Quantifying single-cell diacylglycerol signaling kinetics after uncaging

Abstract

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.

Significance

Cells constantly process information. They use many types of molecules in their information processing (signaling) networks, including fats or lipids, which are then called lipid messengers. Studying these lipids in living cells is challenging, as they cannot readily be observed. We have used photochemical tools to analyze their dynamic behavior and their interactions with cellular proteins in a quantitative fashion in single living cells and find that subtle chemical differences between individual fat species can have large effects on cellular information processing networks.

Introduction

Biological signaling networks process information through biochemical reactions. However, individual cells differ in shape, size, and molecular composition and are also subject to different sources of noise and variability (1). An accurate description of cell signaling thus requires methodologies to quantitatively analyze the kinetics of the underlying biochemical reactions in single cells (2,3,4). To investigate fast biological processes in the second-to-minute timescale, light-induced perturbations such as optogenetics, photoswitching, or uncaging approaches are commonly employed due to their high spatial and temporal precision (5,6). While initially pioneered for soluble metabolites and cytoplasmic proteins, optical perturbations have been increasingly used to investigate dynamic processes in lipid and membrane biology over the last decade. Photoswitching and uncaging experiments have been instrumental for analyzing cellular lipid signaling events, e.g., revealing important details about the PIP₂-synaptotagmin interaction during synaptic vesicle fusion (7) or the role of arachidonic acid signaling in insulin secretion (8). The cellular functions of the second messenger diacylglycerol (DAG) represent a particularly intriguing case. Various DAG species that differ in acyl chain length, unsaturation, and positioning at the glycerol backbone are generated intracellularly through the action of phospholipases C and D (PLC and PLD) after receptor activation. These DAG species recruit cytosolic effector proteins such as protein kinase C isoforms (9) or MUNC13 (10) proteins to the plasma membrane through C1 domain-DAG interactions, ultimately triggering downstream signaling responses. Early reports suggested that the structural diversity is functionally relevant for the signaling outcome (11,12,13). We recently provided the mechanistic underpinning for this notion using a combination of plasma-membrane-specific DAG uncaging and mathematical modeling of C1 domain recruitment dynamics to the plasma membrane (14). In these experiments, we equipped native DAG species with a photoremovable group that blocked their biological functions and prelocalized the resulting caged DAGs to the outer leaflet of the plasma membrane. Light-induced cleavage of the photoremovable group induces a well-defined concentration increase of a specific DAG species at the plasma membrane. We demonstrated that this approach can be used to extract quantitative lipid-protein affinities and rates of lipid trans-bilayer movement across the plasma membrane from population-average time trace data. This approach represents a robust way of identifying model parameters in lipid signaling events, but it involves laborious experimental workflows including the quantification of photoreaction yields, which relies on the precise chemical structure of the utilized probes. The strategy is currently limited to lipid uncaging experiments and is not readily transferable to other types of photoactivation experiments.

We thus asked whether we could use this well-characterized system to develop a strategy to fully parametrize quantitative kinetic models that would minimize effort on the experimental side (in particular, with regard to experimentally determining live-cell photoreaction yields) while also being, in principle, applicable for other types of photostimulation experiments. We decided to exploit the full information content of single-cell trajectories to infer lipid-protein affinities and kinetic parameters. The key challenge for quantifying photoinduced biochemical reactions in single cells is the fact that photoreaction yields are influenced by cell architecture, cell-cycle stages, and other factors that contribute to cellular heterogeneity. While average photoreaction yields for lipid uncaging at the plasma membrane can be determined in principle, it is currently not possible to simultaneously measure signaling trajectories and photoreaction yield in the same cell because the utilized assays require independent experimental approaches. One way to address this problem is to include the number of photoreleased molecules for each cell as an unknown model parameter and infer it together with all other parameters. How well this approach works in practice, however, depends on whether the additional degree of freedom will affect parameter identifiability. This can be systematically determined using identifiability analyses such as the profile likelihood method. Based on the profile likelihood analysis, model parameters can then be classified into three categories: 1) identifiable parameters that can be uniquely determined from a given set of measurements, 2) practically nonidentifiable parameters due to insufficient data amount or quality, and 3) structurally nonidentifiable parameters resulting from the mathematical structure of the underlying model (15). Note that the last type of nonidentifiability, typically resulting from an overparameterization of the model, cannot be resolved by collecting more or more accurate data.

Using simulated single-cell time-lapse data, we first determined the DAG signaling model structure and data characteristics that are needed to satisfy structural and practical identifiability. We found that all parameters of the models we previously proposed for DAG signaling dynamics were structurally identifiable despite treating single-cell lipid uncaging yields as unknown parameters. However, we found that model parameters easily become practically nonidentifiable with a decreasing signal/noise ratio. Practical identifiability can be partially recovered by including a greater number of single-cell traces in the analysis, so we used this approach to determine rate parameters and photoreaction yields from experimental single-cell traces of six structurally different DAG species. Two of the considered DAG species (stearoyl-arachidonylglycerol [SAG] and stearoyl-oleoylglycerol [SOG]), were also featured in our previous work (14) and thus allowed a direct comparison of the respective methodologies utilized for data analysis. Our results suggest that increasing acyl chain unsaturation leads to higher rates of lipid trans-bilayer movement and turnover and that lipid-protein affinities are affected by both acyl chain length and unsaturation degree. Taken together, our study demonstrates the feasibility of inferring the photoreaction yield of uncaging experiments together with model parameters while accounting for cell-to-cell heterogeneity. Our analytical approach should be generally applicable to other optical perturbation experiments in living cells where photoreaction yields are experimentally difficult to obtain—making quantitative analysis of dynamic processes in cell biology more readily accessible.

Materials and methods

Materials and methods and additional results are described in the supporting material. Data and code used for analysis are available in the Edmond repository https://doi.org/10.17617/3.3JM5WX.

Results

Model of DAG-driven protein recruitment to the plasma membrane

DAG signaling typically involves the production of the signaling DAG species at the plasma membrane after receptor activation. Subsequently, the generated DAGs either activate integral membrane proteins (e.g. transient-receptor potential channels) by allosteric modulation or recruit C1-domain-containing cytoplasmic effector proteins (e.g., novel protein kinase C isoforms). We consider the latter process here. Receptor-induced production of DAGs can be mimicked by photorelease of native DAGs at the plasma membrane, which allows us to study the effects of individual, structurally unique DAG species. Experimentally, the signaling event can then be monitored in time by observing the intracellular localization of DAG reporter proteins such as the C1-EGFP-nuclear export sequence (NES) construct (14). To analyze such data, we consider a minimal model of DAG signaling as shown in Fig. 1. Cells are initially loaded with a caged DAG (cgDAG) in the outer leaflet of the cell membrane. The caging group prevents the DAG from flipping into the inner leaflet of the membrane. Upon photoactivation by exposure to 405 nm laser light, the caging group is cleaved, and the DAG is liberated. Free DAG can move between the inner and outer leaflets of the membrane. Once DAG is in the inner leaflet, it can be metabolized by the cell or can recruit the C1-EGFP-NES reporter from the cytosol. This process can be mathematically described by

$$\frac{\mathrm{d}}{\text{dt}}\left[{\text{DAG}}_{\text{ext}}\right]=-{\mathrm{k}}_{\text{in}}\left[{\text{DAG}}_{\text{ext}}\right]+{\mathrm{k}}_{\text{out}}{\mathrm{K}}_{\mathrm{d}}\left(\frac{{\left[\mathrm{C}1\right]}_0-\left[\mathrm{C}1\right]}{\left[\mathrm{C}1\right]}\right),\text{and}$$ (1)

$$\frac{\mathrm{d}}{\text{dt}}\left[\mathrm{C}1\right]=\frac{-{\mathrm{k}}_{\text{in}}\left[{\text{DAG}}_{\text{ext}}\right]+\left({\mathrm{k}}_{\text{out}}+{\mathrm{k}}_{\text{met}}\right){\mathrm{K}}_{\mathrm{d}}\left(\frac{{\left[\mathrm{C}1\right]}_0-\left[\mathrm{C}1\right]}{\left[\mathrm{C}1\right]}\right)}{\left(\frac{{\mathrm{K}}_{\mathrm{d}}{\left[\mathrm{C}1\right]}_0}{{\left[\mathrm{C}1\right]}^2}+1\right)}\text{,}$$ (2)

where DAG_ext is the uncaged DAG in the outer leaflet, C1 is the C1-EGFP-NES reporter in the cytosol, k_in and k_out are the rate constants of DAG flip flop between the inner and outer leaflets, k_met is the rate constant of DAG turnover in the inner leaflet, and K_d is the equilibrium constant of DAG with C1 (see Section S1 of the supporting material for model derivation).

Figure 1.

Photoactivation and DAG signaling dynamics. (A) Photoactivation or uncaging of caged diacylglycerols (cgDAG) in the outer leaflet of the cell membrane initiates DAG signaling dynamics. Activated DAG can flip flop between the outer and inner leaflets of the membrane. In the inner leaflet, DAG can either be metabolized by the cell or recruit the C1-EGFP-NES effector protein to form the DAG-C1 lipid-protein complex. (B) In an uncaging experiment, cells expressing C1-EGFP-NES are preloaded with cgDAG on the outer leaflet of the cell membrane. C1-EGFP-NES concentrations in the cytosol are monitored over time by confocal microscopy during the uncaging experiment. As cgDAG is uncaged, DAG molecules flip into the inner leaflet and recruit C1-EGFP-NES from the cytosol. This results in a drop of C1-EGFP-NES in the cytosol. As the cell metabolizes DAG molecules, C1-EGFP-NES returns into the cytosol. To see this figure in color, go online.

In our previous work, we observed that, for some DAG species, the inside-out trans-bilayer movement (k_out) is virtually zero (e.g., for SOG) and can be omitted from the model (14). In the model version without k_out, terms with k_out in Eqs. 1 and 2 disappear. Brackets denote the effective concentration of the species over the cell volume. Subscripts of zero indicate initial conditions at t = 0 s. After uncaging DAGs by 405 nm light, cytosolic C1-EGFP-NES levels drop as DAG flips into the inner leaflet and recruits C1-EGFP-NES to the membrane. The cytosolic C1-EGFP-NES level then slowly recovers as DAGs are metabolized by the cell and C1-EGFP-NES is returned to the cytosol (Fig. 1 B). The cytosolic levels of the C1-EGFP-NES reporter in single cells can be monitored over time using confocal time-lapse microscopy. In contrast, DAG levels and C1-EGFP-NES densities on the inner leaflet cannot be quantified readily in a time-dependent fashion. In our previous study, identifying the model parameters k_in, k_out, k_met, and K_d in Eqs. 1 and 2 (14) required measuring both initial DAG concentrations and C1-EGFP-NES levels as population-average time traces. This requires the ability to measure photoreaction yields from optical perturbations, which is currently impossible in single cells. We therefore assessed whether all model parameters can still be identified if only a single photostimulation magnitude is used and photoreaction yields in individual cells are not known. Specifically, we assume the model parameters k_in, k_out, k_met, and K_d to be identical in all cells (fixed parameters), whereas the initial DAG and C1-EGFP-NES concentrations are allowed to vary across the population (random parameters). We hypothesized that the additional information content of single-cell traces may be sufficient to carry out such an analysis. The choice of fixed and random parameters is based on the notion that the values of four rate parameters are all primarily dependent on tightly regulated cellular processes, specifically plasma membrane lipid composition for k_in and k_out, signaling lipid metabolism and transport for k_met, and effector protein recruitment for K_d, and thus are likely to be less variable. Initial DAG and C1-EGFP-NES concentrations are much more dependent on external factors such as DAG and loading and photoreaction efficiency and transfection efficiency, respectively. We note that all parameters are likely to be heterogeneous to some extent, but allowing more than one to vary freely renders model parameters nonidentifiable without further experimental constraints.

In silico experiments show that the minimal model of DAG-driven protein recruitment can be fully parametrized

We decided to use simulated data and profile likelihood analysis to determine whether the model parameters can be identified in principle from noisy data. Parameters were chosen semirandomly, and initially, data from a single cell without measurement noise at different levels of uncaged DAG were used to determine the parameter identifiability based on profile likelihood analysis (15,16). A profile likelihood shows the maximal likelihood (or minimized negative log likelihood) of a model for a given observed dataset while sweeping one single parameter across different values. If a parameter is identifiable, its profile likelihood should exhibit an optimum in the considered parameter space. This is used to determine identifiability and likelihood-based confidence intervals of a parameter (see Section S4 of the supporting material). In the model versions with and without k_out, all model parameters were found to be identifiable using a single trace without measurement noise (Figs. 2, B and D, and S1, B and D). Adding increasing levels of Gaussian measurement noise resulted in impaired identifiability indicated by the gradual flattening of the profile likelihoods (Figs. 2, C and E, and S1, C and E). The effect of increasing measurement noise was much stronger for the more complex model with inside-out trans-bilayer movement, as k_out, k_met, and K_d were already weakly identifiable with [C1] measurement noise of 0.001 μM (standard deviation), which is much lower than typical experimental measurement noise levels of around 0.1 μM. We then tested whether practical nonidentifiability stemming from measurement noise could be remedied by simultaneously fitting 10–200 single-cell traces with 0.1 μM measurement noise. When using multiple cell traces, we consider all rate parameters to be fixed over the population of cells, while each individual cell can have different initial values of [DAG] and [C1]. In the model without k_out, all parameter nonidentifiabilities were recovered at 50–200 traces (Figs. 2 F, S2, and 3; Table S1), while k_out, k_met, and K_d remained nonidentifiable for the model with k_out with 100 traces (Fig. S4). Overall, using simulated data, we found that our models of DAG lipid signaling dynamics are structurally identifiable; in fact, a single-cell trace with no measurement noise is sufficient to identify all model parameters and the initial DAG concentration. However, measurement noise and additional model parameters (k_out) can significantly affect practical identifiability. Analyzing multiple cell traces can help alleviate this problem to some extent, but improvements become quickly marginal as the number of cells increases. We thus decided to limit our analysis of experimental data to the simplified model.

Figure 2.

Approach and testing of parameter identifiability in a model of signaling lipid dynamics using simulated data. (A) Schematic of a model for signaling lipid dynamics. DAG at the outer leaflet of the cell membrane (DAG_ext) can flip into the inner leaflet (DAG_int), where it can either be metabolized or recruit C1-EGFP-NES proteins in the cytosol to for the membrane-associated complex DAG-C1. Rate parameters (k_in, k_met, K_d) of the model are shown in red. Simulated single-cell traces of C1-EGFP-NES at (B) different uncaged DAG concentrations (0.1, 0.25, 0.5, 1.0, and 2.0 μM) and no measurement noise and (C) different levels of measurement noise (0.001, 0.01, 0.05, 0.1, and 0.15 μM) and fixed uncaged DAG at 1.5 μM. Fits of each individual cell are shown in black dashed lines. Red vertical dotted line indicates the time of ultraviolet exposure that results in DAG uncaging. Profile likelihoods of the model parameters from each individual cell at different uncaged DAG concentrations and levels of measurement noise are shown in (D) and (E), respectively. (F) Profile likelihoods of the model parameters using data from traces of 100 cells with a fixed measurement noise of 0.1 μM. Profile likelihoods of uncaged DAG are shown for five representative cells only. For all profile likelihood plots, gray horizontal dashed lines indicate the 95% likelihood-based confidence interval threshold, blue vertical dotted lines indicate the true value of the parameter, and red circles indicate the maximum likelihood estimation of the parameter. True parameter values for the model are k_in = 0.098 s⁻¹, k_met = 0.01823 s⁻¹, and K_d = 0.866 μM. The parameter SD is an additional fitting parameter that represents the standard deviation of the measurement noise. To see this figure in color, go online.

Figure 3.

Chemistry of DAGs. (A) Chemical structures of the different DAGs used in this study sorted by increasing saturation degree (top to bottom). 1,3-Dioleoylglycerol does not recruit the C1-containing effector protein and is used as a negative control. (B) Confocal fluorescence microscopy of HeLa Kyoto cells with cgDAGs localizing in the plasma membrane. To see this figure in color, go online.

Measurement of DAG-driven protein recruitment in uncaging experiments

Having established that model parameters can be identified in principle without knowing the photoreaction yield, we next tested whether this holds true for experimental time trace data. In order to sample signaling dynamics across the chemical diversity of cellular DAG species, we expanded the repertoire of cgDAGs by synthesizing various new probes in addition to the previously reported species (14) (Fig. 3 A). DAG structures were chosen to reflect the physiologically available chemical space featuring fatty acid chain lengths between 14 and 20 carbon atoms containing between 0 and 8 double bonds per DAG. Among the generated probes, dimyristoylglycerol, which contains two saturated (14:0) chains, is the DAG with the shortest acyl chains commonly found in mammalian cells. Diarachidonylglycerol (DArG) contains two (20:4) chains and represents a species with long side chains and a high unsaturation degree. SOG, the most common DAG in mammalian cells, bears an oleoyl (18:1) residue at the Sn2 position and a stearoyl (18:0) residue at the Sn1 position. Oleoyl-stearoylglycerol (OSG), featuring the same residues with switched attachment sites, was included to provide insight into the influence of fatty acid positioning. SAG, which is the major product of PLC-mediated PI(4,5)P₂ cleavage and widely considered to be the archetypical signaling DAG, bears an arachidonyl (20:4) residue at the Sn2 position and a stearoyl (18:0) residue at the Sn1 position. Finally, the biologically inactive regioisomer 1,3-dioleoylglycerol features two oleoyl (18:1) chains at the Sn1 and Sn3 positions and was used as a negative control in this study. cgDAGs were synthesized according to previously published procedures (14). All new compounds were characterized by NMR and high-resolution mass spectrometry, and coumarin-containing compounds were photochemically characterized (see Section S9 of the supporting material for details on the synthesis of cgDAGs). Quantification of cgDAG loading was carried out as described before (14). Briefly, cgDAGs were loaded into the plasma membrane by exposing cells to a brief pulse (4 min) of the respective probe in imaging buffer. The cellular localization was analyzed for all compounds by monitoring the intrinsic fluorescence of the coumarin group by confocal fluorescence microscopy. All compounds were found to localize to the plasma membrane (Fig. 3 B). Loading concentrations were adjusted to achieve comparable incorporation levels for all cgDAGs (Fig. S19).

During live-cell uncaging experiments, cells transiently expressing the C1-EGFP-NES sensor were loaded with the respective cgDAG. Uncaging was carried out by scanning the entire field of view using a 405 nm laser with identical settings between experiments over a period of approximately 5 s after acquiring a short baseline of five frames. We monitored the concentration of C1-EGFP-NES by comparing the time-dependent fluorescence intensity with a calibration curve obtained by measuring the fluorescence intensity of purified protein samples of defined concentration (see Section S7 of the supporting material for fluorescence calibration details). Single-cell time traces were obtained by semiautomated image analysis (Fig. 4, A and C). Briefly, cells were automatically segmented and cytosolic regions determined by eroding the detected cell shapes. The data were manually curated by removing traces from apoptotic cells and cells that moved too much during the acquisition (see Sections S7 and S8 of the supporting material for details on uncaging experiments and image analysis). Quantitative single-cell time traces were obtained by converting fluorescence intensities into absolute concentrations with the calibration curve (Fig. 4, B–C). Using this method, we acquired quantified single-cell traces (80–280 cells for each DAG species) of cytosolic C1-EGFP-NES protein recruitment dynamics to the plasma membrane for the different DAG species. We also measured average photoreaction yields (Section S7 of the supporting material), which are required for performing a population-level analysis using our previously reported methodology (14), and compared these results to our new single-cell approach (Table S5).

Figure 4.

Timelapse microscopy and image analysis of DAG uncaging experiments. (A) Representative time-lapse images of two cells during a DAG uncaging experiment. From the raw images, the segmented cytosolic regions are used to obtain single cell fluorescence values in the cytosol that are calibrated to protein concentration values. (B) Extracted data of C1-EGFP-NES concentration versus time of the two representative cells in the DAG uncaging experiment. (C) Calibration curve of concentration (μM) versus fluorescence signal (relative fluorescence units) of C1-EGFP-NES in solution using the same confocal microscopy imaging settings. Gray dots are raw data points, and green dots with error bars are mean and standard deviations. Red dashed line is the linear fit of the calibration curve (y = 273.6x + 4.9). To see this figure in color, go online.

Inference of rate parameters and photoreaction yields from single-cell time trace data

We used the obtained single-cell traces from uncaging experiments of each DAG species to parameterize the model of lipid signaling dynamics in Eqs. 1 and 2. We decided to use the simplified model featuring solely the inward trans-bilayer movement of the DAG (without k_out), as most parameters of the model with k_out remained practically nonidentifiable even when using data from 100 cell traces in our analysis with simulated data (Fig. S4). Utilizing the model without k_out is justifiable for many DAG species. For example, our previous work showed small differences in Akaike’s information criterion and differences less than 0.5% in residual sum of squares between both models for SAG and SOG. In addition, SOG had negligible k_out rates in the more complex model (14). For the sake of simplicity, we therefore decided to use the simpler model where k_out is considered to be 0. We remark, however, that inside-out trans-bilayer movement may play a significant role for certain DAG species and/or membrane compositions, in which case the more complex model would have to be considered. From results of the simulated dataset using the model without k_out, we expected that the available number of single-cell traces would be sufficient to avoid practical nonidentifiability. Representative inference results for SAG are shown in Fig. 5, A–C (see Section S6 of the supporting material for the remaining DAG species). For each DAG species, the model could fit all single-cell traces from the heterogeneous population despite allowing only two parameters, the initial DAG concentration and the C1 concentration per cell, to vary across the population. Initial DAG concentrations were bounded between 0 and 10 μM during parameter estimation. This boundary was based on a number of practical considerations: If we assume an average cell volume of 3000 μm³ (14), an estimated outer leaflet cell membrane surface area of 5000 μm² (see Section S8 of the supporting material), a phospholipid area on the cell membrane of 0.65 nm² (17), cgDAG loading at 0.2% of the total lipid content of the outer leaflet cell membrane, and not more than 50% cgDAGs uncaging with our methodology (14), this corresponds to approximately 4.26 μM uncaged DAG per cell, which is well below the set upper bound of 10 μM. The mean values of inferred initial DAG concentrations were all within 1–4 μM and comparable to our measured average uncaged DAG concentrations (Figs. 5 B and S12; Table S5), which indicates that our fitting results are within reasonable and relevant ranges. Rate parameters and their respective 95% likelihood-based confidence intervals of each DAG are shown in Fig. 5 D for comparison. Most parameters are identifiable, except for k_in for DArG. We observed a trend of higher k_in rates with increasing acyl chain unsaturation. In the case of the highly unsaturated DArG, where k_in is nonidentifiable, the profile likelihood still indicates a lower limit of k_in that is larger than the upper confidence bounds of all other species. The inferred K_d values exhibited a similar behavior, indicating that C1 effector protein affinities to DAGs are species specific. For example, different engineered isoforms of the C1 domain are known to have different conformational dynamics of the DAG binding site, which will affect DAG affinity and specificity (18,19).

Figure 5.

Fitting and parameter inference on single-cell experimental data. (A) Single-cell traces of C1-EGFP-NES dynamics (gray lines) after uncaging of SAG. Ten representative cell traces (green lines) and their respective fits (dashed black lines) are shown. Red vertical dotted line indicates the time of ultraviolet exposure that results in SAG uncaging. (B) Correlation between inferred uncaged SAG and measured C1-EGFP-NES recruitment in the cell population. Each gray dot refers to a single cell. Black dots with error bars show five representative cells and their 95% likelihood-based confidence intervals. Vertical solid and dashed lines indicate the experimentally measured mean and standard deviation of uncaged SAG. Marginal histograms of uncaged SAG and C1-EGFP-NES recruitment are shown on each axis. (C) Profile likelihoods of the model parameters. Gray horizontal dashed lines indicate the 95% likelihood-based confidence interval threshold, and red circles indicate the fit maximum likelihood estimation of the parameter. Profile likelihoods of uncaged SAG are shown for the same five representative cells as in (B). (D) Inferred model parameters and 95% likelihood-based confidence intervals of the different DAG lipid species. To see this figure in color, go online.

To challenge our choice of initial C1 and DAG concentrations as variable parameters, we first compared the coefficient of variation of initial uncaged DAG for experimental measurements (0.413, calculated from the known variabilities of surface area/volume ratio, DAG loading, and uncaging efficiency) and the observed coefficient of variation (0.66) from the inferred results (see Section S8 of the supporting material). This suggests that the initial DAG concentration is likely the main, but not the only, source of variability in the single-cell traces. In addition, we tested other model variants where each of the otherwise fixed parameters are allowed to vary instead of the initial uncaged DAG. We found that the models using DAG, k_met, or K_d as the variable parameter all fit the data well but that the latter two cases return biologically improbable results (see Tables S6 and S7; Figs. S19–S22). Specifically, unphysiologically high values for k_met (up to 130 1/s) and K_d (up to 130 μM) were obtained for all lipids, which would indicate complete turnover of signaling DAGs on the inner leaflet in fractions of a second or very weak interactions between signaling lipid and effector protein. Choosing k_in as a variable parameter also led to significantly worse fitting accuracy compared to the other variable parameters. Taken together, these observations suggest that the main cause of cell-to-cell variability of the observed protein recruitment trajectories is indeed introduced by initial DAG levels.

Assessment of methodological limitations and comparison with previous work

We further compared the inferred parameters with the results from our previous study, where we analyzed SOG and SAG using population-averaged time traces. For SAG, we found all parameters to be in relatively good agreement with our previous study, and the obtained differences can be explained by differences in the experimental design and statistical analysis. For SOG, the rate constants k_in and k_met were in good agreement with previous values, while notable differences were observed for the inferred K_d value (4.67 instead of 0.017 μM). We believe that this discrepancy mainly originates from additional nonlinearities in SOG-driven protein recruitment, which are not captured by our simple model. As an example, our model considers protein binding affinities to be constant over the entire concentration range, which neglects, e.g., coincidence detection of multiple lipids by a single protein or nano-domain formation due to changes in lipid composition. In line with this, we have previously observed in DAG titration experiments that SOG-driven protein recruitment saturated even before all cytosolic protein was bound at the membrane. This indicated that only a certain fraction of the theoretically possible lipid-protein complexes could be formed. In our previous work, we accounted for this phenomenologically by introducing a nonlinear correction for available average C1-EGFP-NES concentration into the model, which was necessary to explain the data. Using our single-cell approach, a similar correction is potentially problematic since individual traces show substantial heterogeneity in terms of initial protein concentration and recruitment. However, since initial DAG concentration is a free parameter in the single-cell model, these nonlinear effects are still captured. Specifically, it can compensate for saturation behavior in protein recruitment by lowering the amount of liberated DAG. For species where such nonlinear effects are significant, the inferred initial DAG concentration has to be considered as an effective quantity capturing the fraction of liberated DAG, which is available for the formation of lipid-protein complexes. The distribution of inferred DAG values for SOG was indeed shifted toward lower values when compared to the other DAGs (Fig. S12), and the inferred average liberated DAG was lower than experimental measurements (Table S5). Intriguingly, the same trend was observed for the highly unsaturated DArG but not for the regioisomer OSG. This suggests that species-specific effects may play an important role in DAG signaling.

Discussion

In this study, we quantified kinetic parameters and lipid-protein affinities describing DAG signaling events from single-cell time traces. We triggered perturbations of cellular DAG levels by DAG uncaging at the plasma membrane and monitored the formation of lipid-protein complexes by observing the recruitment of a C1-EGFP-NES reporter protein to the plasma membrane. We used a series of known and newly generated cgDAG probes in live-cell photoactivation experiments to characterize the structure-activity relationships in DAG signaling processes, with a particular focus on the influence of side-chain unsaturation degree. We found that higher unsaturation degree and acyl chain length can result in faster outside-in rates (k_in) and turnover rates (k_met), as shown with DArG. Interestingly, SOG and OSG show significant differences (i.e., nonoverlapping confidence intervals) in turnover rates (k_met) despite being DAG isomers.

Directly measuring single-cell uncaging photoreaction yields is not possible using our previously published methodology, which requires separate experiments for photoreaction yield determination and acquisition of time trace data. To address this, we treated the initial photoreaction yield as an additional parameter that is inferred simultaneously with other parameters such as lipid-protein affinities and rates for trans-bilayer movement and turnover. We find that the resulting model can still be fully parameterized from time trace data if the data quality is sufficient. This is remarkable because our previous population-level analysis required the acquisition of dose-response curves via uncaging light titrations to uniquely identify all model parameters. This seems to be the case as our current approach exploits natural protein level variations to sample the concentration space. This is remarkable because our previous population-level analysis required the acquisition of several dose-response curves via uncaging light titrations to uniquely identify all model parameters. Our current approach similarly samples the concentration space by exploiting the natural protein level variations of the population. The number of cell traces used can also improve parameter identifiability but results in more computational effort, and improvements begin to diminish after a certain number of cells (n = ∼100). This suggests that improvements in imaging technology and image analysis pipelines will directly result in improved capability for extracting quantitative parameters from live-cell time trace data.

The main aim of our study was twofold: we attempted to obtain quantitative kinetic parameters for DAG signaling dynamics while minimizing experimental complexity and accounting for cell-to-cell heterogeneity. Together with the additional requirement that all model parameters should be uniquely identifiable, this places significant constraints on model complexity and the number of variable parameters. Our analytical pipeline is thus based on a relatively simple model with assumptions (i.e., no k_out and fixed rate and lipid-protein binding parameters) that may not capture all relevant dynamic properties of the investigated signaling events. There are a number of hints in the current dataset and our previous study (14) that this is in fact the case. For example, SOG-driven C1 domain recruitment appears to involve an unknown rate-limiting step that is not included in the model. Similarly, we have assumed that cell-to-cell variability is predominantly due to variable photoreaction yields and C1-EGFP-NES concentrations, whereas other parameters may be subject to heterogeneity as well. However, including additional heterogeneous parameters would increase model complexity and likely impair parameter identifiability when using the current experimental data. In fact, while the parameters for lipid trans-bilayer movement and protein-lipid interactions are reflecting well-defined reactions, k_met is an effective rate representing a complex phenomenon that is likely a mixture of DAG metabolism via DAG lipases (DAGLα and DAGLβ) or kinases and lipid transport to the endoplasmic reticulum via extended synaptotagmins. It is thus likely that this parameter exhibits cell-to-cell heterogeneity, but k_met variability alone is not sufficient to explain the observed data in a physiologically meaningful manner. Capturing these individual processes would require a combination of lipid uncaging and genetic or pharmacological perturbations. In the future, these limitations may also be addressed by extending our approach to include more information-rich datasets, such as laser power titration series or more complex temporal perturbation patterns (20). In summary, our study demonstrates how kinetic parameters of DAG-uncaging-induced lipid signaling events can be quantified from single-cell traces without the need to experimentally measure photoreaction yields. Such approaches will help in understanding cellular information processing during lipid signaling on the single-cell level.

Author contributions

D.T.G., M.S., C.Z., and A.N. conceptualized research and designed experiments. M.S. synthesized photochemical probes. M.S., H.M.L., S.M.K., and P.B. performed photoactivation experiments. M.S., H.M.L., S.M.K., P.B., and J.M.I.-A. analyzed imaging data. D.T.G. and C.Z. built the kinetic analysis pipeline and performed mathematical modeling. A.N., C.Z., D.T.G., and M.S. wrote the manuscript. All authors proofread and corrected the draft.

Editor: Ilya Levental.