Binomial models uncover biological variation during feature selection of droplet-based single-cell RNA sequencing.

Effective analysis of single-cell RNA sequencing (scRNA-seq) data requires a rigorous distinction between technical noise and biological variation. In this work, we propose a simple feature selection model, termed "Differentially Distributed Genes" or DDGs, where a binomial sampling process for each mRNA species produces a null model of technical variation. Using scRNA-seq data where cell identities have been established a priori, we find that the DDG model of biological variation outperforms existing methods. We demonstrate that DDGs distinguish a validated set of real biologically varying genes, minimize neighborhood distortion, and enable accurate partitioning of cells into their established cell-type groups.

Modeling reveals the strength of weak interactions in stacked-ring assembly.

Cells employ many large macromolecular machines for the execution and regulation of processes that are vital for cell and organismal viability. Interestingly, cells cannot synthesize these machines as functioning units. Instead, cells synthesize the molecular parts that must then assemble into the functional complex. Many important machines, including chaperones such as GroEL and proteases such as the proteasome, comprise protein rings that are stacked on top of one another. While there is some experimental data regarding how stacked-ring complexes such as the proteasome self-assemble, a comprehensive understanding of the dynamics of stacked-ring assembly is currently lacking. Here, we developed a mathematical model of stacked-trimer assembly and performed an analysis of the assembly of the stacked homomeric trimer, which is the simplest stacked-ring architecture. We found that stacked rings are particularly susceptible to a form of kinetic trapping that we term "deadlock," in which the system gets stuck in a state where there are many large intermediates that are not the fully assembled structure but that cannot productively react. When interaction affinities are uniformly strong, deadlock severely limits assembly yield. We thus predicted that stacked rings would avoid situations where all interfaces in the structure have high affinity. Analysis of available crystal structures indicated that indeed the majority-if not all-of stacked trimers do not contain uniformly strong interactions. Finally, to better understand the origins of deadlock, we developed a formal pathway analysis and showed that, when all the binding affinities are strong, many of the possible pathways are utilized. In contrast, optimal assembly strategies utilize only a small number of pathways. Our work suggests that deadlock is a critical factor influencing the evolution of macromolecular machines and provides general principles for understanding the self-assembly efficiency of existing machines.

Novel metrics reveal new structure and unappreciated heterogeneity in Caenorhabditis elegans development.

High throughput experimental approaches are increasingly allowing for the quantitative description of cellular and organismal phenotypes. Distilling these large volumes of complex data into meaningful measures that can drive biological insight remains a central challenge. In the quantitative study of development, for instance, one can resolve phenotypic measures for single cells onto their lineage history, enabling joint consideration of heritable signals and cell fate decisions. Most attempts to analyze this type of data, however, discard much of the information content contained within lineage trees. In this work we introduce a generalized metric, which we term the branch edit distance, that allows us to compare any two embryos based on phenotypic measurements in individual cells. This approach aligns those phenotypic measurements to the underlying lineage tree, providing a flexible and intuitive framework for quantitative comparisons between, for instance, Wild-Type (WT) and mutant developmental programs. We apply this novel metric to data on cell-cycle timing from over 1300 WT and RNAi-treated Caenorhabditis elegans embryos. Our new metric revealed surprising heterogeneity within this data set, including subtle batch effects in WT embryos and dramatic variability in RNAi-induced developmental phenotypes, all of which had been missed in previous analyses. Further investigation of these results suggests a novel, quantitative link between pathways that govern cell fate decisions and pathways that pattern cell cycle timing in the early embryo. Our work demonstrates that the branch edit distance we propose, and similar metrics like it, have the potential to revolutionize our quantitative understanding of organismal phenotype.

Novel metrics reveal new structure and unappreciated heterogeneity in C. elegans development.

High throughput experimental approaches are increasingly allowing for the quantitative description of cellular and organismal phenotypes. Distilling these large volumes of complex data into meaningful measures that can drive biological insight remains a central challenge. In the quantitative study of development, for instance, one can resolve phenotypic measures for single cells onto their lineage history, enabling joint consideration of heritable signals and cell fate decisions. Most attempts to analyze this type of data, however, discard much of the information content contained within lineage trees. In this work we introduce a generalized metric, which we term the branch distance, that allows us to compare any two embryos based on phenotypic measurements in individual cells. This approach aligns those phenotypic measurements to the underlying lineage tree, providing a flexible and intuitive framework for quantitative comparisons between, for instance, Wild-Type (WT) and mutant developmental programs. We apply this novel metric to data on cell-cycle timing from over 1300 WT and RNAi-treated Caenorhabditis elegans embryos. Our new metric revealed surprising heterogeneity within this data set, including subtle batch effects in WT embryos and dramatic variability in RNAi-induced developmental phenotypes, all of which had been missed in previous analyses. Further investigation of these results suggests a novel, quantitative link between pathways that govern cell fate decisions and pathways that pattern cell cycle timing in the early embryo. Our work demonstrates that the branch distance we propose, and similar metrics like it, have the potential to revolutionize our quantitative understanding of organismal phenotype.

Altered physical phenotypes of leukemia cells that survive chemotherapy treatment.

The recurrence of cancer following chemotherapy treatment is a major cause of death across solid and hematologic cancers. In B-cell acute lymphoblastic leukemia (B-ALL), relapse after initial chemotherapy treatment leads to poor patient outcomes. Here we test the hypothesis that chemotherapy-treated versus control B-ALL cells can be characterized based on cellular physical phenotypes. To quantify physical phenotypes of chemotherapy-treated leukemia cells, we use cells derived from B-ALL patients that are treated for 7 days with a standard multidrug chemotherapy regimen of vincristine, dexamethasone, and L-asparaginase (VDL). We conduct physical phenotyping of VDL-treated versus control cells by tracking the sequential deformations of single cells as they flow through a series of micron-scale constrictions in a microfluidic device; we call this method Quantitative Cyclical Deformability Cytometry. Using automated image analysis, we extract time-dependent features of deforming cells including cell size and transit time (TT) with single-cell resolution. Our findings show that VDL-treated B-ALL cells have faster TTs and transit velocity than control cells, indicating that VDL-treated cells are more deformable. We then test how effectively physical phenotypes can predict the presence of VDL-treated cells in mixed populations of VDL-treated and control cells using machine learning approaches. We find that TT measurements across a series of sequential constrictions can enhance the classification accuracy of VDL-treated cells in mixed populations using a variety of classifiers. Our findings suggest the predictive power of cell physical phenotyping as a complementary prognostic tool to detect the presence of cells that survive chemotherapy treatment. Ultimately such complementary physical phenotyping approaches could guide treatment strategies and therapeutic interventions. Insight box Cancer cells that survive chemotherapy treatment are major contributors to patient relapse, but the ability to predict recurrence remains a challenge. Here we investigate the physical properties of leukemia cells that survive treatment with chemotherapy drugs by deforming individual cells through a series of micron-scale constrictions in a microfluidic channel. Our findings reveal that leukemia cells that survive chemotherapy treatment are more deformable than control cells. We further show that machine learning algorithms applied to physical phenotyping data can predict the presence of cells that survive chemotherapy treatment in a mixed population. Such an integrated approach using physical phenotyping and machine learning could be valuable to guide patient treatments.

Docking-based long timescale simulation of cell-size protein systems at atomic resolution.

Computational methodologies are increasingly addressing modeling of the whole cell at the molecular level. Proteins and their interactions are the key component of cellular processes. Techniques for modeling protein interactions, thus far, have included protein docking and molecular simulation. The latter approaches account for the dynamics of the interactions but are relatively slow, if carried out at all-atom resolution, or are significantly coarse grained. Protein docking algorithms are far more efficient in sampling spatial coordinates. However, they do not account for the kinetics of the association (i.e., they do not involve the time coordinate). Our proof-of-concept study bridges the two modeling approaches, developing an approach that can reach unprecedented simulation timescales at all-atom resolution. The global intermolecular energy landscape of a large system of proteins was mapped by the pairwise fast Fourier transform docking and sampled in space and time by Monte Carlo simulations. The simulation protocol was parametrized on existing data and validated on a number of observations from experiments and molecular dynamics simulations. The simulation protocol performed consistently across very different systems of proteins at different protein concentrations. It recapitulated data on the previously observed protein diffusion rates and aggregation. The speed of calculation allows reaching second-long trajectories of protein systems that approach the size of the cells, at atomic resolution.

Understanding the separation of timescales in bacterial proteasome core particle assembly.

The 20S proteasome core particle (CP) is a molecular machine that is a key component of cellular protein degradation pathways. Like other molecular machines, it is not synthesized in an active form but rather as a set of subunits that assemble into a functional complex. The CP is conserved across all domains of life and is composed of 28 subunits, 14 α and 14 ß, arranged in four stacked seven-member rings (α7ß7ß7α7). While details of CP assembly vary across species, the final step in the assembly process is universally conserved: two half proteasomes (HPs; α7ß7) dimerize to form the CP. In the bacterium Rhodococcus erythropolis, experiments have shown that the formation of the HP is completed within minutes, while the dimerization process takes hours. The N-terminal propeptide of the ß subunit, which is autocatalytically cleaved off after CP formation, plays a key role in regulating this separation of timescales. However, the detailed molecular mechanism of how the propeptide achieves this regulation is unclear. In this work, we used molecular dynamics simulations to characterize HP conformations and found that the HP exists in two states: one where the propeptide interacts with key residues in the HP dimerization interface and likely blocks dimerization, and one where this interface is free. Furthermore, we found that a propeptide mutant that dimerizes extremely slowly is essentially always in the nondimerizable state, while the wild-type rapidly transitions between the two. Based on these simulations, we designed a propeptide mutant that favored the dimerizable state in molecular dynamics simulations. In vitro assembly experiments confirmed that this mutant dimerizes significantly faster than wild-type. Our work thus provides unprecedented insight into how this critical step in CP assembly is regulated, with implications both for efforts to inhibit proteasome assembly and for the evolution of hierarchical assembly pathways.

Robustness and the evolution of length control strategies in the T3SS and flagellar hook.

Bacterial cells construct many structures, such as the flagellar hook and the type III secretion system (T3SS) injectisome, that aid in crucial physiological processes such as locomotion and pathogenesis. Both of these structures involve long extracellular channels, and the length of these channels must be highly regulated in order for these structures to perform their intended functions. There are two leading models for how length control is achieved in the flagellar hook and T3SS needle: the substrate switching model, in which the length is controlled by assembly of an inner rod, and the ruler model, in which a molecular ruler controls the length. Although there is qualitative experimental evidence to support both models, comparatively little has been done to quantitatively characterize these mechanisms or make detailed predictions that could be used to unambiguously test these mechanisms experimentally. In this work, we constructed a mathematical model of length control based on the ruler mechanism and found that the predictions of this model are consistent with experimental data-not just for the scaling of the average length with the ruler protein length, but also for the variance. Interestingly, we found that the ruler mechanism allows for the evolution of needles with large average lengths without the concomitant large increase in variance that occurs in the substrate switching mechanism. In addition to making further predictions that can be tested experimentally, these findings shed new light on the trade-offs that may have led to the evolution of different length control mechanisms in different bacterial species.

Crosstalk and ultrasensitivity in protein degradation pathways.

Protein turnover is vital to cellular homeostasis. Many proteins are degraded efficiently only after they have been post-translationally "tagged" with a polyubiquitin chain. Ubiquitylation is a form of Post-Translational Modification (PTM): addition of a ubiquitin to the chain is catalyzed by E3 ligases, and removal of ubiquitin is catalyzed by a De-UBiquitylating enzyme (DUB). Nearly four decades ago, Goldbeter and Koshland discovered that reversible PTM cycles function like on-off switches when the substrates are at saturating concentrations. Although this finding has had profound implications for the understanding of switch-like behavior in biochemical networks, the general behavior of PTM cycles subject to synthesis and degradation has not been studied. Using a mathematical modeling approach, we found that simply introducing protein turnover to a standard modification cycle has profound effects, including significantly reducing the switch-like nature of the response. Our findings suggest that many classic results on PTM cycles may not hold in vivo where protein turnover is ubiquitous. We also found that proteins sharing an E3 ligase can have closely related changes in their expression levels. These results imply that it may be difficult to interpret experimental results obtained from either overexpressing or knocking down protein levels, since changes in protein expression can be coupled via E3 ligase crosstalk. Understanding crosstalk and competition for E3 ligases will be key in ultimately developing a global picture of protein homeostasis.

Machine learning classification can reduce false positives in structure-based virtual screening.

With the recent explosion in the size of libraries available for screening, virtual screening is positioned to assume a more prominent role in early drug discovery's search for active chemical matter. In typical virtual screens, however, only about 12% of the top-scoring compounds actually show activity when tested in biochemical assays. We argue that most scoring functions used for this task have been developed with insufficient thoughtfulness into the datasets on which they are trained and tested, leading to overly simplistic models and/or overtraining. These problems are compounded in the literature because studies reporting new scoring methods have not validated their models prospectively within the same study. Here, we report a strategy for building a training dataset (D-COID) that aims to generate highly compelling decoy complexes that are individually matched to available active complexes. Using this dataset, we train a general-purpose classifier for virtual screening (vScreenML) that is built on the XGBoost framework. In retrospective benchmarks, our classifier shows outstanding performance relative to other scoring functions. In a prospective context, nearly all candidate inhibitors from a screen against acetylcholinesterase show detectable activity; beyond this, 10 of 23 compounds have IC50 better than 50 µM. Without any medicinal chemistry optimization, the most potent hit has IC50 280 nM, corresponding to Ki of 173 nM. These results support using the D-COID strategy for training classifiers in other computational biology tasks, and for vScreenML in virtual screening campaigns against other protein targets. Both D-COID and vScreenML are freely distributed to facilitate such efforts.

Cooperativity in Proteasome Core Particle Maturation.

Proteasomes are multi-subunit protease complexes found in all domains of life. The maturation of the core particle (CP), which harbors the active sites, involves dimerization of two half CPs (HPs) and an autocatalytic cleavage that removes ß propeptides. How these steps are regulated remains poorly understood. Here, we used the Rhodococcus erythropolis CP to dissect this process in vitro. Our data show that propeptides regulate the dimerization of HPs through flexible loops we identified. Furthermore, N-terminal truncations of the propeptides accelerated HP dimerization and decelerated CP auto-activation. We identified cooperativity in autocatalysis and found that the propeptide can be partially cleaved by adjacent active sites, potentially aiding an otherwise strictly autocatalytic mechanism. We propose that cross-processing during bacterial CP maturation is the underlying mechanism leading to the observed cooperativity of activation. Our work suggests that the bacterial ß propeptide plays an unexpected and complex role in regulating dimerization and autocatalytic activation.

Signal integration and information transfer in an allosterically regulated network.

A biological reaction network may serve multiple purposes, processing more than one input and impacting downstream processes via more than one output. These networks operate in a dynamic cellular environment in which the levels of network components may change within cells and across cells. Recent evidence suggests that protein concentration variability could explain cell fate decisions. However, systems with multiple inputs, multiple outputs, and changing input concentrations have not been studied in detail due to their complexity. Here, we take a systems biochemistry approach, combining physiochemical modeling and information theory, to investigate how cyclooxygenase-2 (COX-2) processes simultaneous input signals within a complex interaction network. We find that changes in input levels affect the amount of information transmitted by the network, as does the correlation between those inputs. This, and the allosteric regulation of COX-2 by its substrates, allows it to act as a signal integrator that is most sensitive to changes in relative input levels.

Computational approaches to macromolecular interactions in the cell.

Structural modeling of a cell is an evolving strategic direction in computational structural biology. It takes advantage of new powerful modeling techniques, deeper understanding of fundamental principles of molecular structure and assembly, and rapid growth of the amount of structural data generated by experimental techniques. Key modeling approaches to principal types of macromolecular assemblies in a cell already exist. The main challenge, along with the further development of these modeling approaches, is putting them together in a consistent, unified whole cell model. This opinion piece addresses the fundamental aspects of modeling macromolecular assemblies in a cell, and the state-of-the-art in modeling of the principal types of such assemblies.

Intrinsic limits of information transmission in biochemical signalling motifs.

All living things have evolved to sense changes in their environment in order to respond in adaptive ways. At the cellular level, these sensing systems generally involve receptor molecules at the cell surface, which detect changes outside the cell and relay those changes to the appropriate response elements downstream. With the advent of experimental technologies that can track signalling at the single-cell level, it has become clear that many signalling systems exhibit significant levels of 'noise,' manifesting as differential responses of otherwise identical cells to the same environment. This noise has a large impact on the capacity of cell signalling networks to transmit information from the environment. Application of information theory to experimental data has found that all systems studied to date encode less than 2.5 bits of information, with the majority transmitting significantly less than 1 bit. Given the growing interest in applying information theory to biological data, it is crucial to understand whether the low values observed to date represent some sort of intrinsic limit on information flow given the inherently stochastic nature of biochemical signalling events. In this work, we used a series of computational models to explore how much information a variety of common 'signalling motifs' can encode. We found that the majority of these motifs, which serve as the basic building blocks of cell signalling networks, can encode far more information (4-6 bits) than has ever been observed experimentally. In addition to providing a consistent framework for estimating information-theoretic quantities from experimental data, our findings suggest that the low levels of information flow observed so far in living system are not necessarily due to intrinsic limitations. Further experimental work will be needed to understand whether certain cell signalling systems actually can approach the intrinsic limits described here, and to understand the sources and purpose of the variation that reduces information flow in living cells.

Chemical Stability of the Botanical Drug Substance Crofelemer: A Model System for Comparative Characterization of Complex Mixture Drugs.

As the second of a 3-part series of articles in this issue concerning the development of a mathematical model for comparative characterization of complex mixture drugs using crofelemer (CF) as a model compound, this work focuses on the evaluation of the chemical stability profile of CF. CF is a biopolymer containing a mixture of proanthocyanidin oligomers which are primarily composed of gallocatechin with a small contribution from catechin. CF extracted from drug product was subjected to molecular weight-based fractionation and thiolysis. Temperature stress and metal-catalyzed oxidation were selected for accelerated and forced degradation studies. Stressed CF samples were size fractionated, thiolyzed, and analyzed with a combination of negative-ion electrospray ionization mass spectrometry (ESI-MS) and reversed-phase-HPLC with UV absorption and fluorescence detection. We further analyzed the chemical stability data sets for various CF samples generated from reversed-phase-HPLC-UV and ESI-MS using data-mining and machine learning approaches. In particular, calculations based on mutual information of over 800,000 data points in the ESI-MS analytical data set revealed specific CF cleavage and degradation products that were differentially generated under specific storage/degradation conditions, which were not initially identified using traditional analysis of the ESI-MS results.

The Botanical Drug Substance Crofelemer as a Model System for Comparative Characterization of Complex Mixture Drugs.

Crofelemer is a botanical polymeric proanthocyanidin that inhibits chloride channel activity and is used clinically for treating HIV-associated secretory diarrhea. Crofelemer lots may exhibit significant physicochemical variation due to the natural source of the raw material. A variety of physical, chemical, and biological assays were used to identify potential critical quality attributes (CQAs) of crofelemer, which may be useful in characterizing differently sourced and processed drug products. Crofelemer drug substance was extracted from tablets of one commercial drug product lot, fractionated, and subjected to accelerated thermal degradation studies to produce derivative lots with variations in chemical and physical composition potentially representative of manufacturing and raw material variation. Liquid chromatography, UV absorbance spectroscopy, mass spectrometry, and nuclear magnetic resonance analysis revealed substantial changes in the composition of derivative lots. A chloride channel inhibition cell-based bioassay suggested that substantial changes in crofelemer composition did not necessarily result in major changes to bioactivity. In 2 companion papers, machine learning and data mining approaches were applied to the analytical and biological data sets presented herein, along with chemical stability data sets derived from forced degradation studies, to develop an integrated mathematical model that can identify CQAs which are most relevant in distinguishing between different populations of crofelemer.

Comparative Characterization of Crofelemer Samples Using Data Mining and Machine Learning Approaches With Analytical Stability Data Sets.

There is growing interest in generating physicochemical and biological analytical data sets to compare complex mixture drugs, for example, products from different manufacturers. In this work, we compare various crofelemer samples prepared from a single lot by filtration with varying molecular weight cutoffs combined with incubation for different times at different temperatures. The 2 preceding articles describe experimental data sets generated from analytical characterization of fractionated and degraded crofelemer samples. In this work, we use data mining techniques such as principal component analysis and mutual information scores to help visualize the data and determine discriminatory regions within these large data sets. The mutual information score identifies chemical signatures that differentiate crofelemer samples. These signatures, in many cases, would likely be missed by traditional data analysis tools. We also found that supervised learning classifiers robustly discriminate samples with around 99% classification accuracy, indicating that mathematical models of these physicochemical data sets are capable of identifying even subtle differences in crofelemer samples. Data mining and machine learning techniques can thus identify fingerprint-type attributes of complex mixture drugs that may be used for comparative characterization of products.

Crosstalk and the evolvability of intracellular communication.

Metazoan signalling networks are complex, with extensive crosstalk between pathways. It is unclear what pressures drove the evolution of this architecture. We explore the hypothesis that crosstalk allows different cell types, each expressing a specific subset of signalling proteins, to activate different outputs when faced with the same inputs, responding differently to the same environment. We find that the pressure to generate diversity leads to the evolution of networks with extensive crosstalk. Using available data, we find that human tissues exhibit higher levels of diversity between cell types than networks with random expression patterns or networks with no crosstalk. We also find that crosstalk and differential expression can influence drug activity: no protein has the same impact on two tissues when inhibited. In addition to providing a possible explanation for the evolution of crosstalk, our work indicates that consideration of cellular context will likely be crucial for targeting signalling networks.

Fundamental trade-offs between information flow in single cells and cellular populations.

Signal transduction networks allow eukaryotic cells to make decisions based on information about intracellular state and the environment. Biochemical noise significantly diminishes the fidelity of signaling: networks examined to date seem to transmit less than 1 bit of information. It is unclear how networks that control critical cell-fate decisions (e.g., cell division and apoptosis) can function with such low levels of information transfer. Here, we use theory, experiments, and numerical analysis to demonstrate an inherent trade-off between the information transferred in individual cells and the information available to control population-level responses. Noise in receptor-mediated apoptosis reduces information transfer to approximately 1 bit at the single-cell level but allows 3-4 bits of information to be transmitted at the population level. For processes such as eukaryotic chemotaxis, in which single cells are the functional unit, we find high levels of information transmission at a single-cell level. Thus, low levels of information transfer are unlikely to represent a physical limit. Instead, we propose that signaling networks exploit noise at the single-cell level to increase population-level information transfer, allowing extracellular ligands, whose levels are also subject to noise, to incrementally regulate phenotypic changes. This is particularly critical for discrete changes in fate (e.g., life vs. death) for which the key variable is the fraction of cells engaged. Our findings provide a framework for rationalizing the high levels of noise in metazoan signaling networks and have implications for the development of drugs that target these networks in the treatment of cancer and other diseases.

Mathematical Model for Length Control by the Timing of Substrate Switching in the Type III Secretion System.

Type III Secretion Systems (T3SS) are complex bacterial structures that provide gram-negative pathogens with a unique virulence mechanism whereby they grow a needle-like structure in order to inject bacterial effector proteins into the cytoplasm of a host cell. Numerous experiments have been performed to understand the structural details of this nanomachine during the past decade. Despite the concerted efforts of molecular and structural biologists, several crucial aspects of the assembly of this structure, such as the regulation of the length of the needle itself, remain unclear. In this work, we used a combination of mathematical and computational techniques to better understand length control based on the timing of substrate switching, which is a possible mechanism for how bacteria ensure that the T3SS needles are neither too short nor too long. In particular, we predicted the form of the needle length distribution based on this mechanism, and found excellent agreement with available experimental data from Salmonella typhimurium with only a single free parameter. Although our findings provide preliminary evidence in support of the substrate switching model, they also make a set of quantitative predictions that, if tested experimentally, would assist in efforts to unambiguously characterize the regulatory mechanisms that control the growth of this crucial virulence factor.