Mesenchymal cell migration on one-dimensional micropatterns.

Quantitative studies of mesenchymal cell motion are important to elucidate cytoskeleton function and mechanisms of cell migration. To this end, confinement of cell motion to one dimension (1D) significantly simplifies the problem of cell shape in experimental and theoretical investigations. Here we review 1D migration assays employing micro-fabricated lanes and reflect on the advantages of such platforms. Data are analyzed using biophysical models of cell migration that reproduce the rich scenario of morphodynamic behavior found in 1D. We describe basic model assumptions and model behavior. It appears that mechanical models explain the occurrence of universal relations conserved across different cell lines such as the adhesion-velocity relation and the universal correlation between speed and persistence (UCSP). We highlight the unique opportunity of reproducible and standardized 1D assays to validate theory based on statistical measures from large data of trajectories and discuss the potential of experimental settings embedding controlled perturbations to probe response in migratory behavior.

An integrate-and-fire approach to Ca2+ signaling. Part II: Cumulative refractoriness.

Inositol 1,4,5-trisphosphate-induced Ca2+ signaling is a second messenger system used by almost all eukaryotic cells. The agonist concentration stimulating Ca2+ signals is encoded in the frequency of a Ca2+ concentration spike sequence. When a cell is stimulated, the interspike intervals (ISIs) often show a distinct transient during which they gradually increase, a system property we refer to as cumulative refractoriness. We extend a previously published stochastic model to include the Ca2+ concentration in the intracellular Ca2+ store as a slow adaptation variable. This model can reproduce both stationary and transient statistics of experimentally observed ISI sequences. We derive approximate expressions for the mean and coefficient of variation of the stationary ISIs. We also consider the response to the onset of a constant stimulus and estimate the length of the transient and the strength of the adaptation of the ISI. We show that the adaptation sets the coefficient of variation in agreement with current ideas derived from experiments. Moreover, we explain why, despite a pronounced transient behavior, ISI correlations can be weak, as often observed in experiments. Finally, we fit our model to reproduce the transient statistics of experimentally observed ISI sequences in stimulated HEK cells. The fitted model is able to qualitatively reproduce the relationship between the stationary interval correlations and the number of transient intervals, as well as the strength of the ISI adaptation. We also find positive correlations in the experimental sequence that cannot be explained by our model.

Modeling IP3-induced Ca2+ signaling based on its interspike interval statistics.

Inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ signaling is a second messenger system used by almost all eukaryotic cells. Recent research demonstrated randomness of Ca2+ signaling on all structural levels. We compile eight general properties of Ca2+ spiking common to all cell types investigated and suggest a theory of Ca2+ spiking starting from the random behavior of IP3 receptor channel clusters mediating the release of Ca2+ from the endoplasmic reticulum capturing all general properties and pathway-specific behavior. Spike generation begins after the absolute refractory period of the previous spike. According to its hierarchical spreading from initiating channel openings to cell level, we describe it as a first passage process from none to all clusters open while the cell recovers from the inhibition which terminated the previous spike. Our theory reproduces the exponential stimulation response relation of the average interspike interval Tav and its robustness properties, random spike timing with a linear moment relation between Tav and the interspike interval SD and its robustness properties, sensitive dependency of Tav on diffusion properties, and nonoscillatory local dynamics. We explain large cell variability of Tav observed in experiments by variability of channel cluster coupling by Ca2+-induced Ca2+ release, the number of clusters, and IP3 pathway component expression levels. We predict the relation between puff probability and agonist concentration and [IP3] and agonist concentration. Differences of spike behavior between cell types and stimulating agonists are explained by the different types of negative feedback terminating spikes. In summary, the hierarchical random character of spike generation explains all of the identified general properties.

On multistability and constitutive relations of cell motion on fibronectin lanes.

Cell motility on flat substrates exhibits coexisting steady and oscillatory morphodynamics, the biphasic adhesion-velocity relation, and the universal correlation between speed and persistence (UCSP) as simultaneous observations common to many cell types. Their universality and concurrency suggest a unifying mechanism causing all three of them. Stick-slip models for cells on one-dimensional lanes suggest multistability to arise from the nonlinear friction of retrograde flow. This study suggests a mechanical mechanism controlled by integrin signaling on the basis of a biophysical model and analysis of trajectories of MDA-MB-231 cells on fibronectin lanes, which additionally explains the constitutive relations. The experiments exhibit cells with steady or oscillatory morphodynamics and either spread or moving with spontaneous transitions between the dynamic regimes, spread and moving, and spontaneous direction reversals. Our biophysical model is based on the force balance at the protrusion edge, the noisy clutch of retrograde flow, and a response function of friction and membrane drag to integrin signaling. The theory reproduces the experimentally observed cell states, characteristics of oscillations, and state probabilities. Analysis of experiments with the biophysical model establishes a stick-slip oscillation mechanism, and explains multistability of cell states and the statistics of state transitions. It suggests protrusion competition to cause direction reversal events, the statistics of which explain the UCSP. The effect of integrin signaling on drag and friction explains the adhesion-velocity relation and cell behavior at fibronectin density steps. The dynamics of our mechanism are nonlinear flow mechanics driven by F-actin polymerization and shaped by the noisy clutch of retrograde flow friction, protrusion competition via membrane tension, and drag forces. Integrin signaling controls the parameters of the mechanical system.

An integrate-and-fire approach to Ca2+ signaling. Part I: Renewal model.

In computational neuroscience integrate-and-fire models capture the spike generation by a subthreshold dynamics supplemented by a simple fire-and-reset rule; they allow for a numerically efficient and analytically tractable description of stochastic single cell as well as network dynamics. Stochastic spiking is also a prominent feature of Ca2+ signaling which suggests to adopt the integrate-and-fire approach for this fundamental biophysical process. The model introduced here consists of two components describing 1) activity of clusters of inositol-trisphosphate receptor channels and 2) dynamics of the global Ca2+ concentrations in the cytosol. The cluster dynamics is given in terms of a cyclic Markov chain, capturing the puff, i.e., the punctuated release of Ca2+ from intracellular stores. The cytosolic Ca2+ concentration is described by an integrate-and-fire dynamics driven by the puff current. For the cyclic Markov chain we derive expressions for the statistics of the interpuff interval, the single-puff strength and the puff current assuming constant cytosolic Ca2+. The latter condition is often well approximated because cytosolic Ca2+ varies much slower than the cluster activity does. Furthermore, because the detailed two-component model is numerically expensive to simulate and difficult to treat analytically, we develop an analytical framework to approximate the driving puff current of the stochastic cytosolic Ca2+ dynamics by a temporally uncorrelated Gaussian noise. This approximation reduces our two-component system to an integrate-and-fire model with a nonlinear drift function and a multiplicative Gaussian white noise, a model that is known to generate a renewal spike train, i.e., a point process with statistically independent interspike intervals. The model allows for fast numerical simulations, permits to derive analytical expressions for the rate of Ca2+ spiking and the coefficient of variation of the interspike interval, and to approximate the interspike interval density and the spike train power spectrum. Comparison of these statistics to experimental data is discussed.

Disease- and sex-specific differences in patients with heart valve disease: a proteome study.

Pressure overload in patients with aortic valve stenosis and volume overload in mitral valve regurgitation trigger specific forms of cardiac remodeling; however, little is known about similarities and differences in myocardial proteome regulation. We performed proteome profiling of 75 human left ventricular myocardial biopsies (aortic stenosis = 41, mitral regurgitation = 17, and controls = 17) using high-resolution tandem mass spectrometry next to clinical and hemodynamic parameter acquisition. In patients of both disease groups, proteins related to ECM and cytoskeleton were more abundant, whereas those related to energy metabolism and proteostasis were less abundant compared with controls. In addition, disease group-specific and sex-specific differences have been observed. Male patients with aortic stenosis showed more proteins related to fibrosis and less to energy metabolism, whereas female patients showed strong reduction in proteostasis-related proteins. Clinical imaging was in line with proteomic findings, showing elevation of fibrosis in both patient groups and sex differences. Disease- and sex-specific proteomic profiles provide insight into cardiac remodeling in patients with heart valve disease and might help improve the understanding of molecular mechanisms and the development of individualized treatment strategies.

SLAM-Drop-seq reveals mRNA kinetic rates throughout the cell cycle.

RNA abundance is tightly regulated in eukaryotic cells by modulating the kinetic rates of RNA production, processing, and degradation. To date, little is known about time­dependent kinetic rates during dynamic processes. Here, we present SLAM­Drop­seq, a method that combines RNA metabolic labeling and alkylation of modified nucleotides in methanol­fixed cells with droplet­based sequencing to detect newly synthesized and preexisting mRNAs in single cells. As a first application, we sequenced 7280 HEK293 cells and calculated gene­specific kinetic rates during the cell cycle using the novel package Eskrate. Of the 377 robust­cycling genes that we identified, only a minor fraction is regulated solely by either dynamic transcription or degradation (6 and 4%, respectively). By contrast, the vast majority (89%) exhibit dynamically regulated transcription and degradation rates during the cell cycle. Our study thus shows that temporally regulated mRNA degradation is fundamental for the correct expression of a majority of cycling genes. SLAM­Drop­seq, combined with Eskrate, is a powerful approach to understanding the underlying mRNA kinetics of single­cell gene expression dynamics in continuous biological processes.

Receptor-associated independent cAMP nanodomains mediate spatiotemporal specificity of GPCR signaling.

G protein-coupled receptors (GPCRs) relay extracellular stimuli into specific cellular functions. Cells express many different GPCRs, but all these GPCRs signal to only a few second messengers such as cAMP. It is largely unknown how cells distinguish between signals triggered by different GPCRs to orchestrate their complex functions. Here, we demonstrate that individual GPCRs signal via receptor-associated independent cAMP nanodomains (RAINs) that constitute self-sufficient, independent cell signaling units. Low concentrations of glucagon-like peptide 1 (GLP-1) and isoproterenol exclusively generate highly localized cAMP pools around GLP-1- and ß2-adrenergic receptors, respectively, which are protected from cAMP originating from other receptors and cell compartments. Mapping local cAMP concentrations with engineered GPCR nanorulers reveals gradients over only tens of nanometers that define the size of individual RAINs. The coexistence of many such RAINs allows a single cell to operate thousands of independent cellular signals simultaneously, rather than function as a simple "on/off" switch.

On the relation between input and output distributions of scRNA-seq experiments.

MOTIVATION: Single-cell RNA sequencing determines RNA copy numbers per cell for a given gene. However, technical noise poses the question how observed distributions (output) are connected to their cellular distributions (input). RESULTS: We model a single-cell RNA sequencing setup consisting of PCR amplification and sequencing, and derive probability distribution functions for the output distribution given an input distribution. We provide copy number distributions arising from single transcripts during PCR amplification with exact expressions for mean and variance. We prove that the coefficient of variation of the output of sequencing is always larger than that of the input distribution. Experimental data reveals the variance and mean of the input distribution to obey characteristic relations, which we specifically determine for a HeLa dataset. We can calculate as many moments of the input distribution as are known of the output distribution (up to all). This, in principle, completely determines the input from the output distribution. AVAILABILITY AND IMPLEMENTATION: Source code freely available at https://github.com/danielschw188/InputOutputSCRNASeq. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Computational toolbox for ultrastructural quantitative analysis of filament networks in cryo-ET data.

A precise quantitative description of the ultrastructural characteristics underlying biological mechanisms is often key to their understanding. This is particularly true for dynamic extra- and intracellular filamentous assemblies, playing a role in cell motility, cell integrity, cytokinesis, tissue formation and maintenance. For example, genetic manipulation or modulation of actin regulatory proteins frequently manifests in changes of the morphology, dynamics, and ultrastructural architecture of actin filament-rich cell peripheral structures, such as lamellipodia or filopodia. However, the observed ultrastructural effects often remain subtle and require sufficiently large datasets for appropriate quantitative analysis. The acquisition of such large datasets has been enabled by recent advances in high-throughput cryo-electron tomography (cryo-ET) methods. This also necessitates the development of complementary approaches to maximize the extraction of relevant biological information. We have developed a computational toolbox for the semi-automatic quantification of segmented and vectorized filamentous networks from pre-processed cryo-electron tomograms, facilitating the analysis and cross-comparison of multiple experimental conditions. GUI-based components simplify the processing of data and allow users to obtain a large number of ultrastructural parameters describing filamentous assemblies. We demonstrate the feasibility of this workflow by analyzing cryo-ET data of untreated and chemically perturbed branched actin filament networks and that of parallel actin filament arrays. In principle, the computational toolbox presented here is applicable for data analysis comprising any type of filaments in regular (i.e. parallel) or random arrangement. We show that it can ease the identification of key differences between experimental groups and facilitate the in-depth analysis of ultrastructural data in a time-efficient manner.

Stochastic reaction-diffusion modeling of calcium dynamics in 3D dendritic spines of Purkinje cells.

Calcium (Ca2+) is a second messenger assumed to control changes in synaptic strength in the form of both long-term depression and long-term potentiation at Purkinje cell dendritic spine synapses via inositol trisphosphate (IP3)-induced Ca2+ release. These Ca2+ transients happen in response to stimuli from parallel fibers (PFs) from granule cells and climbing fibers (CFs) from the inferior olivary nucleus. These events occur at low numbers of free Ca2+, requiring stochastic single-particle methods when modeling them. We use the stochastic particle simulation program MCell to simulate Ca2+ transients within a three-dimensional Purkinje cell dendritic spine. The model spine includes the endoplasmic reticulum, several Ca2+ transporters, and endogenous buffer molecules. Our simulations successfully reproduce properties of Ca2+ transients in different dynamical situations. We test two different models of the IP3 receptor (IP3R). The model with nonlinear concentration response of binding of activating Ca2+ reproduces experimental results better than the model with linear response because of the filtering of noise. Our results also suggest that Ca2+-dependent inhibition of the IP3R needs to be slow to reproduce experimental results. Simulations suggest the experimentally observed optimal timing window of CF stimuli arises from the relative timing of CF influx of Ca2+ and IP3 production sensitizing IP3R for Ca2+-induced Ca2+ release. We also model ataxia, a loss of fine motor control assumed to be the result of malfunctioning information transmission at the granule to Purkinje cell synapse, resulting in a decrease or loss of Ca2+ transients. Finally, we propose possible ways of recovering Ca2+ transients under ataxia.

On the adhesion-velocity relation and length adaptation of motile cells on stepped fibronectin lanes.

The biphasic adhesion-velocity relation is a universal observation in mesenchymal cell motility. It has been explained by adhesion-promoted forces pushing the front and resisting motion at the rear. Yet, there is little quantitative understanding of how these forces control cell velocity. We study motion of MDA-MB-231 cells on microlanes with fields of alternating Fibronectin densities to address this topic and derive a mathematical model from the leading-edge force balance and the force-dependent polymerization rate. It reproduces quantitatively our measured adhesion-velocity relation and results with keratocytes, PtK1 cells, and CHO cells. Our results confirm that the force pushing the leading-edge membrane drives lamellipodial retrograde flow. Forces resisting motion originate along the whole cell length. All motion-related forces are controlled by adhesion and velocity, which allows motion, even with higher Fibronectin density at the rear than at the front. We find the pathway from Fibronectin density to adhesion structures to involve strong positive feedbacks. Suppressing myosin activity reduces the positive feedback. At transitions between different Fibronectin densities, steady motion is perturbed and leads to changes of cell length and front and rear velocity. Cells exhibit an intrinsic length set by adhesion strength, which, together with the length dynamics, suggests a spring-like front-rear interaction force. We provide a quantitative mechanistic picture of the adhesion-velocity relation and cell response to adhesion changes integrating force-dependent polymerization, retrograde flow, positive feedback from integrin to adhesion structures, and spring-like front-rear interaction.

The transcriptome dynamics of single cells during the cell cycle.

The cell cycle is among the most basic phenomena in biology. Despite advances in single-cell analysis, dynamics and topology of the cell cycle in high-dimensional gene expression space remain largely unknown. We developed a linear analysis of transcriptome data which reveals that cells move along a planar circular trajectory in transcriptome space during the cycle. Non-cycling gene expression adds a third dimension causing helical motion on a cylinder. We find in immortalized cell lines that cell cycle transcriptome dynamics occur largely independently from other cellular processes. We offer a simple method ("Revelio") to order unsynchronized cells in time. Precise removal of cell cycle effects from the data becomes a straightforward operation. The shape of the trajectory implies that each gene is upregulated only once during the cycle, and only two dynamic components represented by groups of genes drive transcriptome dynamics. It indicates that the cell cycle has evolved to minimize changes of transcriptional activity and the related regulatory effort. This design principle of the cell cycle may be of relevance to many other cellular differentiation processes.

Optical Mapping of cAMP Signaling at the Nanometer Scale.

Cells relay a plethora of extracellular signals to specific cellular responses by using only a few second messengers, such as cAMP. To explain signaling specificity, cAMP-degrading phosphodiesterases (PDEs) have been suggested to confine cAMP to distinct cellular compartments. However, measured rates of fast cAMP diffusion and slow PDE activity render cAMP compartmentalization essentially impossible. Using fluorescence spectroscopy, we show that, contrary to earlier data, cAMP at physiological concentrations is predominantly bound to cAMP binding sites and, thus, immobile. Binding and unbinding results in largely reduced cAMP dynamics, which we term "buffered diffusion." With a large fraction of cAMP being buffered, PDEs can create nanometer-size domains of low cAMP concentrations. Using FRET-cAMP nanorulers, we directly map cAMP gradients at the nanoscale around PDE molecules and the areas of resulting downstream activation of cAMP-dependent protein kinase (PKA). Our study reveals that spatiotemporal cAMP signaling is under precise control of nanometer-size domains shaped by PDEs that gate activation of downstream effectors.

Phase Separation of a PKA Regulatory Subunit Controls cAMP Compartmentation and Oncogenic Signaling.

The fidelity of intracellular signaling hinges on the organization of dynamic activity architectures. Spatial compartmentation was first proposed over 30 years ago to explain how diverse G protein-coupled receptors achieve specificity despite converging on a ubiquitous messenger, cyclic adenosine monophosphate (cAMP). However, the mechanisms responsible for spatially constraining this diffusible messenger remain elusive. Here, we reveal that the type I regulatory subunit of cAMP-dependent protein kinase (PKA), RIα, undergoes liquid-liquid phase separation (LLPS) as a function of cAMP signaling to form biomolecular condensates enriched in cAMP and PKA activity, critical for effective cAMP compartmentation. We further show that a PKA fusion oncoprotein associated with an atypical liver cancer potently blocks RIα LLPS and induces aberrant cAMP signaling. Loss of RIα LLPS in normal cells increases cell proliferation and induces cell transformation. Our work reveals LLPS as a principal organizer of signaling compartments and highlights the pathological consequences of dysregulating this activity architecture.

Lamellipodin tunes cell migration by stabilizing protrusions and promoting adhesion formation.

Efficient migration on adhesive surfaces involves the protrusion of lamellipodial actin networks and their subsequent stabilization by nascent adhesions. The actin-binding protein lamellipodin (Lpd) is thought to play a critical role in lamellipodium protrusion, by delivering Ena/VASP proteins onto the growing plus ends of actin filaments and by interacting with the WAVE regulatory complex, an activator of the Arp2/3 complex, at the leading edge. Using B16-F1 melanoma cell lines, we demonstrate that genetic ablation of Lpd compromises protrusion efficiency and coincident cell migration without altering essential parameters of lamellipodia, including their maximal rate of forward advancement and actin polymerization. We also confirmed lamellipodia and migration phenotypes with CRISPR/Cas9-mediated Lpd knockout Rat2 fibroblasts, excluding cell type-specific effects. Moreover, computer-aided analysis of cell-edge morphodynamics on B16-F1 cell lamellipodia revealed that loss of Lpd correlates with reduced temporal protrusion maintenance as a prerequisite of nascent adhesion formation. We conclude that Lpd optimizes protrusion and nascent adhesion formation by counteracting frequent, chaotic retraction and membrane ruffling.This article has an associated First Person interview with the first author of the paper.

A Statistical View on Calcium Oscillations.

Transient rises and falls of the intracellular calcium concentration have been observed in numerous cell types and under a plethora of conditions. There is now a growing body of evidence that these whole-cell calcium oscillations are stochastic, which poses a significant challenge for modelling. In this review, we take a closer look at recently developed statistical approaches to calcium oscillations. These models describe the timing of whole-cell calcium spikes, yet their parametrisations reflect subcellular processes. We show how non-stationary calcium spike sequences, which e.g. occur during slow depletion of intracellular calcium stores or in the presence of time-dependent stimulation, can be analysed with the help of so-called intensity functions. By utilising Bayesian concepts, we demonstrate how values of key parameters of the statistical model can be inferred from single cell calcium spike sequences and illustrate what information whole-cell statistical models can provide about the subcellular mechanistic processes that drive calcium oscillations. In particular, we find that the interspike interval distribution of HEK293 cells under constant stimulation is captured by a Gamma distribution.

Long-term effects of Na+ /Ca2+ exchanger inhibition with ORM-11035 improves cardiac function and remodelling without lowering blood pressure in a model of heart failure with preserved ejection fraction.

AIMS: Heart failure with preserved ejection fraction (HFpEF) is increasingly common but there is currently no established pharmacological therapy. We hypothesized that ORM-11035, a novel specific Na+ /Ca2+ exchanger (NCX) inhibitor, improves cardiac function and remodelling independent of effects on arterial blood pressure in a model of cardiorenal HFpEF. METHODS AND RESULTS: Rats were subjected to subtotal nephrectomy (NXT) or sham operation. Eight weeks after intervention, treatment for 16 weeks with ORM-11035 (1 mg/kg body weight) or vehicle was initiated. At 24 weeks, blood pressure measurements, echocardiography and pressure-volume loops were performed. Contractile function, Ca2+ transients and NCX-mediated Ca2+ extrusion were measured in isolated ventricular cardiomyocytes. NXT rats (untreated) showed a HFpEF phenotype with left ventricular (LV) hypertrophy, LV end-diastolic pressure (LVEDP) elevation, increased brain natriuretic peptide (BNP) levels, preserved ejection fraction and pulmonary congestion. In cardiomyocytes from untreated NXT rats, early relaxation was prolonged and NCX-mediated Ca2+ extrusion was decreased. Chronic treatment with ORM-11035 significantly reduced LV hypertrophy and cardiac remodelling without lowering systolic blood pressure. LVEDP [14 ± 3 vs. 9 ± 2 mmHg; NXT (n = 12) vs. NXT + ORM (n = 12); P = 0.0002] and BNP levels [71 ± 12 vs. 49 ± 11 pg/mL; NXT (n = 12) vs. NXT + ORM (n = 12); P < 0.0001] were reduced after ORM treatment. LV cardiomyocytes from ORM-treated rats showed improved active relaxation and diastolic cytosolic Ca2+ decay as well as restored NCX-mediated Ca2+ removal, indicating NCX modulation with ORM-11035 as a promising target in the treatment of HFpEF. CONCLUSION: Chronic inhibition of NCX with ORM-11035 significantly attenuated cardiac remodelling and diastolic dysfunction without lowering systemic blood pressure in this model of HFpEF. Therefore, long-term treatment with selective NCX inhibitors such as ORM-11035 should be evaluated further in the treatment of heart failure.