Cell responses only partially shape cell-to-cell variations in protein abundances in Escherichia coli chemotaxis.

Cell-to-cell variations in protein abundance in clonal cell populations are ubiquitous in living systems. Because protein composition determines responses in individual cells, it stands to reason that the variations themselves are subject to selective pressures. However, the functional role of these cell-to-cell differences is not well understood. One way to tackle questions regarding relationships between form and function is to perturb the form (e.g., change the protein abundances) and observe the resulting changes in some function. Here, we take on the form-function relationship from the inverse perspective, asking instead what specific constraints on cell-to-cell variations in protein abundance are imposed by a given functional phenotype. We develop a maximum entropy-based approach to posing questions of this type and illustrate the method by application to the well-characterized chemotactic response in Escherichia coli. We find that full determination of observed cell-to-cell variations in protein abundances is not inherent in chemotaxis itself but, in fact, appears to be jointly imposed by the chemotaxis program in conjunction with other factors (e.g., the protein synthesis machinery and/or additional nonchemotactic cell functions, such as cell metabolism). These results illustrate the power of maximum entropy as a tool for the investigation of relationships between biological form and function.

Host-to-host variation of ecological interactions in polymicrobial infections.

Host-to-host variability with respect to interactions between microorganisms and multicellular hosts are commonly observed in infection and in homeostasis. However, the majority of mechanistic models used to analyze host-microorganism relationships, as well as most of the ecological theories proposed to explain coevolution of hosts and microbes, are based on averages across a host population. By assuming that observed variations are random and independent, these models overlook the role of differences between hosts. Here, we analyze mechanisms underlying host-to-host variations of bacterial infection kinetics, using the well characterized experimental infection model of polymicrobial otitis media (OM) in chinchillas, in combination with population dynamic models and a maximum entropy (MaxEnt) based inference scheme. We find that the nature of the interactions between bacterial species critically regulates host-to-host variations in these interactions. Surprisingly, seemingly unrelated phenomena, such as the efficiency of individual bacterial species in utilizing nutrients for growth, and the microbe-specific host immune response, can become interdependent in a host population. The latter finding suggests a potential mechanism that could lead to selection of specific strains of bacterial species during the coevolution of the host immune response and the bacterial species.

Data-driven quantification of the robustness and sensitivity of cell signaling networks.

Robustness and sensitivity of responses generated by cell signaling networks has been associated with survival and evolvability of organisms. However, existing methods analyzing robustness and sensitivity of signaling networks ignore the experimentally observed cell-to-cell variations of protein abundances and cell functions or contain ad hoc assumptions. We propose and apply a data-driven maximum entropy based method to quantify robustness and sensitivity of Escherichia coli (E. coli) chemotaxis signaling network. Our analysis correctly rank orders different models of E. coli chemotaxis based on their robustness and suggests that parameters regulating cell signaling are evolutionary selected to vary in individual cells according to their abilities to perturb cell functions. Furthermore, predictions from our approach regarding distribution of protein abundances and properties of chemotactic responses in individual cells based on cell population averaged data are in excellent agreement with their experimental counterparts. Our approach is general and can be used to evaluate robustness as well as generate predictions of single cell properties based on population averaged experimental data in a wide range of cell signaling systems.

The effect of ascertainment on penetrance estimates for rare variants: Implications for establishing pathogenicity and for genetic counselling.

Next-generation sequencing has led to an explosion of genetic findings for many rare diseases. However, most of the variants identified are very rare and were also identified in small pedigrees, which creates challenges in terms of penetrance estimation and translation into genetic counselling in the setting of cascade testing. We use simulations to show that for a rare (dominant) disorder where a variant is identified in a small number of small pedigrees, the penetrance estimate can both have large uncertainty and be drastically inflated, due to underlying ascertainment bias. We have developed PenEst, an app that allows users to investigate the phenomenon across ranges of parameter settings. We also illustrate robust ascertainment corrections via the LOD (logarithm of the odds) score, and recommend a LOD-based approach to assessing pathogenicity of rare variants in the presence of reduced penetrance.

A genome-wide association analysis of loss of ambulation in dystrophinopathy patients suggests multiple candidate modifiers of disease severity.

The major determinant of disease severity in Duchenne muscular dystrophy (DMD) or milder Becker muscular dystrophy (BMD) is whether the dystrophin gene (DMD) mutation truncates the mRNA reading frame or allows expression of a partially functional protein. However, even in the complete absence of dystrophin, variability in disease severity is observed, and candidate gene studies have implicated several genes as modifiers. Here we present the largest genome-wide search to date for loci influencing severity in N = 419 DMD patients. Availability of subjects for such studies is quite limited, leading to modest sample sizes, which present a challenge for GWAS design. We have therefore taken special steps to minimize heterogeneity within our dataset at the DMD locus itself, taking a novel approach to mutation classification to effectively exclude the possibility of residual dystrophin expression, and utilized statistical methods that are well adapted to smaller sample sizes, including the use of a novel linear regression-like residual for time to ambulatory loss and the application of evidential statistics for the GWAS approach. Finally, we applied an unbiased in silico pipeline, utilizing functional genomic datasets to explore the potential impact of the best supported SNPs. In all, we obtained eight SNPs (out of 1,385,356 total) with posterior probability of trait-marker association (PPLD) ≥ 0.4, representing six distinct loci. Our analysis prioritized likely non-coding SNP regulatory effects on six genes (ETAA1, PARD6G, GALNTL6, MAN1A1, ADAMTS19, and NCALD), each with plausibility as a DMD modifier. These results support both recurrent and potentially new pathways for intervention in the dystrophinopathies.

KELVIN: a software package for rigorous measurement of statistical evidence in human genetics.

This paper describes the software package KELVIN, which supports the PPL (posterior probability of linkage) framework for the measurement of statistical evidence in human (or more generally, diploid) genetic studies. In terms of scope, KELVIN supports two-point (trait-marker or marker-marker) and multipoint linkage analysis, based on either sex-averaged or sex-specific genetic maps, with an option to allow for imprinting; trait-marker linkage disequilibrium (LD), or association analysis, in case-control data, trio data, and/or multiplex family data, with options for joint linkage and trait-marker LD or conditional LD given linkage; dichotomous trait, quantitative trait and quantitative trait threshold models; and certain types of gene-gene interactions and covariate effects. Features and data (pedigree) structures can be freely mixed and matched within analyses. The statistical framework is specifically tailored to accumulate evidence in a mathematically rigorous way across multiple data sets or data subsets while allowing for multiple sources of heterogeneity, and KELVIN itself utilizes sophisticated software engineering to provide a powerful and robust platform for studying the genetics of complex disorders.

Global and non-Global slow oscillations differentiate in their depth profiles.

Sleep slow oscillations (SOs, 0.5-1.5 Hz) are thought to organize activity across cortical and subcortical structures, leading to selective synaptic changes that mediate consolidation of recent memories. Currently, the specific mechanism that allows for this selectively coherent activation across brain regions is not understood. Our previous research has shown that SOs can be classified on the scalp as Global, Local or Frontal, where Global SOs are found in most electrodes within a short time delay and gate long-range information flow during NREM sleep. The functional significance of space-time profiles of SOs hinges on testing if these differential SOs scalp profiles are mirrored by differential depth structure of SOs in the brain. In this study, we built an analytical framework to allow for the characterization of SO depth profiles in space-time across cortical and sub-cortical regions. To test if the two SO types could be differentiated in their cortical-subcortical activity, we trained 30 machine learning classification algorithms to distinguish Global and non-Global SOs within each individual, and repeated this analysis for light (Stage 2, S2) and deep (slow wave sleep, SWS) NREM stages separately. Multiple algorithms reached high performance across all participants, in particular algorithms based on k-nearest neighbors classification principles. Univariate feature ranking and selection showed that the most differentiating features for Global vs. non-Global SOs appeared around the trough of the SO, and in regions including cortex, thalamus, caudate nucleus, and brainstem. Results also indicated that differentiation during S2 required an extended network of current from cortical-subcortical regions, including all regions found in SWS and other basal ganglia regions, and amygdala and hippocampus, suggesting a potential functional differentiation in the role of Global SOs in S2 vs. SWS. We interpret our results as supporting the potential functional difference of Global and non-Global SOs in sleep dynamics.

The PPLD has advantages over conventional regression methods in application to moderately sized genome-wide association studies.

In earlier work, we have developed and evaluated an alternative approach to the analysis of GWAS data, based on a statistic called the PPLD. More recently, motivated by a GWAS for genetic modifiers of the X-linked Mendelian disorder Duchenne Muscular Dystrophy (DMD), we adapted the PPLD for application to time-to-event (TE) phenotypes. Because DMD itself is relatively rare, this is a setting in which the very large sample sizes generally assembled for GWAS are simply not attainable. For this reason, statistical methods specially adapted for use in small data sets are required. Here we explore the behavior of the TE-PPLD via simulations, comparing the TE-PPLD with Cox Proportional Hazards analysis in the context of small to moderate sample sizes. Our results will help to inform our approach to the DMD study going forward, and they illustrate several respects in which the TE-PPLD, and by extension the original PPLD, offer advantages over regression-based approaches to GWAS in this context.

A new linear regression-like residual for survival analysis, with application to genome wide association studies of time-to-event data.

In linear regression, a residual measures how far a subject's observation is from expectation; in survival analysis, a subject's Martingale or deviance residual is sometimes interpreted similarly. Here we consider ways in which a linear regression-like interpretation is not appropriate for Martingale and deviance residuals, and we develop a novel time-to-event residual which does have a linear regression-like interpretation. We illustrate the utility of this new residual via simulation of a time-to-event genome-wide association study, motivated by a real study seeking genetic modifiers of Duchenne Muscular Dystrophy. By virtue of its linear regression-like characteristics, our new residual may prove useful in other contexts as well.

In silico modeling of Itk activation kinetics in thymocytes suggests competing positive and negative IP4 mediated feedbacks increase robustness.

The inositol-phosphate messenger inositol(1,3,4,5)tetrakisphosphate (IP4) is essential for thymocyte positive selection by regulating plasma-membrane association of the protein tyrosine kinase Itk downstream of the T cell receptor (TCR). IP4 can act as a soluble analog of the phosphoinositide 3-kinase (PI3K) membrane lipid product phosphatidylinositol(3,4,5)trisphosphate (PIP3). PIP3 recruits signaling proteins such as Itk to cellular membranes by binding to PH and other domains. In thymocytes, low-dose IP4 binding to the Itk PH domain surprisingly promoted and high-dose IP4 inhibited PIP3 binding of Itk PH domains. However, the mechanisms that underlie the regulation of membrane recruitment of Itk by IP4 and PIP3 remain unclear. The distinct Itk PH domain ability to oligomerize is consistent with a cooperative-allosteric mode of IP4 action. However, other possibilities cannot be ruled out due to difficulties in quantitatively measuring the interactions between Itk, IP4 and PIP3, and in generating non-oligomerizing Itk PH domain mutants. This has hindered a full mechanistic understanding of how IP4 controls Itk function. By combining experimentally measured kinetics of PLCγ1 phosphorylation by Itk with in silico modeling of multiple Itk signaling circuits and a maximum entropy (MaxEnt) based computational approach, we show that those in silico models which are most robust against variations of protein and lipid expression levels and kinetic rates at the single cell level share a cooperative-allosteric mode of Itk regulation by IP4 involving oligomeric Itk PH domains at the plasma membrane. This identifies MaxEnt as an excellent tool for quantifying robustness for complex TCR signaling circuits and provides testable predictions to further elucidate a controversial mechanism of PIP3 signaling.

Fast and accurate calculation of a computationally intensive statistic for mapping disease genes.

Many statistical methods in biology utilize numerical integration in order to deal with moderately high-dimensional parameter spaces without closed form integrals. One such method is the PPL, a class of models for mapping and modeling genes for complex human disorders. While the most common approach to numerical integration in statistics is MCMC, this is not a good option for the PPL for a variety of reasons, leading us to develop an alternative integration method for this application. We utilize an established sub-region adaptive integration method, but adapt it to specific features of our application. These include division of the multi-dimensional integrals into three separate layers, implementing internal constraints on the parameter space, and calibrating the approximation to ensure adequate precision of results for our application. The proposed approach is compared with an empirically driven fixed grid scheme as well as other numerical integration methods. The new method is shown to require far fewer function evaluations compared to the alternatives while matching or exceeding the best of them in terms of accuracy. The savings in evaluations is sufficiently large that previously intractable problems are now feasible in real time.

A matrix-based multilevel approach to identify functional protein modules.

Identifying functional modules is believed to reveal most cellular processes. There have been many computational approaches to investigate the underlying biological structures (Bader and Hogue, 2003; Dhillon et al., 2005; Krogan et al., 2006; Ramadan et al., 2005; Xiong et al., 2005; Zhang et al., 2004). A spectral clustering method plays a critical role identifying functional modules in a yeast protein-protein network (Ramadan et al., 2005). We present an unweighted-graph version of a multilevel spectral algorithm which more accurately identifies protein complexes with less computational time.