Interpretation and Implications of Lognormal Linear Regression Used for Bacterial Enumeration.

BACKGROUND: Bacterial enumeration data are typically log transformed to realize a more normal distribution and stabilize the variance. Unfortunately, statistical results from log transformed data are often misinterpreted as data within the arithmetic domain. OBJECTIVE: To explore the implication of slope and intercept from an unweighted linear regression and compare it to the results of the regression of log transformed data. METHOD: Mathematical formulae inferencing explained using real dataset. RESULTS: For y=Ax+B+ε, where y is the recovery (CFU/g) and x is the target concentration (CFU/g) with error ε homogeneous across x. When B=0, slope A estimates percent recovery R. In the regression of log transformed data, logy=αlogx+ß+εz (equivalent to equation y=Axα·ω), it is the intercept ß=logyx=logA that estimates the percent recovery in logarithm when slope α=1, which means that R doesn't vary over x. Error term ω is multiplicative to x, while εz or log(ω) is additive to log(x). Whether the data should be transformed or not is not a choice, but a decision based on the distribution of the data. Significant difference was not found between the five models (the linear regression of log transformed data, three generalized linear models and a nonlinear model) regarding their predicted percent recovery when applied to our data. An acceptable regression model should result in approximately the best normal distribution of residuals. CONCLUSIONS: Statistical procedures making use of log transformed data should be studied separately and documented as such, not collectively reported and interpreted with results studied in arithmetic domain. HIGHLIGHTS: The way to interpret statistical results developed from arithmetic domain does not apply to that of the log transformed data.

The small RbcS-like domains of the ß-carboxysome structural protein CcmM bind RubisCO at a site distinct from that binding the RbcS subunit.

Carboxysomes are compartments in bacterial cells that promote efficient carbon fixation by sequestering RubisCO and carbonic anhydrase within a protein shell that impedes CO2 escape. The key to assembling this protein complex is CcmM, a multidomain protein whose C-terminal region is required for RubisCO recruitment. This CcmM region is built as a series of copies (generally 3-5) of a small domain, CcmMS, joined by unstructured linkers. CcmMS domains have weak, but significant, sequence identity to RubisCO's small subunit, RbcS, suggesting that CcmM binds RubisCO by displacing RbcS. We report here the 1.35-Å structure of the first Thermosynechococcus elongatus CcmMS domain, revealing that it adopts a compact, well-defined structure that resembles that of RbcS. CcmMS, however, lacked key RbcS RubisCO-binding determinants, most notably an extended N-terminal loop. Nevertheless, individual CcmMS domains are able to bind RubisCO in vitro with 1.16 µm affinity. Two or four linked CcmMS domains did not exhibit dramatic increases in this affinity, implying that short, disordered linkers may frustrate successive CcmMS domains attempting to simultaneously bind a single RubisCO oligomer. Size-exclusion chromatography-coupled right-angled light scattering (SEC-RALS) and native MS experiments indicated that multiple CcmMS domains can bind a single RubisCO holoenzyme and, moreover, that RbcS is not released from these complexes. CcmMS bound equally tightly to a RubisCO variant in which the α/ß domain of RbcS was deleted, suggesting that CcmMS binds RubisCO independently of its RbcS subunit. We propose that, instead, the electropositive CcmMS may bind to an extended electronegative pocket between RbcL dimers.

Structure and Mutational Analyses of Escherichia coli ZapD Reveal Charged Residues Involved in FtsZ Filament Bundling.

UNLABELLED: Bacterial cell division is an essential and highly coordinated process. It requires the polymerization of the tubulin homologue FtsZ to form a dynamic ring (Z-ring) at midcell. Z-ring formation relies on a group of FtsZ-associated proteins (Zap) for stability throughout the process of division. In Escherichia coli, there are currently five Zap proteins (ZapA through ZapE), of which four (ZapA, ZapB, ZapC, and ZapD) are small soluble proteins that act to bind and bundle FtsZ filaments. In particular, ZapD forms a functional dimer and interacts with the C-terminal tail of FtsZ, but little is known about its structure and mechanism of action. Here, we present the crystal structure of Escherichia coli ZapD and show it forms a symmetrical dimer with centrally located α-helices flanked by ß-sheet domains. Based on the structure of ZapD and its chemical cross-linking to FtsZ, we targeted nine charged ZapD residues for modification by site-directed mutagenesis. Using in vitro FtsZ sedimentation assays, we show that residues R56, R221, and R225 are important for bundling FtsZ filaments, while transmission electron microscopy revealed that altering these residues results in different FtsZ bundle morphology compared to those of filaments bundled with wild-type ZapD. ZapD residue R116 also showed altered FtsZ bundle morphology but levels of FtsZ bundling similar to that of wild-type ZapD. Together, these results reveal that ZapD residues R116, R221, and R225 likely participate in forming a positively charged binding pocket that is critical for bundling FtsZ filaments. IMPORTANCE: Z-ring assembly underpins the formation of the essential cell division complex known as the divisome and is required for recruitment of downstream cell division proteins. ZapD is one of several proteins in E. coli that associates with the Z-ring to promote FtsZ bundling and aids in the overall fitness of the division process. In the present study, we describe the dimeric structure of E. coli ZapD and identify residues that are critical for FtsZ bundling. Together, these results advance our understanding about the formation and dynamics of the Z-ring prior to bacterial cell division.