Are Quasi-Steady-State Approximated Models Suitable for Quantifying Intrinsic Noise Accurately?

Large gene regulatory networks (GRN) are often modeled with quasi-steady-state approximation (QSSA) to reduce the huge computational time required for intrinsic noise quantification using Gillespie stochastic simulation algorithm (SSA). However, the question still remains whether the stochastic QSSA model measures the intrinsic noise as accurately as the SSA performed for a detailed mechanistic model or not? To address this issue, we have constructed mechanistic and QSSA models for few frequently observed GRNs exhibiting switching behavior and performed stochastic simulations with them. Our results strongly suggest that the performance of a stochastic QSSA model in comparison to SSA performed for a mechanistic model critically relies on the absolute values of the mRNA and protein half-lives involved in the corresponding GRN. The extent of accuracy level achieved by the stochastic QSSA model calculations will depend on the level of bursting frequency generated due to the absolute value of the half-life of either mRNA or protein or for both the species. For the GRNs considered, the stochastic QSSA quantifies the intrinsic noise at the protein level with greater accuracy and for larger combinations of half-life values of mRNA and protein, whereas in case of mRNA the satisfactory accuracy level can only be reached for limited combinations of absolute values of half-lives. Further, we have clearly demonstrated that the abundance levels of mRNA and protein hardly matter for such comparison between QSSA and mechanistic models. Based on our findings, we conclude that QSSA model can be a good choice for evaluating intrinsic noise for other GRNs as well, provided we make a rational choice based on experimental half-life values available in literature.     

Gap Junction Turnover Is Achieved by the Internalization of Small Endocytic Double-Membrane Vesicles

Double-membrane–spanning gap junction (GJ) channels cluster into two-dimensional arrays, termed plaques, to provide direct cell-to-cell communication. GJ plaques often contain circular, channel-free domains (∼0.05–0.5 μm in diameter) identified >30 y ago and termed nonjunctional membrane (NM) domains. We show, by expressing the GJ protein connexin43 (Cx43) tagged with green fluorescent protein, or the novel photoconvertible fluorescent protein Dendra2, that NM domains appear to be remnants generated by the internalization of small GJ channel clusters that bud over time from central plaque areas. Channel clusters internalized within seconds forming endocytic double-membrane GJ vesicles (∼0.18–0.27 μm in diameter) that were degraded by lysosomal pathways. Surprisingly, NM domains were not repopulated by surrounding channels and instead remained mobile, fused with each other, and were expelled at plaque edges. Quantification of internalized, photoconverted Cx43-Dendra2 vesicles indicated a GJ half-life of 2.6 h that falls within the estimated half-life of 1–5 h reported for GJs. Together with previous publications that revealed continuous accrual of newly synthesized channels along plaque edges and simultaneous removal of channels from plaque centers, our data suggest how the known dynamic channel replenishment of functional GJ plaques can be achieved. Our observations may have implications for the process of endocytic vesicle budding in general.     

Sample Preparation and Imaging Conditions Affect mEos3.2 Photophysics in Fission Yeast Cells

Photoconvertible fluorescent proteins (PCFPs) are widely used in super-resolution microscopy and studies of cellular dynamics. However, our understanding of their photophysics is still limited, hampering their quantitative application. For example, we do not know the optimal sample preparation methods or imaging conditions to count protein molecules fused to PCFPs by single-molecule localization microscopy in live and fixed cells. We also do not know how the behavior of PCFPs in live cells compares with fixed cells. Therefore, we investigated how formaldehyde fixation influences the photophysical properties of the popular green-to-red PCFP mEos3.2 in fission yeast cells under a wide range of imaging conditions. We estimated photophysical parameters by fitting a three-state model of photoconversion and photobleaching to the time course of fluorescence signal per yeast cell expressing mEos3.2. We discovered that formaldehyde fixation makes the fluorescence signal, photoconversion rate, and photobleaching rate of mEos3.2 sensitive to the buffer conditions likely by permeabilizing the yeast cell membrane. Under some imaging conditions, the time-integrated mEos3.2 signal per yeast cell is similar in live cells and fixed cells imaged in buffer at pH 8.5 with 1 mM DTT, indicating that light chemical fixation does not destroy mEos3.2 molecules. We also discovered that 405-nm irradiation drove some red-state mEos3.2 molecules to enter an intermediate dark state, which can be converted back to the red fluorescent state by 561-nm illumination. Our findings provide a guide to quantitatively compare conditions for imaging mEos3.2-tagged molecules in yeast cells. Our imaging assay and mathematical model are easy to implement and provide a simple quantitative approach to measure the time-integrated signal and the photoconversion and photobleaching rates of fluorescent proteins in cells.     

Structural Basis for Blocked Excited State Proton Transfer in a Fluorescent,Photoacidic Non-Canonical Amino Acid-Containing Antibody Fragment

The fluorescent non-canonical amino acid (fNCAA) L-(7-hydroxycoumarin-4-yl)ethylglycine (7-HCAA) contains a photoacidic 7-hydroxycoumarin (7-HC) side chain whose fluorescence properties can be tuned by its environment. In proteins, many alterations to 7-HCAA’s fluorescence spectra have been reported including increases and decreases in intensity and red- and blue-shifted emission maxima. The ability to rationally design protein environments that alter 7-HCAA’s fluorescence properties in predictable ways could lead to novel protein-based sensors of biological function. However, these efforts are likely limited by a lack of structural characterization of 7-HCAA-containing proteins. Here, we report the steady-state spectroscopic and x-ray crystallographic characterization of a 7-HCAA-containing antibody fragment (in the apo and antigen-bound forms) in which a substantially blue-shifted 7-HCAA emission maximum (～70 nm) is observed relative to the free amino acid. Our structural characterization of these proteins provides evidence that the blue shift is a consequence of the fact that excited state proton transfer (ESPT) from the 7-HC phenol has been almost completely blocked by interactions with the protein backbone. Furthermore, a direct interaction between a residue in the antigen and the fluorophore served to further block proton transfer relative to the apoprotein. The structural basis of the unprecedented blue shift in 7-HCAA emission reported here provides a framework for the development of new fluorescent protein-based sensors.     

Novel fluorescent protein from Hydnophora rigida possesses green emission

Fluorescent proteins are a family of proteins capable of producing fluorescence at various specific wavelengths of ultra violet light. We have previously reported the identification and characterization of a novel cyan fluorescent protein (HriCFP) from a reef coral species, Hydnophora rigida. In search of new members of the diverse family of fluorescent proteins, here we report a new green fluorescent protein (HriGFP) from H. rigida. HriGFP was identified, cloned, expressed in Escherichia coli and purified to homogeneity by metal affinity and size exclusion chromatography. The dynamic light scattering and gel filtration experiments suggested the presence of monomers in solution. The peptide mass fingerprint on the purified protein established the identity of HriGFP. HriGFP had excitation peak at 507 nm and emission peak at 527 nm. HriGFP was similar to HriCFP except the last 16 amino acid sequence at the C-terminal; however, they have shown least similarity with other known fluorescent proteins. Moreover the computational model suggests that HriGFP is a globular protein which consists of 6 α-helices and 3 β-sheets. Taken together our results suggested that HriGFP is a novel naturally occurring fluorescent protein that exists as a monomer in solution.     

STED nanoscopy reveals molecular details of cholesterol- and cytoskeleton-modulated lipid interactions in living cells

Details about molecular membrane dynamics in living cells, such as lipid-protein interactions, are often hidden from the observer because of the limited spatial resolution of conventional far-field optical microscopy. The superior spatial resolution of stimulated emission depletion (STED) nanoscopy can provide new insights into this process. The application of fluorescence correlation spectroscopy (FCS) in focal spots continuously tuned down to 30 nm in diameter distinguishes between free and anomalous molecular diffusion due to, for example, transient binding of lipids to other membrane constituents, such as lipids and proteins. We compared STED-FCS data recorded on various fluorescent lipid analogs in the plasma membrane of living mammalian cells. Our results demonstrate details about the observed transient formation of molecular complexes. The diffusion characteristics of phosphoglycerolipids without hydroxyl-containing headgroups revealed weak interactions. The strongest interactions were observed with sphingolipid analogs, which showed cholesterol-assisted and cytoskeleton-dependent binding. The hydroxyl-containing headgroup of gangliosides, galactosylceramide, and phosphoinositol assisted binding, but in a much less cholesterol- and cytoskeleton-dependent manner. The observed anomalous diffusion indicates lipid-specific transient hydrogen bonding to other membrane molecules, such as proteins, and points to a distinct connectivity of the various lipids to other membrane constituents. This strong interaction is different from that responsible for forming cholesterol-dependent, liquid-ordered domains in model membranes.     

Quantitative fluorescence correlation spectroscopy reveals a 1000-fold increase in lifetime of protein functionality

We have investigated dilute protein solutions with fluorescence correlation spectroscopy (FCS) and have observed that a rapid loss of proteins occurs from solution. It is commonly assumed that such a loss is the result of protein adsorption to interfaces. A protocol was developed in which this mode of protein loss can be prevented. However, FCS on fluorescent protein (enhanced green fluorescent protein, mCherry, and mStrawberry) solutions enclosed by adsorption-protected interfaces still reveals a decrease of the fluorescent protein concentration, while the diffusion time is stable over long periods of time. We interpret this decay as a loss of protein functionality, probably caused by denaturation of the fluorescent proteins. We show that the typical lifetime of protein functionality in highly dilute, approximately single molecule per femtoliter solutions can be extended more than 1000-fold (typically from a few hours to >40 days) by adding compounds with surfactant behavior. No direct interactions between the surfactant and the fluorescent proteins were observed from the diffusion time measured by FCS. A critical surfactant concentration of more than 23 μM was required to achieve the desired protein stabilization for Triton X-100. The surfactant does not interfere with DNA-protein binding, because similar observations were made using DNA-cutting restriction enzymes. We associate the occurrence of denaturation of proteins with the activity of water at the water-protein interface, which was recently proposed in terms of the “water attack model”. Our observations suggest that soluble biomolecules can extend an influence over much larger distances than suggested by their actual volume.     

A patch-based method for repetitive and transient event detection in fluorescence imaging

Automatic detection and characterization of molecular behavior in large data sets obtained by fast imaging in advanced light microscopy become key issues to decipher the dynamic architectures and their coordination in the living cell. Automatic quantification of the number of sudden and transient events observed in fluorescence microscopy is discussed in this paper. We propose a calibrated method based on the comparison of image patches expected to distinguish sudden appearing/vanishing fluorescent spots from other motion behaviors such as lateral movements. We analyze the performances of two statistical control procedures and compare the proposed approach to a frame difference approach using the same controls on a benchmark of synthetic image sequences. We have then selected a molecular model related to membrane trafficking and considered real image sequences obtained in cells stably expressing an endocytic-recycling trans-membrane protein, the Langerin-YFP, for validation. With this model, we targeted the efficient detection of fast and transient local fluorescence concentration arising in image sequences from a data base provided by two different microscopy modalities, wide field (WF) video microscopy using maximum intensity projection along the axial direction and total internal reflection fluorescence microscopy. Finally, the proposed detection method is briefly used to statistically explore the effect of several perturbations on the rate of transient events detected on the pilot biological model.     

Stochastic modeling of gene positive autoregulation networks involving signal molecules

Positive autoregulation in gene regulation networks has been shown in the past to exhibit stochastic behavior, including stochastic bistability, in which an initially uniform cell population develops into two distinct subpopulations. However, positive autoregulation is often mediated by signal molecules, which have not been considered in prior stochastic analysis of these networks. Here we propose both a full model of such a network that includes a signal molecule, and a simplified model in which the signal molecules have been eliminated through the use of two simplifications. The simplified model is amenable to direct mathematical analysis that shows that stochastic bistability is possible. We use stochastic Petri networks for simulating both types of models. The simulation results show that 1), the stochastic behavior of the two models is similar; and 2), that the analytical steady-state distribution of the simplified model matches well the transient results at times equal to that of a cell generation. A discussion of the simplifications we used in the context of the results indicates the importance of the signal molecule number as a factor determining the presence of bistability. This is further supported from a deterministic steady-state analysis of the full model that is shown to be a useful indicator of potential stochastic bistability. We use the regulation of SdiA in Escherichia coli as an example, due to the importance of this protein and of the signal molecule, a bacterial autoinducer, that is involved. However, the use of kinetic parameter values representing typical cellular activities make the conclusions applicable to other signal-mediated positive autoregulation networks as well.     

Heterogeneous Timing of Gene Induction as a Regulation Strategy

In response to environmental changes, cells often adapt by up-regulating genes to synthesize proteins that generate a benefit in the new environment. Several such cases of gene induction have been reported where the timing was heterogeneous, with some cells responding early and others responding late, although the microbial population was genetically homogeneous and the environment was well mixed. Here, we explore under which conditions heterogeneous timing of gene induction could be advantageous for the population as a whole. We base our study on a mathematical model that accounts for the cost of protein synthesis in terms of resources, which cells must provide immediately, whereas the associated benefit accumulates only slowly over the protein lifetime. Due to this delayed benefit, gene induction can be a risky investment, if resources are scarce and the environment fluctuates rapidly and unpredictably. Unprofitable gene induction then depletes the remaining limiting resource needed for maintenance of cell viability. We show that whenever gene induction is associated with a transient risk but beneficial in the long run, the stochastic timing of gene induction maximizes the reproductive success of a population. In particular, in an environment of stochastic periods of famine and feast, an optimum emerges from a trade-off between short-term growth, favoring rapid and homogeneous responses, and long-term survival, favoring a broadly heterogeneous response. Our analysis suggests that the optimal variability of induction times is just as large as the time required for the amortization of the initial investment into protein synthesis.     

Correcting for the inner filter effect in measurements of fluorescent proteins in high-cell-density cultures

Fluorescent proteins (FPs), such as green fluorescent protein (GFP) and its variants, are well-developed visible markers for analyzing bioprocesses. Accurate measurement of fluorescence emitted from FPs in whole cells is complicated by the inner filter effect (IFE), which is caused by intracellular light absorption and scattering by cell particles. The IFE causes nonlinearity between fluorescence intensity and fluorophore concentrations in FP-harboring cells and can significantly influence the accuracy of FP-based analysis, especially at high cell densities. A mathematical model based on detection of fluorescence intensity using a fluorescence spectrophotometer was developed to provide a simple correction for the IFE in fluorescence intensity detection in high-density cultures. The parameters of this model were determined in three different FP-harboring bacterial strains to give the “real fluorescence” intensity without the IFE. Using these parameters, accurate analysis of FP-labeled Escherichia coli at high cell density in pure culture and in mixed cultures with fluorescent and nonfluorescent strains was easily and successfully achieved.