Ann C. Babtie

What makes an enzyme promiscuous

Kinetic analyses of promiscuous enzymes reveal rate accelerations, (k(cat)/K(M))/k(2), of up to 10(18) for their secondary activities. Such large values suggest that binding and catalysis can be highly efficient for more than one reaction, challenging the notion that proficient catalysis requires specificity. Growing numbers of reported promiscuous activities indicate that catalytic versatility is an inherent property of many enzymes. The examples discussed here illustrate promiscuous molecular recognition mechanisms that, together with knowledge from structural and computational analysis, might be used for the identification or development of catalysts for new reactions.

Simultaneous determination of gene expression and enzymatic activity in individual bacterial cells in microdroplet compartments.

A microfluidic device capable of storing picoliter droplets containing single bacteria at constant volumes has been fabricated in PDMS. Once captured in droplets that remain static in the device, bacteria express both a red fluorescent protein (mRFP1) and the enzyme, alkaline phosphatase (AP), from a biscistronic construct. By measuring the fluorescence intensity of both the mRFP1 inside the cells and a fluorescent product formed as a result of the enzymatic activity outside the cells, gene expression and enzymatic activity can be simultaneously and continuously monitored. By collecting data from many individual cells, the distribution of activities in a cell is quantified and the difference in activity between two AP mutants is measured.

An efficient, multiply promiscuous hydrolase in the alkaline phosphatase superfamily

We report a catalytically promiscuous enzyme able to efficiently promote the hydrolysis of six different substrate classes. Originally assigned as a phosphonate monoester hydrolase (PMH) this enzyme exhibits substantial second-order rate accelerations ((kcat/KM)/kw), ranging from 107 to as high as 1019, for the hydrolyses of phosphate mono-, di-, and triesters, phosphonate monoesters, sulfate monoesters, and sulfonate monoesters. This substrate collection encompasses a range of substrate charges between 0 and -2, transition states of a different nature, and involves attack at two different reaction centers (P and S). Intrinsic reactivities (half-lives) range from 200 days to 105 years under near neutrality. The substantial rate accelerations for a set of relatively difficult reactions suggest that efficient catalysis is not necessarily limited to efficient stabilization of just one transition state. The crystal structure of PMH identifies it as a member of the alkaline phosphatase superfamily. PMH encompasses four of the native activities previously observed in this superfamily and extends its repertoire by two further activities, one of which, sulfonate monoesterase, has not been observed previously for a natural enzyme. PMH is thus one of the most promiscuous hydrolases described to date. The functional links between superfamily activities can be presumed to have played a role in functional evolution by gene duplication.

Efficient Catalytic Promiscuity for Chemically Distinct Reactions

High catalytic proficiencies observed for the native and promiscuous reaction of the Pseudomonas aeruginosa arylsulfatase (PAS; the picture shows transition states of the two substrates with corresponding binding constants K(tx)) suggest that the trade-off between high activity and tight specificity can be substantially relaxed.

Topological sensitivity analysis for systems biology

Significance Mathematical models are widely used to study natural systems. They allow us to test and generate hypotheses, and help us to understand the processes underlying the observed behavior. However, such models are, by necessity, simplified representations of the true systems, so it is critical to understand the impact of assumptions made when using a particular model. Here we provide a method to assess how uncertainty about the structure of a natural system affects the conclusions we can draw from mathematical models of its dynamics. We use biological examples to illustrate the importance of considering uncertainty in both model structure and parameters. We show how solely considering the latter source of uncertainty can result in misleading conclusions and incorrect model inferences. Mathematical models of natural systems are abstractions of much more complicated processes. Developing informative and realistic models of such systems typically involves suitable statistical inference methods, domain expertise, and a modicum of luck. Except for cases where physical principles provide sufficient guidance, it will also be generally possible to come up with a large number of potential models that are compatible with a given natural system and any finite amount of data generated from experiments on that system. Here we develop a computational framework to systematically evaluate potentially vast sets of candidate differential equation models in light of experimental and prior knowledge about biological systems. This topological sensitivity analysis enables us to evaluate quantitatively the dependence of model inferences and predictions on the assumed model structures. Failure to consider the impact of structural uncertainty introduces biases into the analysis and potentially gives rise to misleading conclusions.

Systems biology (un)certainties

How can modelers restore confidence in systems and computational biology? Systems biology, some have claimed (1), attempts the impossible and is doomed to fail. Possible definitions abound, but systems biology is widely understood to be an approach for studying the behavior of systems of interacting biological components that combines experiments with computational and mathematical reasoning. Modeling complex systems occurs throughout the sciences, so it may not be immediately clear why it should attract greater skepticism in molecular and cell biology than in other scientific disciplines. The way in which biological models are often presented and interpreted (and overinterpreted) may be partly to blame. As with experimental results, the key to successfully reporting a mathematical model is to provide an honest appraisal and representation of uncertainty in the models predictions, parameters, and (where appropriate) in the structure of the model itself.

Gene Regulatory Network Inference from Single-Cell Data Using Multivariate Information Measures

Summary While single-cell gene expression experiments present new challenges for data processing, the cell-to-cell variability observed also reveals statistical relationships that can be used by information theory. Here, we use multivariate information theory to explore the statistical dependencies between triplets of genes in single-cell gene expression datasets. We develop PIDC, a fast, efficient algorithm that uses partial information decomposition (PID) to identify regulatory relationships between genes. We thoroughly evaluate the performance of our algorithm and demonstrate that the higher-order information captured by PIDC allows it to outperform pairwise mutual information-based algorithms when recovering true relationships present in simulated data. We also infer gene regulatory networks from three experimental single-cell datasets and illustrate how network context, choices made during analysis, and sources of variability affect network inference. PIDC tutorials and open-source software for estimating PID are available. PIDC should facilitate the identification of putative functional relationships and mechanistic hypotheses from single-cell transcriptomic data.

How to deal with parameters for whole-cell modelling

Dynamical systems describing whole cells are on the verge of becoming a reality. But as models of reality, they are only useful if we have realistic parameters for the molecular reaction rates and cell physiological processes. There is currently no suitable framework to reliably estimate hundreds, let alone thousands, of reaction rate parameters. Here, we map out the relative weaknesses and promises of different approaches aimed at redressing this issue. While suitable procedures for estimation or inference of the whole (vast) set of parameters will, in all likelihood, remain elusive, some hope can be drawn from the fact that much of the cellular behaviour may be explained in terms of smaller sets of parameters. Identifying such parameter sets and assessing their behaviour is now becoming possible even for very large systems of equations, and we expect such methods to become central tools in the development and analysis of whole-cell models.

Stem Cell Differentiation as a Non-Markov Stochastic Process

Summary Pluripotent stem cells can self-renew in culture and differentiate along all somatic lineages in vivo. While much is known about the molecular basis of pluripotency, the mechanisms of differentiation remain unclear. Here, we profile individual mouse embryonic stem cells as they progress along the neuronal lineage. We observe that cells pass from the pluripotent state to the neuronal state via an intermediate epiblast-like state. However, analysis of the rate at which cells enter and exit these observed cell states using a hidden Markov model indicates the presence of a chain of unobserved molecular states that each cell transits through stochastically in sequence. This chain of hidden states allows individual cells to record their position on the differentiation trajectory, thereby encoding a simple form of cellular memory. We suggest a statistical mechanics interpretation of these results that distinguishes between functionally distinct cellular “macrostates” and functionally similar molecular “microstates” and propose a model of stem cell differentiation as a non-Markov stochastic process.

MEANS: python package for Moment Expansion Approximation, iNference and Simulation

Motivation: Many biochemical systems require stochastic descriptions. Unfortunately these can only be solved for the simplest cases and their direct simulation can become prohibitively expensive, precluding thorough analysis. As an alternative, moment closure approximation methods generate equations for the time-evolution of the system’s moments and apply a closure ansatz to obtain a closed set of differential equations; that can become the basis for the deterministic analysis of the moments of the outputs of stochastic systems. Results: We present a free, user-friendly tool implementing an efficient moment expansion approximation with parametric closures that integrates well with the IPython interactive environment. Our package enables the analysis of complex stochastic systems without any constraints on the number of species and moments studied and the type of rate laws in the system. In addition to the approximation method our package provides numerous tools to help non-expert users in stochastic analysis. Availability and implementation: https://github.com/theosysbio/means Contacts: m.stumpf@imperial.ac.uk or e.lakatos13@imperial.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online.