MOTIVATION: When analyzing 1D time series, scientists are often interested in identifying regions where one variable depends linearly on the other. Typically, they use an ad hoc and therefore often subjective method to do so. RESULTS: Here, we develop a statistically rigorous, Bayesian approach to infer the optimal partitioning of a dataset not only into contiguous piece-wise linear segments, but also into contiguous segments described by linear combinations of arbitrary basis functions. We therefore present a general solution to the problem of identifying discontinuous change points. Focusing on microbial growth, we use the algorithm to find the range of optical density where this density is linearly proportional to the number of cells and to automatically find the regions of exponential growth for both Escherichia coli and Saccharomyces cerevisiae. For budding yeast, we consequently are able to infer the Monod constant for growth on fructose. Our algorithm lends itself to automation and high throughput studies, increases reproducibility, and should facilitate data analyses for a broad range of scientists. AVAILABILITY AND IMPLEMENTATION: The corresponding Python package, entitled Nunchaku, is available at PyPI: https://pypi.org/project/nunchaku.

Eukaryotic genomes often encode multiple transporters for the same nutrient. For example, budding yeast has 17 hexose transporters (HXTs), all of which potentially transport glucose. Using mathematical modelling, we show that transporters that use either facilitated diffusion or symport can have a rate-affinity tradeoff, where an increase in the maximal rate of transport decreases the transporter's apparent affinity. These changes affect the import flux non-monotonically, and for a given concentration of extracellular nutrient there is one transporter, characterised by its affinity, that has a higher import flux than any other. Through encoding multiple transporters, cells can therefore mitigate the tradeoff by expressing those transporters with higher affinities in lower concentrations of nutrients. We verify our predictions using fluorescent tagging of seven HXT genes in budding yeast and follow their expression over time in batch culture. Using the known affinities of the corresponding transporters, we show that their regulation in glucose is broadly consistent with a rate-affinity tradeoff: as glucose falls, the levels of the different transporters peak in an order that mostly follows their affinity for glucose. More generally, evolution is constrained by tradeoffs. Our findings indicate that one such tradeoff often occurs in the cellular transport of nutrients.

Responding to change is a fundamental property of life, making time-series data invaluable in biology. For microbes, plate readers are a popular, convenient means to measure growth and also gene expression using fluorescent reporters. Nevertheless, the difficulties of analysing the resulting data can be a bottleneck, particularly when combining measurements from different wells and plates. Here we present omniplate, a Python module that corrects and normalises plate-reader data, estimates growth rates and fluorescence per cell as functions of time, calculates errors, exports in different formats, and enables meta-analysis of multiple plates. The software corrects for autofluorescence, the optical density's non-linear dependence on the number of cells, and the effects of the media. We use omniplate to measure the Monod relationship for the growth of budding yeast in raffinose, showing that raffinose is a convenient carbon source for controlling growth rates. Using fluorescent tagging, we study yeast's glucose transport. Our results are consistent with the regulation of the hexose transporter (HXT) genes being approximately bipartite: the medium and high affinity transporters are predominately regulated by both the high affinity glucose sensor Snf3 and the kinase complex SNF1 via the repressors Mth1, Mig1, and Mig2; the low affinity transporters are predominately regulated by the low affinity sensor Rgt2 via the co-repressor Std1. We thus demonstrate that omniplate is a powerful tool for exploiting the advantages offered by time-series data in revealing biological regulation.

Motivation: Although high-content image cytometry is becoming increasingly routine, processing the large amount of data acquired during time-lapse experiments remains a challenge. The majority of approaches for automated single-cell segmentation focus on flat, uniform fields of view covered with a single layer of cells. In the increasingly popular microfluidic devices that trap individual cells for long term imaging, these conditions are not met. Consequently, most techniques for segmentation perform poorly. Although potentially constraining the generalizability of software, incorporating information about the microfluidic features, flow of media and the morphology of the cells can substantially improve performance. Results: Here we present DISCO (Data Informed Segmentation of Cell Objects), a framework for using the physical constraints imposed by microfluidic traps, the shape based morphological constraints of budding yeast and temporal information about cell growth and motion to allow tracking and segmentation of cells in microfluidic devices. Using manually curated datasets, we demonstrate substantial improvements in both tracking and segmentation when compared with existing software. Availability and implementation: The MATLAB code for the algorithm and for measuring performance is available at https://github.com/pswain/segmentation-software and the test images and the curated ground-truth results used for comparing the algorithms are available at http://datashare.is.ed.ac.uk/handle/10283/2002. Contact: [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

Cells live in changing, dynamic environments. To understand cellular decision-making, we must therefore understand how fluctuating inputs are processed by noisy biomolecular networks. Here we present a general methodology for analyzing the fidelity with which different statistics of a fluctuating input are represented, or encoded, in the output of a signaling system over time. We identify two orthogonal sources of error that corrupt perfect representation of the signal: dynamical error, which occurs when the network responds on average to other features of the input trajectory as well as to the signal of interest, and mechanistic error, which occurs because biochemical reactions comprising the signaling mechanism are stochastic. Trade-offs between these two errors can determine the system's fidelity. By developing mathematical approaches to derive dynamics conditional on input trajectories we can show, for example, that increased biochemical noise (mechanistic error) can improve fidelity and that both negative and positive feedback degrade fidelity, for standard models of genetic autoregulation. For a group of cells, the fidelity of the collective output exceeds that of an individual cell and negative feedback then typically becomes beneficial. We can also predict the dynamic signal for which a given system has highest fidelity and, conversely, how to modify the network design to maximize fidelity for a given dynamic signal. Our approach is general, has applications to both systems and synthetic biology, and will help underpin studies of cellular behavior in natural, dynamic environments.

Cellular decision-making is driven by dynamic behaviours, such as the preparations for sunrise enabled by circadian rhythms and the choice of cell fates enabled by positive feedback. Such behaviours are often built upon ultrasensitive responses where a linear change in input generates a sigmoidal change in output. Phosphorylation-dephosphorylation cycles are one means to generate ultrasensitivity. Using bioinformatics, we show that in vivo levels of kinases and phosphatases frequently exceed the levels of their corresponding substrates in budding yeast. This result is in contrast to the conditions often required by zero-order ultrasensitivity, perhaps the most well known means for how such cycles become ultrasensitive. We therefore introduce a mechanism to generate ultrasensitivity when numbers of enzymes are higher than numbers of substrates. Our model combines distributive and non-distributive actions of the enzymes with two-stage binding and concerted allosteric transitions of the substrate. We use analytical and numerical methods to calculate the Hill number of the response. For a substrate with [Formula: see text] phosphosites, we find an upper bound of the Hill number of [Formula: see text], and so even systems with a single phosphosite can be ultrasensitive. Two-stage binding, where an enzyme must first bind to a binding site on the substrate before it can access the substrate's phosphosites, allows the enzymes to sequester the substrate. Such sequestration combined with competition for each phosphosite provides an intuitive explanation for the sigmoidal shifts in levels of phosphorylated substrate. Additionally, we find cases for which the response is not monotonic, but shows instead a peak at intermediate levels of input. Given its generality, we expect the mechanism described by our model to often underlay decision-making circuits in eukaryotic cells.

Sensing extracellular changes initiates signal transduction and is the first stage of cellular decision-making. Yet relatively little is known about why one form of sensing biochemistry has been selected over another. To gain insight into this question, we studied the sensing characteristics of one of the biochemically simplest of sensors: the allosteric transcription factor. Such proteins, common in microbes, directly transduce the detection of a sensed molecule to changes in gene regulation. Using the Monod-Wyman-Changeux model, we determined six sensing characteristics--the dynamic range, the Hill number, the intrinsic noise, the information transfer capacity, the static gain, and the mean response time--as a function of the biochemical parameters of individual sensors and of the number of sensors. We found that specifying one characteristic strongly constrains others. For example, a high dynamic range implies a high Hill number and a high capacity, and vice versa. Perhaps surprisingly, these constraints are so strong that most of the space of characteristics is inaccessible given biophysically plausible ranges of parameter values. Within our approximations, we can calculate the probability distribution of the numbers of input molecules that maximizes information transfer and show that a population of one hundred allosteric transcription factors can in principle distinguish between more than four bands of input concentrations. Our results imply that allosteric sensors are unlikely to have been selected for high performance in one sensing characteristic but for a compromise in the performance of many.

Much of the complexity of biochemical networks comes from the information-processing abilities of allosteric proteins, be they receptors, ion-channels, signalling molecules or transcription factors. An allosteric protein can be uniquely regulated by each combination of input molecules that it binds. This "regulatory complexity" causes a combinatorial increase in the number of parameters required to fit experimental data as the number of protein interactions increases. It therefore challenges the creation, updating, and re-use of biochemical models. Here, we propose a rule-based modelling framework that exploits the intrinsic modularity of protein structure to address regulatory complexity. Rather than treating proteins as "black boxes", we model their hierarchical structure and, as conformational changes, internal dynamics. By modelling the regulation of allosteric proteins through these conformational changes, we often decrease the number of parameters required to fit data, and so reduce over-fitting and improve the predictive power of a model. Our method is thermodynamically grounded, imposes detailed balance, and also includes molecular cross-talk and the background activity of enzymes. We use our Allosteric Network Compiler to examine how allostery can facilitate macromolecular assembly and how competitive ligands can change the observed cooperativity of an allosteric protein. We also develop a parsimonious model of G protein-coupled receptors that explains functional selectivity and can predict the rank order of potency of agonists acting through a receptor. Our methodology should provide a basis for scalable, modular and executable modelling of biochemical networks in systems and synthetic biology.