On the correct determination of rotational angles for twisted-profiled sweep objects

In the context of the paper of V. Akman and A. Arslan, "Sweeping with All Graphical Ingredients in a Topological Picturebook" [Computers & Graphics, Vol. 16(3), pp. 273-281, 1992], a new construction of the rotational matrix is presented. This fixes a bug discovered by the first author. © 1994

Dose-Response Aligned Circuits in Signaling Systems

Cells use biological signal transduction pathways to respond to environmental stimuli and the behavior of many cell types depends on precise sensing and transmission of external information. A notable property of signal transduction that was characterized in the Saccharomyces cerevisiae yeast cell and many mammalian cells is the alignment of dose-response curves. It was found that the dose response of the receptor matches closely the dose responses of the downstream. This dose-response alignment (DoRA) renders equal sensitivities and concordant responses in different parts of signaling system and guarantees a faithful information transmission. The experimental observations raise interesting questions about the nature of the information transmission through DoRA signaling networks and design principles of signaling systems with this function. Here, we performed an exhaustive computational analysis on network architectures that underlie the DoRA function in simple regulatory networks composed of two and three enzymes. The minimal circuits capable of DoRA were examined with Michaelis-Menten kinetics. Several motifs that are essential for the dynamical function of DoRA were identified. Systematic analysis of the topology space of robust DoRA circuits revealed that, rather than fine-tuning the network's parameters, the function is primarily realized by enzymatic regulations on the controlled node that are constrained in limiting regions of saturation or linearity

Characterization of Membrane Potential Dependency of Mitochondrial Ca2+ Uptake by an Improved Biophysical Model of Mitochondrial Ca2+ Uniporter

Mitochondrial Ca2+ uniporter is the primary influx pathway for Ca2+ into respiring mitochondria, and hence plays a key role in mitochondrial Ca2+ homeostasis. Though the mechanism of extra-matrix Ca2+ dependency of mitochondrial Ca2+ uptake has been well characterized both experimentally and mathematically, the mechanism of membrane potential (ΔΨ) dependency of mitochondrial Ca2+ uptake has not been completely characterized. In this paper, we perform a quantitative reevaluation of a previous biophysical model of mitochondrial Ca2+ uniporter that characterized the possible mechanism of ΔΨ dependency of mitochondrial Ca2+ uptake. Based on a model simulation analysis, we show that model predictions with a variant assumption (Case 2: external and internal Ca2+ binding constants for the uniporter are distinct), that provides the best possible description of the ΔΨ dependency, are highly sensitive to variation in matrix [Ca2+], indicating limitations in the variant assumption (Case 2) in providing physiologically plausible description of the observed ΔΨ dependency. This sensitivity is attributed to negative estimate of a biophysical parameter that characterizes binding of internal Ca2+ to the uniporter. Reparameterization of the model with additional nonnengativity constraints on the biophysical parameters showed that the two variant assumptions (Case 1 and Case 2) are indistinguishable, indicating that the external and internal Ca2+ binding constants for the uniporter may be equal (Case 1). The model predictions in this case are insensitive to variation in matrix [Ca2+] but do not match the ΔΨ dependent data in the domain ΔΨ≤120 mV. To effectively characterize this ΔΨ dependency, we reformulate the ΔΨ dependencies of the rate constants of Ca2+ translocation via the uniporter by exclusively redefining the biophysical parameters associated with the free-energy barrier of Ca2+ translocation based on a generalized, non-linear Goldman-Hodgkin-Katz formulation. This alternate uniporter model has all the characteristics of the previous uniporter model and is also able to characterize the possible mechanisms of both the extra-matrix Ca2+ and ΔΨ dependencies of mitochondrial Ca2+ uptake. In addition, the model is insensitive to variation in matrix [Ca2+], predicting relatively stable physiological operation. The model is critical in developing mechanistic, integrated models of mitochondrial bioenergetics and Ca2+ handling

Mathematical modeling of intracellular signaling pathways

Dynamic modeling and simulation of signal transduction pathways is an important topic in systems biology and is obtaining growing attention from researchers with experimental or theoretical background. Here we review attempts to analyze and model specific signaling systems. We review the structure of recurrent building blocks of signaling pathways and their integration into more comprehensive models, which enables the understanding of complex cellular processes. The variety of mechanisms found and modeling techniques used are illustrated with models of different signaling pathways. Focusing on the close interplay between experimental investigation of pathways and the mathematical representations of cellular dynamics, we discuss challenges and perspectives that emerge in studies of signaling systems

A Hidden Feedback in Signaling Cascades Is Revealed

Cycles involving covalent modification of proteins are key components of the intracellular signaling machinery. Each cycle is comprised of two interconvertable forms of a particular protein. A classic signaling pathway is structured by a chain or cascade of basic cycle units in such a way that the activated protein in one cycle promotes the activation of the next protein in the chain, and so on. Starting from a mechanistic kinetic description and using a careful perturbation analysis, we have derived, to our knowledge for the first time, a consistent approximation of the chain with one variable per cycle. The model we derive is distinct from the one that has been in use in the literature for several years, which is a phenomenological extension of the Goldbeter-Koshland biochemical switch. Even though much has been done regarding the mathematical modeling of these systems, our contribution fills a gap between existing models and, in doing so, we have unveiled critical new properties of this type of signaling cascades. A key feature of our new model is that a negative feedback emerges naturally, exerted between each cycle and its predecessor. Due to this negative feedback, the system displays damped temporal oscillations under constant stimulation and, most important, propagates perturbations both forwards and backwards. This last attribute challenges the widespread notion of unidirectionality in signaling cascades. Concrete examples of applications to MAPK cascades are discussed. All these properties are shared by the complete mechanistic description and our simplified model, but not by previously derived phenomenological models of signaling cascades

Cross-Talk between Signaling Pathways Can Generate Robust Oscillations in Calcium and cAMP

BACKGROUND:To control and manipulate cellular signaling, we need to understand cellular strategies for information transfer, integration, and decision-making. A key feature of signal transduction is the generation of only a few intracellular messengers by many extracellular stimuli. METHODOLOGY/PRINCIPAL FINDINGS:Here we model molecular cross-talk between two classic second messengers, cyclic AMP (cAMP) and calcium, and show that the dynamical complexity of the response of both messengers increases substantially through their interaction. In our model of a non-excitable cell, both cAMP and calcium concentrations can oscillate. If mutually inhibitory, cross-talk between the two second messengers can increase the range of agonist concentrations for which oscillations occur. If mutually activating, cross-talk decreases the oscillation range, but can generate 'bursting' oscillations of calcium and may enable better filtering of noise. CONCLUSION:We postulate that this increased dynamical complexity allows the cell to encode more information, particularly if both second messengers encode signals. In their native environments, it is unlikely that cells are exposed to one stimulus at a time, and cross-talk may help generate sufficiently complex responses to allow the cell to discriminate between different combinations and concentrations of extracellular agonists

Denoising Two-Photon Calcium Imaging Data

Two-photon calcium imaging is now an important tool for in vivo imaging of biological systems. By enabling neuronal population imaging with subcellular resolution, this modality offers an approach for gaining a fundamental understanding of brain anatomy and physiology. Proper analysis of calcium imaging data requires denoising, that is separating the signal from complex physiological noise. To analyze two-photon brain imaging data, we present a signal plus colored noise model in which the signal is represented as harmonic regression and the correlated noise is represented as an order autoregressive process. We provide an efficient cyclic descent algorithm to compute approximate maximum likelihood parameter estimates by combing a weighted least-squares procedure with the Burg algorithm. We use Akaike information criterion to guide selection of the harmonic regression and the autoregressive model orders. Our flexible yet parsimonious modeling approach reliably separates stimulus-evoked fluorescence response from background activity and noise, assesses goodness of fit, and estimates confidence intervals and signal-to-noise ratio. This refined separation leads to appreciably enhanced image contrast for individual cells including clear delineation of subcellular details and network activity. The application of our approach to in vivo imaging data recorded in the ferret primary visual cortex demonstrates that our method yields substantially denoised signal estimates. We also provide a general Volterra series framework for deriving this and other signal plus correlated noise models for imaging. This approach to analyzing two-photon calcium imaging data may be readily adapted to other computational biology problems which apply correlated noise models.National Institutes of Health (U.S.) (DP1 OD003646-01)National Institutes of Health (U.S.) (R01EB006385-01)National Institutes of Health (U.S.) (EY07023)National Institutes of Health (U.S.) (EY017098

Spatial organization of RYRs and BK channels underlying the activation of STOCs by Ca2+ sparks in airway myocytes

Short-lived, localized Ca2+ events mediate Ca2+ signaling with high efficiency and great fidelity largely as a result of the close proximity between Ca2+-permeable ion channels and their molecular targets. However, in most cases, direct evidence of the spatial relationship between these two types of molecules is lacking, and, thus, mechanistic understanding of local Ca2+ signaling is incomplete. In this study, we use an integrated approach to tackling this issue on a prototypical local Ca2+ signaling system composed of Ca2+ sparks resulting from the opening of ryanodine receptors (RYRs) and spontaneous transient outward currents (STOCs) caused by the opening of Ca2+-activated K+ (BK) channels in airway smooth muscle. Biophysical analyses of STOCs and Ca2+ sparks acquired at 333 Hz demonstrate that these two events are associated closely in time, and approximately eight RYRs open to give rise to a Ca2+ spark, which activates ∼15 BK channels to generate a STOC at 0 mV. Dual immunocytochemistry and 3-D deconvolution at high spatial resolution reveal that both RYRs and BK channels form clusters and RYR1 and RYR2 (but not RYR3) localize near the membrane. Using the spatial relationship between RYRs and BK channels, the spatial-temporal profile of [Ca2+] resulting from Ca2+ sparks, and the kinetic model of BK channels, we estimate that an average Ca2+ spark caused by the opening of a cluster of RYR1 or RYR2 acts on BK channels from two to three clusters that are randomly distributed within an ∼600-nm radius of RYRs. With this spatial organization of RYRs and BK channels, we are able to model BK channel currents with the same salient features as those observed in STOCs across a range of physiological membrane potentials. Thus, this study provides a mechanistic understanding of the activation of STOCs by Ca2+ sparks using explicit knowledge of the spatial relationship between RYRs (the Ca2+ source) and BK channels (the Ca2+ target)

Effects of Transmitters and Amyloid-Beta Peptide on Calcium Signals in Rat Cortical Astrocytes: Fura-2AM Measurements and Stochastic Model Simulations

BACKGROUND: To better understand the complex molecular level interactions seen in the pathogenesis of Alzheimer's disease, the results of the wet-lab and clinical studies can be complemented by mathematical models. Astrocytes are known to become reactive in Alzheimer's disease and their ionic equilibrium can be disturbed by interaction of the released and accumulated transmitters, such as serotonin, and peptides, including amyloid- peptides (A). We have here studied the effects of small amounts of A25-35 fragments on the transmitter-induced calcium signals in astrocytes by Fura-2AM fluorescence measurements and running simulations of the detected calcium signals. METHODOLOGY/PRINCIPAL FINDINGS: Intracellular calcium signals were measured in cultured rat cortical astrocytes following additions of serotonin and glutamate, or either of these transmitters together with A25-35. A25-35 increased the number of astrocytes responding to glutamate and exceedingly increased the magnitude of the serotonin-induced calcium signals. In addition to A25-35-induced effects, the contribution of intracellular calcium stores to calcium signaling was tested. When using higher stimulus frequency, the subsequent calcium peaks after the initial peak were of lower amplitude. This may indicate inadequate filling of the intracellular calcium stores between the stimuli. In order to reproduce the experimental findings, a stochastic computational model was introduced. The model takes into account the major mechanisms known to be involved in calcium signaling in astrocytes. Model simulations confirm the principal experimental findings and show the variability typical for experimental measurements. CONCLUSIONS/SIGNIFICANCE: Nanomolar A25-35 alone does not cause persistent change in the basal level of calcium in astrocytes. However, even small amounts of A25-35, together with transmitters, can have substantial synergistic effects on intracellular calcium signals. Computational modeling further helps in understanding the mechanisms associated with intracellular calcium oscillations. Modeling the mechanisms is important, as astrocytes have an essential role in regulating the neuronal microenvironment of the central nervous system

PLoS One

Quantitative analysis of the vascular network anatomy is critical for the understanding of the vasculature structure and function. In this study, we have combined microcomputed tomography (microCT) and computational analysis to provide quantitative three-dimensional geometrical and topological characterization of the normal kidney vasculature, and to investigate how 2 core genes of the Wnt/planar cell polarity, Frizzled4 and Frizzled6, affect vascular network morphogenesis. Experiments were performed on frizzled4 (Fzd4-/-) and frizzled6 (Fzd6-/-) deleted mice and littermate controls (WT) perfused with a contrast medium after euthanasia and exsanguination. The kidneys were scanned with a high-resolution (16 μm) microCT imaging system, followed by 3D reconstruction of the arterial vasculature. Computational treatment includes decomposition of 3D networks based on Diameter-Defined Strahler Order (DDSO). We have calculated quantitative (i) Global scale parameters, such as the volume of the vasculature and its fractal dimension (ii) Structural parameters depending on the DDSO hierarchical levels such as hierarchical ordering, diameter, length and branching angles of the vessel segments, and (iii) Functional parameters such as estimated resistance to blood flow alongside the vascular tree and average density of terminal arterioles. In normal kidneys, fractal dimension was 2.07±0.11 (n = 7), and was significantly lower in Fzd4-/- (1.71±0.04; n = 4), and Fzd6-/- (1.54±0.09; n = 3) kidneys. The DDSO number was 5 in WT and Fzd4-/-, and only 4 in Fzd6-/-. Scaling characteristics such as diameter and length of vessel segments were altered in mutants, whereas bifurcation angles were not different from WT. Fzd4 and Fzd6 deletion increased vessel resistance, calculated using the Hagen-Poiseuille equation, for each DDSO, and decreased the density and the homogeneity of the distal vessel segments. Our results show that our methodology is suitable for 3D quantitative characterization of vascular networks, and that Fzd4 and Fzd6 genes have a deep patterning effect on arterial vessel morphogenesis that may determine its functional efficiency