Tubuloglomerular feedback (TGF) is essential for the renal auto-regulation of flow. TGF is known to induce spontaneous oscillations in single-nephron tubular fluid flow in male kidneys. However, male-female differences in this dynamic behavior have not been studied. Leveraging intravital two-photon microscopy, resting-state magnetic resonance imaging, ultrasound-based and transdermal recordings, we found TGF-mediated oscillations across spatial scales in the rodent kidney, from single-nephron to whole-organ levels, and that male kidneys exhibited higher operating frequencies than females. To understand the mechanisms involved, we developed a dynamical systems model of TGF that agrees with physiological observations. Analysis of the mathematical model indicated that higher reabsorption rate and fluid flow efficiency in male proximal tubules not only result in higher frequencies, but also render male nephrons more susceptible to lose TGF-mediated oscillations. Furosemide abolished TGF-mediated oscillations in male kidneys and upregulated tubular injury marker KIM-1, suggesting that the propensity to lose TGF-mediated oscillations underlies the heightened risk for injury in males. Our analysis also indicated that SGLT-2 inhibition confers renoprotection by preserving TGF-mediated oscillations in hyperglycemia. Combining quantitative imaging and mathematical modeling, this study provides mechanistic insights into the transition from normal physiology to pathophysiology in the kidney.

Manifold learning builds on the "manifold hypothesis," which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to define manifolds mathematically. These tools also cannot assess whether the manifold hypothesis holds true for a dataset. Here, we describe DeepAtlas, an algorithm that generates lower-dimensional representations of the data's local neighborhoods, then trains deep neural networks that map between these local embeddings and the original data. Topological distortion is used to determine whether a dataset is drawn from a manifold and, if so, its dimensionality. Application to test datasets indicates that DeepAtlas can successfully learn manifold structures. Interestingly, many real datasets, including single-cell RNA-sequencing, do not conform to the manifold hypothesis. In cases where data is drawn from a manifold, DeepAtlas builds a model that can be used generatively and promises to allow the application of powerful tools from differential geometry to a variety of datasets.

Age-related decline of renal function is faster in males than in age-matched females, manifesting in increased susceptibility to both chronic and acute kidney diseases among males. In the mouse kidney, sexually dimorphic gene activity maps predominantly to proximal tubule (PT) segments, where most reabsorption of water and salt happens, with a high energetic demand. Recent work suggests that male PTs undergo excessive oxidative stress to meet the high energetic demand, while female PTs exhibit an anti-oxidation state. However, it remains elusive how the observed molecular differences relate to sex disparities in renal physiology and pathophysiology. Glomerular filtration rate (GFR) is tightly regulated by tubuloglomerular feedback (TGF) within renal tubules to optimize ultrafiltration of plasma and reabsorption of essential molecules. Importantly, GFR shows a sustained oscillatory pattern over time in rodents, and loss of GFR oscillations is associated with cessation of reabsorption activities and with the occurrence of ischemia-reperfusion injuries in the kidney, as well as with systemic hypertension. To study the relationship between intracellular metabolic events and renal physiology, we developed a mathematical model of TGF linking metabolic regulation within PT cells to fluid handling and salt reabsorption in the nephron, using renal blood flow and intra-vital imaging data. Analysis of this model revealed that dynamical properties of the system differ between male and female kidneys, resulting in male kidneys being more prone to stress-induced damage, thus building towards an explanation for sexual dimorphism in renal aging and diseases. With this mechanistic model, our work also provides insight into how pharmacological interventions can be employed to confer renoprotection. The authors received no funding for this study. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

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.

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.

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.

ABSTRACT According to the WHO, one in three people in the world has a latent tuberculosis infection. Tuberculosis is caused by the bacterium Mycobacterium tuberculosis (M.tb). The development of multi-drug resistant (MDR) tuberculosis indicates a need for novel treatments. Hence, it is important to find a second line of treatment for patients infected with MDR tuberculosis. The proteasome is known to be necessary for survival under stress and pathogenicity in M.tb . However, our ability to use the proteasome as drug target has been limited by our abilities to screen for inhibitor compounds in vitro. The proteasome is a protease complex that degrades proteins and is crucial for the maintenance of protein homeostasis within cells. Like many protein complexes, the proteasome must assemble into a specific quaternary structure in order to be active. Specifically, the proteolytically-active proteasome Core Particle (CP) consists of 28 subunits (14 α and 14 β) that must assemble into a barrel-like structure in order to become catalytically active. Hence, understanding the assembly process in not only important from a basic cell biological perspective, but may also serve as the basis for the discovery of novel assembly inhibitors. In this study, we have established for the first time a protocol to express and purify the M.tb α and β subunits separately in vitro. The subunits are soluble monomers on purification and only assemble into active CPs upon reconstitution. Our assembly experiments revealed that M.tb CP assembly pathway is almost certainly identical to that seen in previous experiments on the CP from the bacterium Rhodococcus erythropolis ( R.e ), but assembly in M.tb is much slower. Interestingly, we found that subunits from M.tb and R.e spontaneously self-assembled into active hybrid proteasomes on reconstitution with each other, despite having only 65% sequence similarity. Our work thus strongly suggests that the CP assembly pathway is conserved across bacteria, and the ability to perform in vitro assembly experiments on the M.tb proteasome opens up the possibility of performing critical experiments, including screening for potential molecules that could inhibit assembly, directly in this clinically-relevant organism.

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.

There is a growing realization that traditional "Calculus for Life Sciences" courses do not show their applicability to the Life Sciences and discourage student interest. There have been calls from the AAAS, the Howard Hughes Medical Institute, the NSF, and the American Association of Medical Colleges for a new kind of math course for biology students, that would focus on dynamics and modeling, to understand positive and negative feedback relations, in the context of important biological applications, not incidental "examples." We designed a new course, LS 30, based on the idea of modeling biological relations as dynamical systems, and then visualizing the dynamical system as a vector field, assigning "change vectors" to every point in a state space. The resulting course, now being given to approximately 1400 students/year at UCLA, has greatly improved student perceptions toward math in biology, reduced minority performance gaps, and increased students' subsequent grades in physics and chemistry courses. This new course can be customized easily for a broad range of institutions. All course materials, including lecture plans, labs, homeworks and exams, are available from the authors; supporting videos are posted online.

— A prevailing interpretation of Waddington’s landscape is that cells with similar physiologies exist within a shared basin of attraction and exhibit similar gene expression patterns. To test this hypothesis, we used graph theory to characterize the distribution of cells in epigenetic space. Within a variety of single-cell omics datasets, we find that cell types exist in the same regions of epigenetic space, with a density distribution that is approximately power law. These findings are inconsistent with the idea that cell types are produced by attractors, and encourage us to consider alternative hypotheses for how epigenetic changes maintain physiological stability.

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.

The prevailing interpretation of Waddington’s landscape is that attractors in gene expression space produce and stabilize distinct cell types. This notion is often applied in single-cell omics data, where groups of cells are clustered for analysis. Here we apply graph theory to characterize the distribution of cells in epigenetic space, using data from various tissues and organisms as well as various single-cell omics technologies. We found that cell types exist in the same regions of epigenetic space, with highly heterogeneous density distributions that are inconsistent with expected densities near an attractor. The lack of attractor structure could not be explained by technical noise, scale variance among genes, nor the subset of genes that were used; nor could it be rescued by any standard set of transformations. These findings pose a challenge for the robust analysis of single-cell data and open the possibility for alternative explanations of canalization during development.

Short Abstract — Waddington’s Landscape is an influential paradigm describing how single cells develop and differentiate into their mature forms. For over 60 years, the landscape has been quantitatively characterized as representing a dynamical system built on and on top of gene expression, with cell types corresponding to regions around attractors in the dynamics of the underlying gene regulatory network. With the advent of scRNA-seq, it was thought that these attractor regions would be seen in the high-dimensional space of mRNA levels. Our analysis shows, however, that this isn’t the case, recontextualizing expected heterogeneity amongst single cells during development

Cellular responses to environmental changes are encoded in the complex temporal patterns of signaling proteins. However, quantifying the accumulation of information over time to direct cellular decision-making remains an unsolved challenge. This is, in part, due to the combinatorial explosion of possible configurations that need to be evaluated for information in time-course measurements. Here, we develop a quantitative framework, based on inferred trajectory probabilities, to calculate the mutual information encoded in signaling dynamics while accounting for cell-cell variability. We use it to understand NFκB transcriptional dynamics in response to different immune threats, and reveal that some threats are distinguished faster than others. Our analyses also suggest specific temporal phases during which information distinguishing threats becomes available to immune response genes; one specific phase could be mapped to the functionality of the IκBα negative feedback circuit. The framework is generally applicable to single-cell time series measurements, and enables understanding how temporal regulatory codes transmit information over time.

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.

Proteasomes are molecular machines found in bacteria, archaea, and eukaryotes. They degrade intracellular proteins and are involved in many critical cell functions. The proteasome complex comprises of a Core Particle (CP) capped by one or more Regulatory Particles (RP). The CP is highly conserved and consists of four heptameric rings. The α and β subunits form the outer and inner rings respectively, with an α7β7β7α7stoichiometry. The β subunits are catalytically active but are expressed in an inactive precursor form with a propeptide sequence at the N terminus. The CP assembles by first forming Half Proteasomes (“HP”:α7β7), which then dimerize to form the CP. Experimental work on bacterial proteasomes shows that the HP forms completely within minutes, while HP dimerization to form CPs takes hours complete. In this study, we aim to understand the molecular mechanism behind this separation of time scales. Experiments on Rhodococcus erythropolis (Re), a close relative of M.tuberculosis suggest that the β propeptide plays a role in HP dimerization. To obtain atomic insights, we used Molecular Dynamics (MD) simulations on the Re HP structure and observed that the propeptide is highly dynamic and extends outside the HP. We hypothesized that certain propeptide interactions delay HP dimerization. Therefore, we ran MD simulations (on Anton) with wild type, fast dimerizing and slow dimerizing propeptide mutants. Simulations revealed that propeptide forms hydrogen bonds with key residues that are crucial for dimerization. These bonds occur more frequently in the slow mutant and less frequently in the fast mutant. Subsequent experimental work validated these predictions. Currently, we are exploring the free energy conformational space and studying allosteric communication among subunits. These findings will elucidate molecular events in proteasome assembly and guide in developing specific assembly inhibitors for treating tuberculosis and other diseases.

The complexity of proteins usually requires the use of multiple, moderate resolution experimental techniques to provide an information-rich picture of their structure and stability. Here we describe a technique known as the empirical phase diagram (EPD), which can be used to present such multidimensional data in picture form. Data from various spectroscopic, hydrodynamic, and calorimetric methods, among others, are created in matrix form and converted to a colored picture as a function of variables such as temperature, pH, ionic strength, etc. Additional methods such as radar charts and Chernoff faces are also discussed. The use of EPDs in the characterization and formulation of biomolecules is described. Further methods based on machine learning are also considered. A wide range of examples are employed to illustrate the power and utility of these approaches.

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 β 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 β propeptide plays an unexpected and complex role in regulating dimerization and autocatalytic activation.