Phosphate sensing in health and disease.

PURPOSE OF REVIEW: Disruptions of phosphate homeostasis are associated with a multitude of diseases with insufficient treatments. Our knowledge regarding the mechanisms underlying metazoan phosphate homeostasis and sensing is limited. Here, we highlight four major advancements in this field during the last 12-18 months. RECENT FINDINGS: First, kidney glycolysis senses filtered phosphate, which results in the release of glycerol 3-phosphate (G-3-P). Circulating G-3-P then stimulates synthesis of the phosphaturic hormone fibroblast growth factor 23 in bone. Second, the liver serves as a postprandial phosphate reservoir to limit serum phosphate excursions. It senses phosphate ingestion and triggers renal excretion of excess phosphate through a nerve-dependent mechanism. Third, phosphate-starvation in cells massively induces the phosphate transporters SLC20A1/PiT1 and SLC20A2/PiT2, implying direct involvement of cellular phosphate sensing. Under basal phosphate-replete conditions, PiT1 is produced but immediately destroyed, which suggests a novel mechanism for the regulation of PiT1 abundance. Fourth, Drosophila melanogaster intestinal cells contain novel organelles called PXo bodies that limit intracellular phosphate excursions. Phosphate starvation leads to PXo body dissolution, which triggers midgut proliferation. SUMMARY: These studies have opened novel avenues to dissect the mechanisms that govern metazoan phosphate sensing and homeostasis with the potential to identify urgently needed therapeutic targets.

A local polynomial moment approximation for compartmentalized biochemical systems.

Compartmentalized biochemical reactions are a ubiquitous building block of biological systems. The interplay between chemical and compartmental dynamics can drive rich and complex dynamical behaviors that are difficult to analyze mathematically - especially in the presence of stochasticity. We have recently proposed an effective moment equation approach to study the statistical properties of compartmentalized biochemical systems. So far, however, this approach is limited to polynomial rate laws and moreover, it relies on suitable moment closure approximations, which can be difficult to find in practice. In this work we propose a systematic method to derive closed moment dynamics for compartmentalized biochemical systems. We show that for the considered class of systems, the moment equations involve expectations over functions that factorize into two parts, one depending on the molecular content of the compartments and one depending on the compartment number distribution. Our method exploits this structure and approximates each function with suitable polynomial expansions, leading to a closed system of moment equations. We demonstrate the method using three systems inspired by cell populations and organelle networks and study its accuracy across different dynamical regimes.

Quantifying single-cell diacylglycerol signaling kinetics after uncaging.

Studying the role of molecularly distinct lipid species in cell signaling remains challenging due to a scarcity of methods for performing quantitative lipid biochemistry in living cells. We have recently used lipid uncaging to quantify lipid-protein affinities and rates of lipid trans-bilayer movement and turnover in the diacylglycerol signaling pathway. This approach is based on acquiring live-cell dose-response curves requiring light dose titrations and experimental determination of uncaging photoreaction efficiency. We here aimed to develop a methodological approach that allows us to retrieve quantitative kinetic data from uncaging experiments that 1) require only typically available datasets without the need for specialized additional constraints and 2) should in principle be applicable to other types of photoactivation experiments. Our new analysis framework allows us to identify model parameters such as diacylglycerol-protein affinities and trans-bilayer movement rates, together with initial uncaged diacylglycerol levels, using noisy single-cell data for a broad variety of structurally different diacylglycerol species. We find that lipid unsaturation degree and side-chain length generally correlate with faster lipid trans-bilayer movement and turnover and also affect lipid-protein affinities. In summary, our work demonstrates how rate parameters and lipid-protein affinities can be quantified from single-cell signaling trajectories with sufficient sensitivity to resolve the subtle kinetic differences caused by the chemical diversity of cellular signaling lipid pools.

Integrating single-cell imaging and RNA sequencing datasets links differentiation and morphogenetic dynamics of human pancreatic endocrine progenitors.

Basic helix-loop-helix genes, particularly proneural genes, are well-described triggers of cell differentiation, yet information on their dynamics is limited, notably in human development. Here, we focus on Neurogenin 3 (NEUROG3), which is crucial for pancreatic endocrine lineage initiation. By monitoring both NEUROG3 gene expression and protein in single cells using a knockin dual reporter in 2D and 3D models of human pancreas development, we show an approximately 2-fold slower expression of human NEUROG3 than that of the mouse. We observe heterogeneous peak levels of NEUROG3 expression and reveal through long-term live imaging that both low and high NEUROG3 peak levels can trigger differentiation into hormone-expressing cells. Based on fluorescence intensity, we statistically integrate single-cell transcriptome with dynamic behaviors of live cells and propose a data-mapping methodology applicable to other contexts. Using this methodology, we identify a role for KLK12 in motility at the onset of NEUROG3 expression.

Deterministic and probabilistic fate decisions co-exist in a single retinal lineage.

Correct nervous system development depends on the timely differentiation of progenitor cells into neurons. While the output of progenitor differentiation is well investigated at the population and clonal level, how stereotypic or variable fate decisions are during development is still more elusive. To fill this gap, we here follow the fate outcome of single neurogenic progenitors in the zebrafish retina over time using live imaging. We find that neurogenic progenitor divisions produce two daughter cells, one of deterministic and one of probabilistic fate. Interference with the deterministic branch of the lineage affects lineage progression. In contrast, interference with fate probabilities of the probabilistic branch results in a broader range of fate possibilities than in wild-type and involves the production of any neuronal cell type even at non-canonical developmental stages. Combining the interference data with stochastic modelling of fate probabilities revealed that a simple gene regulatory network is able to predict the observed fate decision probabilities during wild-type development. These findings unveil unexpected lineage flexibility that could ensure robust development of the retina and other tissues.

Cellular abundance of sodium phosphate cotransporter SLC20A1/PiT1 and phosphate uptake are controlled post-transcriptionally by ESCRT.

Inorganic phosphate is essential for human life. The widely expressed mammalian sodium/phosphate cotransporter SLC20A1/PiT1 mediates phosphate uptake into most cell types; however, while SLC20A1 is required for development, and elevated SLC20A1 expression is associated with vascular calcification and aggressive tumor growth, the mechanisms regulating SLC20A1 protein abundance are unknown. Here, we found that SLC20A1 protein expression is low in phosphate-replete cultured cells but is strikingly induced following phosphate starvation, whereas mRNA expression is high in phosphate-replete cells and only mildly increased by phosphate starvation. To identify regulators of SLC20A1 protein levels, we performed a genome-wide CRISPR-based loss-of-function genetic screen in phosphate-replete cells using SLC20A1 protein induction as readout. Our screen revealed that endosomal sorting complexes required for transport (ESCRT) machinery was essential for proper SLC20A1 protein downregulation in phosphate-replete cells. We show that SLC20A1 colocalizes with ESCRT and that ESCRT deficiency increases SLC20A1 protein and phosphate uptake into cells. We also found numerous additional candidate regulators of mammalian phosphate homeostasis, including genes modifying protein ubiquitination and the Krebs cycle and oxidative phosphorylation pathways. Many of these targets have not been previously implicated in this process. We present here a model in which SLC20A1 protein abundance and phosphate uptake are tonically negatively regulated post-transcriptionally in phosphate-replete cells through direct ESCRT-mediated SLC20A1 degradation. Moreover, our screening results provide a comprehensive resource for future studies to elucidate the mechanisms governing cellular phosphate homeostasis. We conclude that genome-wide CRISPR-based genetic screening is a powerful tool to discover proteins and pathways relevant to physiological processes.

Dynamics of CTCF- and cohesin-mediated chromatin looping revealed by live-cell imaging.

Animal genomes are folded into loops and topologically associating domains (TADs) by CTCF and loop-extruding cohesins, but the live dynamics of loop formation and stability remain unknown. Here, we directly visualized chromatin looping at the Fbn2 TAD in mouse embryonic stem cells using super-resolution live-cell imaging and quantified looping dynamics by Bayesian inference. Unexpectedly, the Fbn2 loop was both rare and dynamic, with a looped fraction of approximately 3 to 6.5% and a median loop lifetime of approximately 10 to 30 minutes. Our results establish that the Fbn2 TAD is highly dynamic, and about 92% of the time, cohesin-extruded loops exist within the TAD without bridging both CTCF boundaries. This suggests that single CTCF boundaries, rather than the fully CTCF-CTCF looped state, may be the primary regulators of functional interactions.

Cell-Free Gene Expression Dynamics in Synthetic Cell Populations.

The ability to build synthetic cellular populations from the bottom-up provides the groundwork to realize minimal living tissues comprising single cells which can communicate and bridge scales into multicellular systems. Engineered systems made of synthetic micron-sized compartments and integrated reaction networks coupled with mathematical modeling can facilitate the design and construction of complex and multiscale chemical systems from the bottom-up. Toward this goal, we generated populations of monodisperse liposomes encapsulating cell-free expression systems (CFESs) using double-emulsion microfluidics and quantified transcription and translation dynamics within individual synthetic cells of the population using a fluorescent Broccoli RNA aptamer and mCherry protein reporter. CFE dynamics in bulk reactions were used to test different coarse-grained resource-limited gene expression models using model selection to obtain transcription and translation rate parameters by likelihood-based parameter estimation. The selected model was then applied to quantify cell-free gene expression dynamics in populations of synthetic cells. In combination, our experimental and theoretical approaches provide a statistically robust analysis of CFE dynamics in bulk and monodisperse synthetic cell populations. We demonstrate that compartmentalization of CFESs leads to different transcription and translation rates compared to bulk CFE and show that this is due to the semipermeable lipid membrane that allows the exchange of materials between the synthetic cells and the external environment.

Hypophosphatemia in acute liver failure of a broad range of etiologies is associated with phosphaturia without kidney damage or phosphatonin elevation.

Hypophosphatemia is a common and dangerous complication of acute liver failure (ALF) of various etiologies. While various mechanisms for ALF-associated hypophosphatemia have been proposed including high phosphate uptake into regenerating hepatocytes, acetaminophen (APAP)-associated hypophosphatemia was linked to renal phosphate wasting, and APAP-induced renal tubular injury was proposed as underlying mechanism. We studied 30 normophosphatemic and 46 hypophosphatemic (serum phosphate < 2.5 mg/dL) patients from the Acute Liver Failure Study Group registry with APAP- or non-APAP-induced ALF. Since kidney injury affects phosphate excretion, patients with elevated serum creatinine (>1.2 mg/dL) were excluded. Maximal amount of renal tubular phosphate reabsorption per filtered volume (TmP/GFR) was calculated from simultaneous serum and urine phosphate and creatinine levels to assess renal phosphate handling. Instead of enhanced renal phosphate reabsorption as would be expected during hypophosphatemia of non-renal causes, serum phosphate was positively correlated with TmP/GFR in both APAP- and non-APAP-induced ALF patients (R2 = 0.66 and 0.46, respectively; both P < 0.0001), indicating renal phosphate wasting. Surprisingly, there was no evidence of kidney damage based on urinary markers including neutrophil gelatinase-associated lipocalin and cystatin C even in the APAP group. Additionally, there was no evidence that the known serum phosphatonins parathyroid hormone, fibroblast growth factor 23, and α-Klotho contribute to the observed hypophosphatemia. We conclude that the observed hypophosphatemia with renal phosphate wasting in both APAP- and non-APAP-mediated ALF is likely the result of renal tubular phosphate leak from yet-to-be identified factor(s) with no evidence for proximal tubular damage or contribution of known phosphatonins.

Compartor: a toolbox for the automatic generation of moment equations for dynamic compartment populations.

SUMMARY: Many biochemical processes in living organisms take place inside compartments that can interact with each other and remodel over time. In a recent work, we have shown how the stochastic dynamics of a compartmentalized biochemical system can be effectively studied using moment equations. With this technique, the time evolution of a compartment population is summarized using a finite number of ordinary differential equations, which can be analyzed very efficiently. However, the derivation of moment equations by hand can become time-consuming for systems comprising multiple reactants and interactions. Here we present Compartor, a toolbox that automatically generates the moment equations associated with a user-defined compartmentalized system. Through the moment equation method, Compartor renders the analysis of stochastic population models accessible to a broader scientific community. AVAILABILITY AND IMPLEMENTATION: Compartor is provided as a Python package and is available at https://pypi.org/project/compartor/. Source code and usage tutorials for Compartor are available at https://github.com/zechnerlab/Compartor.

Promoters adopt distinct dynamic manifestations depending on transcription factor context.

Cells respond to external signals and stresses by activating transcription factors (TF), which induce gene expression changes. Prior work suggests that signal-specific gene expression changes are partly achieved because different gene promoters exhibit distinct induction dynamics in response to the same TF input signal. Here, using high-throughput quantitative single-cell measurements and a novel statistical method, we systematically analyzed transcriptional responses to a large number of dynamic TF inputs. In particular, we quantified the scaling behavior among different transcriptional features extracted from the measured trajectories such as the gene activation delay or duration of promoter activity. Surprisingly, we found that even the same gene promoter can exhibit qualitatively distinct induction and scaling behaviors when exposed to different dynamic TF contexts. While it was previously known that promoters fall into distinct classes, here we show that the same promoter can switch between different classes depending on context. Thus, promoters can adopt context-dependent "manifestations". Our analysis suggests that the full complexity of signal processing by genetic circuits may be significantly underestimated when studied in only specific contexts.

Stochastic reaction networks in dynamic compartment populations.

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress toward addressing this problem in the context of specific biological systems, but a general and sufficiently effective approach remains lacking. In this work, we propose a mathematical framework based on counting processes that allows us to study dynamic compartment populations with arbitrary interactions and internal biochemistry. We derive an efficient description of the dynamics in terms of differential equations which capture the statistics of the population. We demonstrate the relevance of our approach by analyzing models inspired by different biological processes, including subcellular compartmentalization and tissue homeostasis.

Stochasticity and determinism in cell fate decisions.

During development, cells need to make decisions about their fate in order to ensure that the correct numbers and types of cells are established at the correct time and place in the embryo. Such cell fate decisions are often classified as deterministic or stochastic. However, although these terms are clearly defined in a mathematical sense, they are sometimes used ambiguously in biological contexts. Here, we provide some suggestions on how to clarify the definitions and usage of the terms stochastic and deterministic in biological experiments. We discuss the frameworks within which such clear definitions make sense and highlight when certain ambiguity prevails. As an example, we examine how these terms are used in studies of neuronal cell fate decisions and point out areas in which definitions and interpretations have changed and matured over time. We hope that this Review will provide some clarification and inspire discussion on the use of terminology in relation to fate decisions.

Control of Hox transcription factor concentration and cell-to-cell variability by an auto-regulatory switch.

The variability in transcription factor concentration among cells is an important developmental determinant, yet how variability is controlled remains poorly understood. Studies of variability have focused predominantly on monitoring mRNA production noise. Little information exists about transcription factor protein variability, as this requires the use of quantitative methods with single-molecule sensitivity. Using Fluorescence Correlation Spectroscopy (FCS), we have characterized the concentration and variability of 14 endogenously tagged TFs in live Drosophila imaginal discs. For the Hox TF Antennapedia, we investigated whether protein variability results from random stochastic events or is developmentally regulated. We found that Antennapedia transitioned from low concentration/high variability early, to high concentration/low variability later, in development. FCS and temporally resolved genetic studies uncovered that Antennapedia itself is necessary and sufficient to drive a developmental regulatory switch from auto-activation to auto-repression, thereby reducing variability. This switch is controlled by progressive changes in relative concentrations of preferentially activating and repressing Antennapedia isoforms, which bind chromatin with different affinities. Mathematical modeling demonstrated that the experimentally supported auto-regulatory circuit can explain the increase of Antennapedia concentration and suppression of variability over time.

Selected-node stochastic simulation algorithm.

Stochastic simulations of biochemical networks are of vital importance for understanding complex dynamics in cells and tissues. However, existing methods to perform such simulations are associated with computational difficulties and addressing those remains a daunting challenge to the present. Here we introduce the selected-node stochastic simulation algorithm (snSSA), which allows us to exclusively simulate an arbitrary, selected subset of molecular species of a possibly large and complex reaction network. The algorithm is based on an analytical elimination of chemical species, thereby avoiding explicit simulation of the associated chemical events. These species are instead described continuously in terms of statistical moments derived from a stochastic filtering equation, resulting in a substantial speedup when compared to Gillespie's stochastic simulation algorithm (SSA). Moreover, we show that statistics obtained via snSSA profit from a variance reduction, which can significantly lower the number of Monte Carlo samples needed to achieve a certain performance. We demonstrate the algorithm using several biological case studies for which the simulation time could be reduced by orders of magnitude.

The Hormone FGF21 Stimulates Water Drinking in Response to Ketogenic Diet and Alcohol.

Alcohol and ketogenic diets increase water consumption. Here, we show that the hormone FGF21 is required for this drinking response in mice. Circulating levels of FGF21 are increased by alcohol consumption in humans and by both alcohol and ketogenic diets in mice. Pharmacologic administration of FGF21 stimulates water drinking behavior in mice within 2 hr. Concordantly, mice lacking FGF21 fail to increase water intake in response to either alcohol or a ketogenic diet. The effect of FGF21 on drinking is mediated in part by SIM1-positive neurons of the hypothalamus and is inhibited by ß-adrenergic receptor antagonists. Given that FGF21 also is known to suppress alcohol intake in favor of pure water, this work identifies FGF21 as a fundamental neurotropic hormone that governs water balance in response to specific nutrient stresses that can cause dehydration.

Uniform gene expression in embryos is achieved by temporal averaging of transcription noise.

Transcription is often stochastic. This is seemingly incompatible with the importance of gene expression during development. Here we show that during zebrafish embryogenesis, transcription activation is stochastic due to (1) genes acquiring transcriptional competence at different times in different cells, (2) differences in cell cycle stage between cells, and (3) the stochastic nature of transcription. Initially, stochastic transcription causes large cell-to-cell differences in transcript levels. However, variability is reduced by lengthening cell cycles and the accumulation of transcription events in each cell. Temporal averaging might provide a general context in which to understand how embryos deal with stochastic transcription.

Sensitivity estimation for stochastic models of biochemical reaction networks in the presence of extrinsic variability.

Determining the sensitivity of certain system states or outputs to variations in parameters facilitates our understanding of the inner working of that system and is an essential design tool for the de novo construction of robust systems. In cell biology, the output of interest is often the response of a certain reaction network to some input (e.g., stressors or nutrients) and one aims to quantify the sensitivity of this response in the presence of parameter heterogeneity. We argue that for such applications, parametric sensitivities in their standard form do not paint a complete picture of a system's robustness since one assumes that all cells in the population have the same parameters and are perturbed in the same way. Here, we consider stochasticreaction networks in which the parameters are randomly distributed over the population and propose a new sensitivity index that captures the robustness of system outputs upon changes in the characteristics of the parameter distribution, rather than the parameters themselves. Subsequently, we make use of Girsanov's likelihood ratio method to construct a Monte Carlo estimator of this sensitivity index. However, it turns out that this estimator has an exceedingly large variance. To overcome this problem, we propose a novel estimation algorithm that makes use of a marginalization of the path distribution of stochasticreaction networks and leads to Rao-Blackwellized estimators with reduced variance.

Parameter inference for stochastic single-cell dynamics from lineage tree data.

BACKGROUND: With the advance of experimental techniques such as time-lapse fluorescence microscopy, the availability of single-cell trajectory data has vastly increased, and so has the demand for computational methods suitable for parameter inference with this type of data. Most of currently available methods treat single-cell trajectories independently, ignoring the mother-daughter relationships and the information provided by the population structure. However, this information is essential if a process of interest happens at cell division, or if it evolves slowly compared to the duration of the cell cycle. RESULTS: In this work, we propose a Bayesian framework for parameter inference on single-cell time-lapse data from lineage trees. Our method relies on a combination of Sequential Monte Carlo for approximating the parameter likelihood function and Markov Chain Monte Carlo for parameter exploration. We demonstrate our inference framework on two simple examples in which the lineage tree information is crucial: one in which the cell phenotype can only switch at cell division and another where the cell state fluctuates slowly over timescales that extend well beyond the cell-cycle duration. CONCLUSION: There exist several examples of biological processes, such as stem cell fate decisions or epigenetically controlled phase variation in bacteria, where the cell ancestry is expected to contain important information about the underlying system dynamics. Parameter inference methods that discard this information are expected to perform poorly for such type of processes. Our method provides a simple and computationally efficient way to take into account single-cell lineage tree data for the purpose of parameter inference and serves as a starting point for the development of more sophisticated and powerful approaches in the future.