Modulation of transcription factor dynamics allows versatile information transmission.

Cells detect changes in their environment and generate responses, often involving changes in gene expression. In this paper we use information theory and a simple transcription model to analyze whether the resulting gene expression serves to identify extracellular stimuli and assess their intensity when they are encoded in the amplitude, duration or frequency of pulses of a transcription factor's nuclear concentration (or activation state). We find, for all cases, that about three ranges of input strengths can be distinguished and that maximum information transmission occurs for fast and high activation threshold promoters. The three input modulation modes differ in the sensitivity to changes in the promoters parameters. Frequency modulation is the most sensitive and duration modulation, the least. This is key for signal identification: there are promoter parameters that yield a relatively high information transmission for duration or amplitude modulation and a much smaller value for frequency modulation. The reverse situation cannot be found with a single promoter transcription model. Thus, pulses of transcription factors can selectively activate the "frequency-tuned" promoter while prolonged nuclear accumulation would activate promoters of all three modes simultaneously. Frequency modulation is therefore highly selective and better suited than the other encoding modes for signal identification without requiring other mediators of the transduction process.

Nested pool testing strategy for the diagnosis of infectious diseases.

The progress of the SARS-CoV-2 pandemic requires the design of large-scale, cost-effective testing programs. Pooling samples provides a solution if the tests are sensitive enough. In this regard, the use of the gold standard, RT-qPCR, raises some concerns. Recently, droplet digital PCR (ddPCR) was shown to be 10-100 times more sensitive than RT-qPCR, making it more suitable for pooling. Furthermore, ddPCR quantifies the RNA content directly, a feature that, as we show, can be used to identify nonviable samples in pools. Cost-effective strategies require the definition of efficient deconvolution and re-testing procedures. In this paper we analyze the practical implementation of an efficient hierarchical pooling strategy for which we have recently derived the optimal, determining the best ways to proceed when there are impediments for the use of the absolute optimum or when multiple pools are tested simultaneously and there are restrictions on the throughput time. We also show how the ddPCR RNA quantification and the nested nature of the strategy can be combined to perform self-consistency tests for a better identification of infected individuals and nonviable samples. The studies are useful to those considering pool testing for the identification of infected individuals.

High rates of calcium-free diffusion in the cytosol of living cells.

Calcium (Ca2+) is a universal second messenger that participates in the regulation of innumerous physiological processes. The way in which local elevations of the cytosolic Ca2+ concentration spread in space and time is key for the versatility of the signals. Ca2+ diffusion in the cytosol is hindered by its interaction with proteins that act as buffers. Depending on the concentrations and the kinetics of the interactions, there is a large range of values at which Ca2+ diffusion can proceed. Having reliable estimates of this range, particularly of its highest end, which corresponds to the ions free diffusion, is key to understand how the signals propagate. In this work, we present the first experimental results with which the Ca2+-free diffusion coefficient is directly quantified in the cytosol of living cells. By means of fluorescence correlation spectroscopy experiments performed in Xenopus laevis oocytes and in cells of Saccharomyces cerevisiae, we show that the ions can freely diffuse in the cytosol at a higher rate than previously thought.

Changes in Ca2+ Removal Can Mask the Effects of Geometry During IP3R Mediated Ca2+ Signals.

Calcium (Ca2+) signals are ubiquitous. Most intracellular Ca2+ signals involve the release of Ca2+ from the endoplasmic reticulum (ER) through Inositol 1,4,5-Trisphosphate Receptors (IP3Rs). The non-uniform spatial organization of IP3Rs and the fact that their individual openings are coupled via cytosolic Ca2+ are key factors for the variety of spatio-temporal distributions of the cytosolic [Ca2+] and the versatility of the signals. In this paper we combine experiments performed in untreated and in progesterone-treated Xenopus laevis oocytes and mathematical models to investigate how the interplay between geometry (the IP3R spatial distribution) and dynamics (the processes that characterize the release, transport, and removal of cytosolic Ca2+) affects the resulting signals. Signal propagation looks more continuous and spatially uniform in treated (mature) than in untreated (immature) oocytes. This could be due to the different underlying IP3R spatial distribution that has been observed in both cell types. The models, however, show that the rate of cytosolic Ca2+ removal, which is also different in both cell types, plays a key role affecting the coupling between Ca2+ release sites in such a way that the effect of the underlying IP3R spatial distribution can be modified.

Correction: Fluctuations, Correlations and the Estimation of Concentrations inside Cells.

[This corrects the article DOI: 10.1371/journal.pone.0151132.].

Fluorescence correlation spectroscopy experiments to quantify free diffusion coefficients in reaction-diffusion systems: The case of Ca

Many cell signaling pathways involve the diffusion of messengers that bind and unbind to and from intracellular components. Quantifying their net transport rate under different conditions then requires having separate estimates of their free diffusion coefficient and binding or unbinding rates. In this paper, we show how performing sets of fluorescence correlation spectroscopy (FCS) experiments under different conditions, it is possible to quantify free diffusion coefficients and on and off rates of reaction-diffusion systems. We develop the theory and present a practical implementation for the case of the universal second messenger, calcium (Ca^{2+}) and single-wavelength dyes that increase their fluorescence upon Ca^{2+} binding. We validate the approach with experiments performed in aqueous solutions containing Ca^{2+} and Fluo4 dextran (both in its high and low affinity versions). Performing FCS experiments with tetramethylrhodamine-dextran in Xenopus laevis oocytes, we infer the corresponding free diffusion coefficients in the cytosol of these cells. Our approach can be extended to other physiologically relevant reaction-diffusion systems to quantify biophysical parameters that determine the dynamics of various variables of interest.

FCS experiments to quantify Ca2+ diffusion and its interaction with buffers.

Ca2+ signals are ubiquitous. One of the key factors for their versatility is the variety of spatio-temporal distributions that the cytosolic Ca2+ can display. In most cell types Ca2+ signals not only depend on Ca2+ entry from the extracellular medium but also on Ca2+ release from internal stores, a process which is in turn regulated by cytosolic Ca2+ itself. The rate at which Ca2+ is transported, the fraction that is trapped by intracellular buffers, and with what kinetics are thus key features that affect the time and spatial range of action of Ca2+ signals. The quantification of Ca2+ diffusion in intact cells is quite challenging because the transport rates that can be inferred using optical techniques are intricately related to the interaction of Ca2+ with the dye that is used for its observation and with the cellular buffers. In this paper, we introduce an approach that uses Fluorescence Correlation Spectroscopy (FCS) experiments performed at different conditions that in principle allows the quantification of Ca2+ diffusion and of its reaction rates with unobservable (non-fluorescent) Ca2+ buffers. To this end, we develop the necessary theory to interpret the experimental results and then apply it to FCS experiments performed in a set of solutions containing Ca2+, a single wavelength Ca2+ dye, and a non-fluorescent Ca2+ buffer. We show that a judicious choice of the experimental conditions and an adequate interpretation of the fitting parameters can be combined to extract information on the free diffusion coefficient of Ca2+ and of some of the properties of the unobservable buffer. We think that this approach can be applied to other situations, particularly to experiments performed in intact cells.

Fluctuations, Correlations and the Estimation of Concentrations inside Cells.

Information transmission in cells occurs quite accurately even when concentration changes are "read" by individual binding sites. In this paper we study ligand number and site occupancy fluctuations when ligands diffuse and react going beyond the analyses that focus on their asymptotic decay. In this way we show that, for immobile binding sites, fluctuations in the number of bound molecules decay on a relatively fast scale before the asymptotic behavior kicks in. This result can explain the observed co-existence of highly fluctuating instantaneous transcriptional activities with accumulated mRNA concentrations that have relatively small noise levels. We also show that the initial stages of the decay in the bound molecule number fluctuations have one or two characteristic timescales depending on the concentration of free molecules. This transition can explain the changes in enzyme activity observed at the single molecule level.

Ca²âº images obtained in different experimental conditions shed light on the spatial distribution of IP3 receptors that underlie Ca²âº puffs.

Many intracellular Ca(2+) signals involve Ca(2+) release from the endoplasmic reticulum through inositol 1,4,5-trisphosphate receptors (IP3Rs). The open probability of IP3Rs depends on cytosolic Ca(2+) so that these signals involve Ca(2+)-induced Ca(2+)-release (CICR). IP3Rs are organized in clusters. The signals they mediate are observed using single-wavelength dyes and, often, a slow Ca(2+) buffer (EGTA) is added to disrupt CICR between clusters and keep the signals spatially restricted. It is assumed that the presence of the dye or of EGTA does not alter the intra-cluster Ca(2+) dynamics. In this paper we analyze this issue combining experiments and numerical simulations. We compare the properties of local signals known as puffs observed with different dyes and EGTA concentrations. We determine that although the dye or EGTA does not alter the intra-cluster dynamics, the set of observable events is different depending on the degree of inter-cluster uncoupling of the experiment. An analysis of the observations shows that the events that are missed for insufficient inter-cluster uncoupling are those of fastest amplitude growth rate. This agrees with a spatial organization in which the largest amplitude events correspond to clusters with densely packed active IP3Rs.

How long should a system be observed to obtain reliable concentration estimates from the measurement of fluctuations?

The interior of cells is a highly fluctuating environment. Fluctuations set limits to the accuracy with which endogenous processes can occur. The physical principles that rule these limits also affect the experimental quantification of biophysical parameters in situ. The characterization of fluctuations, on the other hand, provides a way to quantify biophysical parameters. But as with any random process, enough data has to be collected to achieve a reliable quantitative description. In this article we study the accuracy with which intracellular concentrations can be estimated using fluorescence correlation spectroscopy. We show that, when the observed molecules interact with immobile species or experience other restrictions to their movement, the hypotheses commonly used to estimate concentrations are no longer valid. The interactions with immobile sites reduce the fluorescence variance by a finite amount. The time that is necessary to obtain an accurate concentration estimate, on the other hand, is hundreds of times larger than the slowest correlation time and is much larger when the sites move slowly than when they are immobile. Our analysis is applicable to other related techniques and it also sheds light on the way in which effector concentrations are read by target molecules in cells.

Messages do diffuse faster than messengers: reconciling disparate estimates of the morphogen bicoid diffusion coefficient.

The gradient of Bicoid (Bcd) is key for the establishment of the anterior-posterior axis in Drosophila embryos. The gradient properties are compatible with the SDD model in which Bcd is synthesized at the anterior pole and then diffuses into the embryo and is degraded with a characteristic time. Within this model, the Bcd diffusion coefficient is critical to set the timescale of gradient formation. This coefficient has been measured using two optical techniques, Fluorescence Recovery After Photobleaching (FRAP) and Fluorescence Correlation Spectroscopy (FCS), obtaining estimates in which the FCS value is an order of magnitude larger than the FRAP one. This discrepancy raises the following questions: which estimate is "correct''; what is the reason for the disparity; and can the SDD model explain Bcd gradient formation within the experimentally observed times? In this paper, we use a simple biophysical model in which Bcd diffuses and interacts with binding sites to show that both the FRAP and the FCS estimates may be correct and compatible with the observed timescale of gradient formation. The discrepancy arises from the fact that FCS and FRAP report on different effective (concentration dependent) diffusion coefficients, one of which describes the spreading rate of the individual Bcd molecules (the messengers) and the other one that of their concentration (the message). The latter is the one that is more relevant for the gradient establishment and is compatible with its formation within the experimentally observed times.

Fluorescence fluctuations and equivalence classes of Ca²âº imaging experiments.

Ca²âº release into the cytosol through inositol 1,4,5-trisphosphate receptors (IP3Rs) plays a relevant role in numerous physiological processes. IP3R-mediated Ca²âº signals involve Ca²âº-induced Ca²âº-release (CICR) whereby Ca²âº release through one open IP3R induces the opening of other channels. IP3Rs are apparently organized in clusters. The signals can remain localized (i.e., Ca²âº puffs) if CICR is limited to one cluster or become waves that propagate between clusters. Ca²âº puffs are the building blocks of Ca²âº waves. Thus, there is great interest in determining puff properties, especially in view of the current controversy on the spatial distribution of activatable IP3Rs. Ca²âº puffs have been observed in intact cells with optical techniques proving that they are intrinsically Ca²âº dyes, slow exogenous buffers (e.g., EGTA) to disrupt inter-cluster CICR and UV-photolyzable caged IP3. Single-wavelength dyes increase their fluorescence upon calcium binding producing images that are strongly dependent on their kinetic, transport and photophysical properties. Determining the artifacts that the imaging setting introduces is particularly relevant when trying to analyze the smallest Ca²âº signals. In this paper we introduce a method to estimate the expected signal-to-noise ratio of Ca²âº imaging experiments that use single-wavelength dyes. The method is based on the Number and rightness technique. It involves the performance of a series of experiments and their subsequent analysis in terms of a fluorescence fluctuation model with which the model parameters are quantified. Using the model, the expected signal-to-noise ratio is then computed. Equivalence classes between different experimental conditions that produce images with similar signal-to-noise ratios can then be established. The method may also be used to estimate the smallest signals that can reliably be observed with each setting.

Intracellular calcium signals display an avalanche-like behavior over multiple lengthscales.

Many natural phenomena display "self-organized criticality" (SOC), (Bak et al., 1987). This refers to spatially extended systems for which patterns of activity characterized by different lengthscales can occur with a probability density that follows a power law with pattern size. Differently from power laws at phase transitions, systems displaying SOC do not need the tuning of an external parameter. Here we analyze intracellular calcium (Ca(2+)) signals, a key component of the signaling toolkit of almost any cell type. Ca(2+) signals can either be spatially restricted (local) or propagate throughout the cell (global). Different models have suggested that the transition from local to global signals is similar to that of directed percolation. Directed percolation has been associated, in turn, to the appearance of SOC. In this paper we discuss these issues within the framework of simple models of Ca(2+) signal propagation. We also analyze the size distribution of local signals ("puffs") observed in immature Xenopus Laevis oocytes. The puff amplitude distribution obtained from observed local signals is not Gaussian with a noticeable fraction of large size events. The experimental distribution of puff areas in the spatio-temporal record of the image has a long tail that is approximately log-normal. The distribution can also be fitted with a power law relationship albeit with a smaller goodness of fit. The power law behavior is encountered within a simple model that includes some coupling among individual signals for a wide range of parameter values. An analysis of the model shows that a global elevation of the Ca(2+) concentration plays a major role in determining whether the puff size distribution is long-tailed or not. This suggests that Ca(2+)-clearing from the cytosol is key to determine whether IP(3)-mediated Ca(2+) signals can display a SOC-like behavior or not.

A dynamic analysis of tuberculosis dissemination to improve control and surveillance.

BACKGROUND: Detailed analysis of the dynamic interactions among biological, environmental, social, and economic factors that favour the spread of certain diseases is extremely useful for designing effective control strategies. Diseases like tuberculosis that kills somebody every 15 seconds in the world, require methods that take into account the disease dynamics to design truly efficient control and surveillance strategies. The usual and well established statistical approaches provide insights into the cause-effect relationships that favour disease transmission but they only estimate risk areas, spatial or temporal trends. Here we introduce a novel approach that allows figuring out the dynamical behaviour of the disease spreading. This information can subsequently be used to validate mathematical models of the dissemination process from which the underlying mechanisms that are responsible for this spreading could be inferred. METHODOLOGY/PRINCIPAL FINDINGS: The method presented here is based on the analysis of the spread of tuberculosis in a Brazilian endemic city during five consecutive years. The detailed analysis of the spatio-temporal correlation of the yearly geo-referenced data, using different characteristic times of the disease evolution, allowed us to trace the temporal path of the aetiological agent, to locate the sources of infection, and to characterize the dynamics of disease spreading. Consequently, the method also allowed for the identification of socio-economic factors that influence the process. CONCLUSIONS/SIGNIFICANCE: The information obtained can contribute to more effective budget allocation, drug distribution and recruitment of human skilled resources, as well as guiding the design of vaccination programs. We propose that this novel strategy can also be applied to the evaluation of other diseases as well as other social processes.

Observable effects of Ca2+ buffers on local Ca2+ signals.

Calcium signals participate in a large variety of physiological processes. In many instances, they involve calcium entry through inositol 1,4,5-trisphosphate (IP(3)) receptors (IP(3)Rs), which are usually organized in clusters. Recent high-resolution optical experiments by Smith & Parker have provided new information on Ca(2+) release from clustered IP(3)Rs. In the present paper, we use the model recently introduced by Solovey & Ponce Dawson to determine how the distribution of the number of IP(3)Rs that become open during a localized release event may change by the presence of Ca(2+) buffers, substances that react with Ca(2+), altering its concentration and transport properties. We then discuss how buffer properties could be extracted from the observation of local signals.

Stochastic fire-diffuse-fire model with realistic cluster dynamics.

Living organisms use waves that propagate through excitable media to transport information. Ca2+ waves are a paradigmatic example of this type of processes. A large hierarchy of Ca2+ signals that range from localized release events to global waves has been observed in Xenopus laevis oocytes. In these cells, Ca2+ release occurs trough inositol 1,4,5-trisphosphate receptors (IP3Rs) which are organized in clusters of channels located on the membrane of the endoplasmic reticulum. In this article we construct a stochastic model for a cluster of IP3R 's that replicates the experimental observations reported in [D. Fraiman, Biophys. J. 90, 3897 (2006)]. We then couple this phenomenological cluster model with a reaction-diffusion equation, so as to have a discrete stochastic model for calcium dynamics. The model we propose describes the transition regimes between isolated release and steadily propagating waves as the IP3 concentration is increased.

Turing patterns inside cells.

Concentration gradients inside cells are involved in key processes such as cell division and morphogenesis. Here we show that a model of the enzymatic step catalized by phosphofructokinase (PFK), a step which is responsible for the appearance of homogeneous oscillations in the glycolytic pathway, displays Turing patterns with an intrinsic length-scale that is smaller than a typical cell size. All the parameter values are fully consistent with classic experiments on glycolytic oscillations and equal diffusion coefficients are assumed for ATP and ADP. We identify the enzyme concentration and the glycolytic flux as the possible regulators of the pattern. To the best of our knowledge, this is the first closed example of Turing pattern formation in a model of a vital step of the cell metabolism, with a built-in mechanism for changing the diffusion length of the reactants, and with parameter values that are compatible with experiments. Turing patterns inside cells could provide a check-point that combines mechanical and biochemical information to trigger events during the cell division process.

Slow time evolution of two-time-scale reaction-diffusion systems: the physical origin of nondiffusive transport.

We study, from a mesoscopic point of view, the slow time-scale dynamics of a mixture of chemicals in which there is a chemical reaction that occurs much faster than all other processes, including diffusion. For a simple paradigmatic model reaction, it is possible to find a reduced set of dynamical equations analytically. This procedure, which yields the same mean field equations as the macroscopic approach described by Strier and Dawson [J. Chem. Phys, 112, 825 (2000)], clarifies the physical origin of some of the terms that appear in the reduced reaction-diffusion equations, such as "negative density dependent cross diffusion terms," whose actual meaning is hard to assess within the macroscopic framework. We also present a two-time-scale reactive lattice gas automaton with which it is possible to check the validity of the analytical results and the conditions under which the reduced description holds. Using this lattice gas we also show how the differential interaction with immobile species can give rise to the formation of stable Turing patterns in a system where all the other chemicals diffuse approximately at the same rate.