that identifies growth models using the wavelet transform. The algorithm stochastically evolves growth models by combining different equation components and parameters. See detailed algorithm description in Text S1. B. An identified model (left panel) using unbalanced growth dynamics of four bacterial strains: MG1655z1 (mg), DH5αPro (dpro), BL21Pro (bpro), and MDS (mds) (right panel). The model can explain growth curves of the four bacterial strains with distinct growth dynamics. In the left panel, green lines represent activation while red lines represent repression. In the right panel, grey cross hairs represent original data. The black lines represent simulated data using the model.