Decoding of calcium oscillations by phosphorylation cycles: analytic results

Modulation of calcium signaling and metabolic pathways in endothelial cells with magnetic fields

Calcium signaling plays a crucial role in various physiological processes, including muscle contraction, cell division, and neurotransmitter release. Dysregulation of calcium levels and signaling has been linked to a range of pathological conditions such as neurodegenerative disorders, cardiovascular disease, and cancer. Here, we propose a theoretical model that predicts the modulation of calcium ion channel activity and calcium signaling in the endothelium through the application of either a time-varying or static gradient magnetic field (MF). This modulation is achieved by exerting magnetic forces or torques on either biogenic or non-biogenic magnetic nanoparticles that are bound to endothelial cell membranes. Since calcium signaling in endothelial cells induces neuromodulation and influences blood flow control, treatment with a magnetic field shows promise for regulating neurovascular coupling and treating vascular dysfunctions associated with aging and neurodegenerative disorders. Furthermore, magnetic treatment can enable control over the decoding of Ca signals, ultimately impacting protein synthesis. The ability to modulate calcium wave frequencies using MFs and the MF-controlled decoding of Ca signaling present promising avenues for treating diseases characterized by calcium dysregulation.

Extracellular ATP-induced calcium oscillations regulating the differentiation of osteoblasts through aerobic oxidation metabolism pathways

INTRODUCTION

The increase of ATP concentration in the extracellular space represents one of the effective signals that stimulate the physiological activities of cells when the bone is exposed to external mechanical stimulation such as stretching and shear stress force throughout life. However, the effects of ATP on osteoblast differentiation and related mechanisms are not well understood.

MATERIALS AND METHODS

In this study, the roles of extracellular ATP on osteoblast differentiation, intracellular calcium ([Ca2+]i) levels, metabolomics, and the expression of proteins related to energy metabolism were investigated.

RESULTS

Our results showed that 100 μM extracellular ATP initiated intracellular calcium ([Ca2+]i) oscillations via the calcium-sensing receptor (P2R) and promoted the differentiation of MC3T3-E1 cells. Metabolomics analysis showed that the differentiation of MC3T3-E1 cells depended on aerobic oxidation, but little glycolysis. Moreover, the differentiation of MC3T3-E1 cells and aerobic oxidation were suppressed with the inhibition of AMP-activated protein kinase (AMPK).

CONCLUSION

These results indicate that calcium oscillations triggered by extracellular ATP can activate aerobic oxidation through AMPK-related signaling pathways and thus promote osteoblast differentiation.

X-ray irradiation triggers immune response in human T-lymphocytes via store-operated Ca2+ entry and NFAT activation

Radiation therapy efficiently eliminates cancer cells and reduces tumor growth. To understand collateral agonistic and antagonistic effects of this treatment on the immune system, we examined the impact of x-ray irradiation on human T cells. We find that, in a major population of leukemic Jurkat T cells and peripheral blood mononuclear cells, clinically relevant radiation doses trigger delayed oscillations of the cytosolic Ca²⁺ concentration. They are generated by store-operated Ca²⁺ entry (SOCE) following x-ray–induced clustering of Orai1 and STIM1 and formation of a Ca²⁺ release–activated Ca²⁺ (CRAC) channel. A consequence of the x-ray–triggered Ca²⁺ signaling cascade is translocation of the transcription factor nuclear factor of activated T cells (NFAT) from the cytosol into the nucleus, where it elicits the expression of genes required for immune activation. The data imply activation of blood immune cells by ionizing irradiation, with consequences for toxicity and therapeutic effects of radiation therapy.

Decoding the Bell-Shaped Calcium Spikes in Phosphorylation Cycles of Flagella

We investigate the messenger role of calcium ions implicated in the regulation of wave-like bending dynamics of flagella. The emphasis is on microtubules of flagellar axoneme serving as nonlinear transmission lines for bell-shaped spikes of calcium ions. The calcium sensitive proteins, such as calmodulin, exhibit activation dependence on the spike train frequency and amplitude. Here, we analyze a Ca²⁺ decoding module IDA-I1 whose activity is controlled by Ca²⁺ activated kinase. We find that trains of Ca²⁺ spikes are advantageous compared to a constant rise in Ca²⁺ concentration as being more efficient and much less prone to noisy fluctuations.

A Hill type equation can predict target gene expression driven by p53 pulsing

Many factors determine target gene expression dynamics under p53 pulsing. In this study, I sought to determine the mechanism by which duration, frequency, binding affinity and maximal transcription rate affect the expression dynamics of target genes. Using an analytical method to solve a simple model, I found that the fold change of target gene expression increases relative to the number of p53 pulses, and the optimal frequency, 0.18 h-1 , from two real p53 pulses drives the maximal fold change with a decay rate of 0.18 h-1 . Moreover, p53 pulses may also lead to a higher fold change than sustained p53. Finally, I discovered that a Hill-type equation, including these effect factors, can characterise target gene expression. The average error between the theoretical predictions and experiments was 23%. Collectively, this equation advances the understanding of transcription factor dynamics, where duration and frequency play a significant role in the fine regulation of target gene expression with higher binding affinity.

Role of protons in calcium signaling

Thirty-six years after the publication of the important article by Busa and Nuccitelli on the variability of intracellular pH (pHi) and the interdependence of pHi and intracellular Ca2+ concentration ([Ca2+]i), little research has been carried out on pHi and calcium signaling. Moreover, the results appear to be contradictory. Some authors claim that the increase in [Ca2+]i is due to a reduction in pHi, others that it is caused by an increase in pHi. The reasons for these conflicting results have not yet been discussed and clarified in an exhaustive manner. The idea that variations in pHi are insignificant, because cellular buffers quickly stabilize the pHi, may be a limiting and fundamentally wrong concept. In fact, it has been shown that protons can move and react in the cell before they are neutralized. Variations in pHi have a remarkable impact on [Ca2+]i and hence on some of the basic biochemical mechanisms of calcium signaling. This paper focuses on the possible triggering role of protons during their short cellular cycle and it suggests a new hypothesis for an IP3 proton dependent mechanism of action.

The Oscillation Amplitude, Not the Frequency of Cytosolic Calcium, Regulates Apoptosis Induction

Although a rising concentration of cytosolic Ca²⁺ has long been recognized as an essential signal for apoptosis, the dynamical mechanisms by which Ca²⁺ regulates apoptosis are not clear yet. To address this, we constructed a computational model that integrates known biochemical reactions and can reproduce the dynamical behaviors of Ca²⁺-induced apoptosis as observed in experiments. Model analysis shows that oscillating Ca²⁺ signals first convert into gradual signals and eventually transform into a switch-like apoptotic response. Via the two processes, the apoptotic signaling pathway filters the frequency of Ca²⁺ oscillations effectively but instead responds acutely to their amplitude. Collectively, our results suggest that Ca²⁺ regulates apoptosis mainly via oscillation amplitude, rather than frequency, modulation. This study not only provides a comprehensive understanding of how oscillatory Ca²⁺ dynamically regulates the complex apoptotic signaling network but also presents a typical example of how Ca²⁺ controls cellular responses through amplitude modulation.

Ca2+ Release via IP3 Receptors Shapes the Cardiac Ca2+ Transient for Hypertrophic Signaling

Calcium (Ca²⁺) plays a central role in mediating both contractile function and hypertrophic signaling in ventricular cardiomyocytes. L-type Ca²⁺ channels trigger release of Ca²⁺ from ryanodine receptors for cellular contraction, whereas signaling downstream of G-protein-coupled receptors stimulates Ca²⁺ release via inositol 1,4,5-trisphosphate receptors (IP₃Rs), engaging hypertrophic signaling pathways. Modulation of the amplitude, duration, and duty cycle of the cytosolic Ca²⁺ contraction signal and spatial localization have all been proposed to encode this hypertrophic signal. Given current knowledge of IP₃Rs, we develop a model describing the effect of functional interaction (cross talk) between ryanodine receptor and IP₃R channels on the Ca²⁺ transient and examine the sensitivity of the Ca²⁺ transient shape to properties of IP₃R activation. A key result of our study is that IP₃R activation increases Ca²⁺ transient duration for a broad range of IP₃R properties, but the effect of IP₃R activation on Ca²⁺ transient amplitude is dependent on IP₃ concentration. Furthermore we demonstrate that IP₃-mediated Ca²⁺ release in the cytosol increases the duty cycle of the Ca²⁺ transient, the fraction of the cycle for which [Ca²⁺] is elevated, across a broad range of parameter values and IP₃ concentrations. When coupled to a model of downstream transcription factor (NFAT) activation, we demonstrate that there is a high correspondence between the Ca²⁺ transient duty cycle and the proportion of activated NFAT in the nucleus. These findings suggest increased cytosolic Ca²⁺ duty cycle as a plausible mechanism for IP₃-dependent hypertrophic signaling via Ca²⁺-sensitive transcription factors such as NFAT in ventricular cardiomyocytes.

IP3-Dependent Ca2+ Oscillations Switch into a Dual Oscillator Mechanism in the Presence of PLC-Linked Hormones

Ca2+ oscillations that depend on inositol-1,4,5-trisphosphate (IP3) have been ascribed to biphasic Ca2+ regulation of the IP3 receptor (IP3R) or feedback mechanisms controlling IP3 levels in different cell types. IP3 uncaging in hepatocytes elicits Ca2+ transients that are often localized at the subcellular level and increase in magnitude with stimulus strength. However, this does not reproduce the broad baseline-separated global Ca2+ oscillations elicited by vasopressin. Addition of hormone to cells activated by IP3 uncaging initiates a qualitative transition from high-frequency spatially disorganized Ca2+ transients, to low-frequency, oscillatory Ca2+ waves that propagate throughout the cell. A mathematical model with dual coupled oscillators that integrates Ca2+-induced Ca2+ release at the IP3R and mutual feedback mechanisms of cross-coupling between Ca2+ and IP3 reproduces this behavior. Thus, multiple Ca2+ oscillation modes can coexist in the same cell, and hormonal stimulation can switch from the simpler to the more complex to yield robust signaling.

Differential equation-based minimal model describing metabolic oscillations in Bacillus subtilis biofilms

Biofilms offer an excellent example of ecological interaction among bacteria. Temporal and spatial oscillations in biofilms are an emerging topic. In this paper, we describe the metabolic oscillations in Bacillus subtilis biofilms by applying the smallest theoretical chemical reaction system showing Hopf bifurcation proposed by Wilhelm and Heinrich in 1995. The system involves three differential equations and a single bilinear term. We specifically select parameters that are suitable for the biological scenario of biofilm oscillations. We perform computer simulations and a detailed analysis of the system including bifurcation analysis and quasi-steady-state approximation. We also discuss the feedback structure of the system and the correspondence of the simulations to biological observations. Our theoretical work suggests potential scenarios about the oscillatory behaviour of biofilms and also serves as an application of a previously described chemical oscillator to a biological system.

A Statistical View on Calcium Oscillations

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

Computational Modeling Reveals Frequency Modulation of Calcium-cAMP/PKA Pathway in Dendritic Spines

Dendritic spines are the primary excitatory postsynaptic sites that act as subcompartments of signaling. Ca²⁺ is often the first and most rapid signal in spines. Downstream of calcium, the cyclic adenosine monophosphate (cAMP)/protein kinase A (PKA) pathway plays a critical role in the regulation of spine formation, morphological modifications, and ultimately, learning and memory. Although the dynamics of calcium are reasonably well-studied, calcium-induced cAMP/PKA dynamics, particularly with respect to frequency modulation, are not fully explored. In this study, we present a well-mixed model for the dynamics of calcium-induced cAMP/PKA dynamics in dendritic spines. The model is constrained using experimental observations in the literature. Further, we measured the calcium oscillation frequency in dendritic spines of cultured hippocampal CA1 neurons and used these dynamics as model inputs. Our model predicts that the various steps in this pathway act as frequency modulators for calcium, and the high frequency of calcium input is filtered by adenylyl cyclase 1 and phosphodiesterases in this pathway such that cAMP/PKA only responds to lower frequencies. This prediction has important implications for noise filtering and long-timescale signal transduction in dendritic spines. A companion manuscript presents a three-dimensional spatial model for the same pathway.

On Information Extraction and Decoding Mechanisms Improved by Noisy Amplification in Signaling Pathways

The cells need to process information about extracellular stimuli. They encode, transmit and decode the information to elicit an appropriate response. Studies aimed at understanding how such information is decoded in the signaling pathways to generate a specific cellular response have become essential. Eukaryotic cells decode information through two different mechanisms: the feed-forward loop and the promoter affinity. Here, we investigate how these two mechanisms improve information transmission. A detailed comparison is made between the stochastic model of the MAPK/ERK pathway and a stochastic minimal decoding model. The maximal amount of transmittable information was computed. The results suggest that the decoding mechanism of the MAPK/ERK pathway improve the channel capacity because it behaves as a noisy amplifier. We show a positive dependence between the noisy amplification and the amount of information extracted. Additionally, we show that the extrinsic noise can be tuned to improve information transmission. This investigation has revealed that the feed-forward loop and the promoter affinity motifs extract information thanks to processes of amplification and noise addition. Moreover, the channel capacity is enhanced when both decoding mechanisms are coupled. Altogether, these findings suggest novel characteristics in how decoding mechanisms improve information transmission.

Memory in plants: Boolean modeling of the learning and store/recall memory functions in response to environmental stimuli

This paper presents a new model of memory functions in plants, which improves the previous approaches done by René Thomas and colleagues. We have decomposed the plant memory processing into three main functions: learning, storing and recalling. We propose as main mechanism for these three functions the occurrence of a calcium wave consecutive to an environmental stimulus, followed by the activation of specific genes and proteins changing their phosphorylated state. Feedback is ensured by Calcium Dependent Protein Kinases and oxidative phosphorylation.

Coding and decoding of oscillatory Ca2+ signals

About 30 years after their first observation, Ca²⁺ oscillations are now recognised as a universal mechanism of signal transduction. These oscillations are driven by periodic cycles of release and uptake of Ca²⁺ between the cytoplasm and the endoplasmic reticulum. Their frequency often increases with the level of stimulation, which can be decoded by some molecules. However, it is becoming increasingly evident that the widespread core oscillatory mechanism is modulated in many ways, depending on the cell type and on the physiological conditions. Interplay with inositol 1,4,5-trisphosphate metabolism and with other Ca²⁺ stores as the extracellular medium or mitochondria can much affect the properties of these oscillations. In many cases, these finely tuned characteristics of Ca²⁺ oscillations impact the physiological response that is triggered by the signal. Moreover, oscillations are intrinsically irregular. This randomness can also be exploited by the cell. In this review, we discuss evidences of these additional manifestations of the versatility of Ca²⁺ signalling.

An Information-Theoretical Approach for Calcium Signaling Specificity

Calcium is a key signaling agent in animals and plants. Its involvement in the regulation of a wide range of processes has led to the question of how calcium signals can activate stimulus-specific responses. We introduce a computational framework for studying intracellular calcium signaling using elements of information theory. We use mutual information to quantify the differential activation of proteins in response to different calcium signals to provide an operational definition of specificity. Using optimization procedures this framework allows us to explore the biochemical determinants of calcium decoding. We explore simple toy models and general binding kinetics approaches to demonstrate the utility and limitations of the proposed framework. Unravelling signaling specificity is key for understanding information processing within cells and for the future design of synthetic nanodevices for molecular communications.

Robustness of frequency vs. amplitude coding of calcium oscillations during changing temperatures

Intracellular calcium oscillations have been widely studied. It is assumed that information is conveyed in the frequency, amplitude and shape of these oscillations. In particular, calcium signalling in mammalian liver cells has repeatedly been reported to display frequency coding so that an increasing amount of stimulus is translated into an increasing frequency of the oscillations. However, recently, we have shown that calcium oscillations in fish liver cells rather exhibit amplitude coding with increasing stimuli being translated into increasing amplitudes. Practical consequences of this difference are unknown so far. Here we investigated advantages and disadvantages of frequency vs. amplitude coding, in particular in environments with substantially changing temperatures (e.g. 10-20 degrees). For this purpose, we use computational modelling and a new approach to generate a calcium model exactly displaying a specific frequency and/or amplitude. We conclude that despite the advantages in flexibility that frequencies might offer for the transmission of information in the cell, amplitude coding is obviously more robust with respect to changes in environmental temperatures. This potentially explains the observed differences between two classes of organisms, one operating at constant temperatures whereas the other is not.

Understanding non-linear effects from Hill-type dynamics with application to decoding of p53 signaling

Analytical equations are derived depicting four possible scenarios resulting from pulsed signaling of a system subject to Hill-type dynamics. Pulsed Hill-type dynamics involves the binding of multiple signal molecules to a receptor and occurs e.g., when transcription factor p53 orchestrates cancer prevention, during calcium signaling, and during circadian rhythms. The scenarios involve: (i) enhancement of high-affinity binders compared to low-affinity ones, (ii) slowing reactions involving high-affinity binders, (iii) transfer of the clocking of low-affinity binders from the signal molecule to the products, and (iv) a unique clocking process that produces incremental increases in the activity of high-affinity binders with each signal pulse. In principle, these mostly non-linear effects could control cellular outcomes. An applications to p53 signaling is developed, with binding to most gene promoters identified as category (iii) responses. However, currently unexplained enhancement of high-affinity promoters such as CDKN1a (p21) by pulsed signaling could be an example of (i). In general, provision for all possible scenarios is required in the design of mathematical models incorporating pulsed Hill-type signaling as some aspect.

Systems and synthetic biology approaches in understanding biological oscillators

Background

Self-sustained oscillations are a ubiquitous and vital phenomenon in living systems. From primitive single-cellular bacteria to the most sophisticated organisms, periodicities have been observed in a broad spectrum of biological processes such as neuron firing, heart beats, cell cycles, circadian rhythms, etc. Defects in these oscillators can cause diseases from insomnia to cancer. Elucidating their fundamental mechanisms is of great significance to diseases, and yet challenging, due to the complexity and diversity of these oscillators.

Results

Approaches in quantitative systems biology and synthetic biology have been most effective by simplifying the systems to contain only the most essential regulators. Here, we will review major progress that has been made in understanding biological oscillators using these approaches. The quantitative systems biology approach allows for identification of the essential components of an oscillator in an endogenous system. The synthetic biology approach makes use of the knowledge to design the simplest, de novo oscillators in both live cells and cell-free systems. These synthetic oscillators are tractable to further detailed analysis and manipulations.

Conclusion

With the recent development of biological and computational tools, both approaches have made significant achievements.

Mesenchymal stem cell differentiation: Control by calcium-activated potassium channels

Mesenchymal stem cells (MSCs) are widely used in modern medicine for which understanding the mechanisms controlling their differentiation is fundamental. Ion channels offer novel insights to this process because of their role in modulating membrane potential and intracellular milieu. Here, we evaluate the contribution of calcium-activated potassium (K_Ca ) channels to the three main components of MSC differentiation: initiation, proliferation, and migration. First, we demonstrate the importance of the membrane potential (V_m ) and the apparent association of hyperpolarization with differentiation. Of K_Ca subtypes, most evidence points to activity of big-conductance channels in inducing initiation. On the other hand, intermediate-conductance currents have been shown to promote progression through the cell cycle. While there is no information on the role of K_Ca channels in migration of MSCs, work from other stem cells and cancer cells suggest that intermediate-conductance and to a lesser extent big-conductance channels drive migration. In all cases, these effects depend on species, tissue origin and lineage. Finally, we present a conceptual model that demonstrates how K_Ca activity could influence differentiation by regulating V_m and intracellular Ca²⁺ oscillations. We conclude that K_Ca channels have significant involvement in MSC differentiation and could potentially enable novel tissue engineering approaches and therapies.

Validation of electrical stimulation models: intracellular calcium measurement in three-dimensional scaffolds

Peripheral nerve injury can be disabling. Regeneration is limited by the rate of axonal extension, and proximal injury to peripheral nerves can take over a year to reach target organs. Electrical stimulation (ES) has been shown to increase the rate of neurite growth, though the mechanism is not yet well understood. In our prior manuscript, we developed a computational model that demonstrates how ES can functionally elevate intracellular calcium concentration ([Ca²⁺]_i) based on ES intensity and duration. In this article, we validate the computation model for the [Ca²⁺]_i changes in neuron soma. Embryonic chicken dorsal root ganglion cells were suspended in 3-dimensional collagen scaffolds. Fura-2 was used to measure [Ca²⁺]_i in response to biphasic ES pulses ranging from 70 to 60,000 V/m in intensity and from 10 µs to 100 ms in duration. The computational model most closely matched the experimental data of the neurons with the highest [Ca²⁺]_i elevation for ES pulses 100 µs or greater in duration. Nickel (200 µM) and cadmium (200 µM) blocked 98-99% of the [Ca²⁺]_i rise, indicating that the rise in [Ca²⁺]_i in response to ES is via voltage-dependent calcium channels. The average [Ca²⁺]_i rise in response to ES was about one-tenth of the peak rise. Therefore, the computational model is validated for elevating [Ca²⁺]_i of neurons and can be used as a tool for designing efficacious ES protocols for improving neuronal regeneration.NEW & NOTEWORTHY Electrical stimulation is used to enhance neuron growth, and the role of neuronal intracellular calcium concentration ([Ca²⁺]_i) is an area of research interest. Widely varying stimulation parameters in the literature make it difficult to compare stimulation protocols. The results in this manuscript are the first to show neuronal [Ca²⁺]_i in response to a broad and defined range of electrical pulse durations and intensities. These results validate our previously published novel computational model of [Ca²⁺]_i.

Calcium Oscillation Frequency-Sensitive Gene Regulation and Homeostatic Compensation in Pancreatic β-Cells

Pancreatic islet [Formula: see text]-cells are electrically excitable cells that secrete insulin in an oscillatory fashion when the blood glucose concentration is at a stimulatory level. Insulin oscillations are the result of cytosolic [Formula: see text] oscillations that accompany bursting electrical activity of [Formula: see text]-cells and are physiologically important. ATP-sensitive [Formula: see text] channels (K(ATP) channels) play the key role in setting the overall activity of the cell and in driving bursting, by coupling cell metabolism to the membrane potential. In humans, when there is a defect in K(ATP) channel function, [Formula: see text]-cells fail to respond appropriately to changes in the blood glucose level, and electrical and [Formula: see text] oscillations are lost. However, mice compensate for K(ATP) channel defects in islet [Formula: see text]-cells by employing alternative mechanisms to maintain electrical and [Formula: see text] oscillations. In a recent study, we showed that in mice islets in which K(ATP) channels are genetically knocked out another [Formula: see text] current, provided by inward-rectifying [Formula: see text] channels, is increased. With mathematical modeling, we demonstrated that a sufficient upregulation in these channels can account for the paradoxical electrical bursting and [Formula: see text] oscillations observed in these [Formula: see text]-cells. However, the question of determining the correct level of upregulation that is necessary for this compensation remained unanswered, and this question motivates the current study. [Formula: see text] is a well-known regulator of gene expression, and several examples have been shown of genes that are sensitive to the frequency of the [Formula: see text] signal. In this mathematical modeling study, we demonstrate that a [Formula: see text] oscillation frequency-sensitive gene transcription network can adjust the gene expression level of a compensating [Formula: see text] channel so as to rescue electrical bursting and [Formula: see text] oscillations in a model [Formula: see text]-cell in which the key K(ATP) current is removed. This is done without the prescription of a target [Formula: see text] level, but evolves naturally as a consequence of the feedback between the [Formula: see text]-dependent enzymes and the cell's electrical activity. More generally, the study indicates how [Formula: see text] can provide the link between gene expression and cellular electrical activity that promotes wild-type behavior in a cell following gene knockout.

Optogenetic Immunomodulation: Shedding Light on Antitumor Immunity

Microbial opsin-based optogenetic tools have been transformative for neuroscience. To extend optogenetic approaches to the immune system to remotely control immune responses with superior spatiotemporal precision, pioneering tools have recently been crafted to modulate lymphocyte trafficking, inflammasome activation, dendritic cell (DC) maturation, and antitumor immunity through the photoactivation of engineered chemokine receptors and calcium release-activated calcium channels. We highlight herein some conceptual design strategies for installing light sensitivities into the immune signaling network and, in parallel, we propose potential solutions for in vivo optogenetic applications in living organisms with near-infrared light-responsive upconversion nanomaterials. Moreover, to move beyond proof-of-concept into translational applications, we discuss future prospects for integrating personalized immunoengineering with optogenetics to overcome critical hurdles in cancer immunotherapy.

Optogenetic Control of Calcium Oscillation Waveform Defines NFAT as an Integrator of Calcium Load

It is known that the calcium-dependent transcription factor NFAT initiates transcription in response to pulsatile loads of calcium signal. However, the relative contributions of calcium oscillation frequency, amplitude, and duty cycle to transcriptional activity remain unclear. Here, we engineer HeLa cells to permit optogenetic control of intracellular calcium concentration using programmable LED arrays. This approach allows us to generate calcium oscillations of constant peak amplitude, in which frequency is varied while holding duty cycle constant, or vice versa. Using this setup and mathematical modeling, we show that NFAT transcriptional activity depends more on duty cycle, defined as the proportion of the integrated calcium concentration over the oscillation period, than on frequency alone. This demonstrates that NFAT acts primarily as a signal integrator of cumulative load rather than a frequency-selective decoder. This approach resolves a fundamental question in calcium encoding and demonstrates the value of optogenetics for isolating individual dynamical components of larger signaling behaviors.

Encoding and decoding time in neural development

The development of a multicellular organism involves time-dependent changes in molecular and cellular states; therefore 'time' is an indispensable mathematical parameter of ontogenesis. Regardless of their inextricable relationship, there is a limited number of events for which the output of developmental phenomena primarily uses temporal cues that are generated through multilevel interactions between molecules, cells, and tissues. In this review, we focus on neural stem cells, which serve as a faithful decoder of temporal cues to transmit biological information and generate specific output in the developing nervous system. We further explore the identity of the temporal information that is encoded in neural development, and how this information is decoded into various cellular fate decisions.

Endothelial mitochondria regulate the intracellular Ca2+ response to fluid shear stress

Shear stress is known to stimulate an intracellular free calcium concentration ([Ca(2+)]i) response in vascular endothelial cells (ECs). [Ca(2+)]i is a key second messenger for signaling that leads to vasodilation and EC survival. Although it is accepted that the shear-induced [Ca(2+)]i response is, in part, due to Ca(2+) release from the endoplasmic reticulum (ER), the role of mitochondria (second largest Ca(2+) store) is unknown. We hypothesized that the mitochondria play a role in regulating [Ca(2+)]i in sheared ECs. Cultured ECs, loaded with a Ca(2+)-sensitive fluorophore, were exposed to physiological levels of shear stress. Shear stress elicited [Ca(2+)]i transients in a percentage of cells with a fraction of them displaying oscillations. Peak magnitudes, percentage of oscillating ECs, and oscillation frequencies depended on the shear level. [Ca(2+)]i transients/oscillations were present when experiments were conducted in Ca(2+)-free solution (plus lanthanum) but absent when ECs were treated with a phospholipase C inhibitor, suggesting that the ER inositol 1,4,5-trisphosphate receptor is responsible for the [Ca(2+)]i response. Either a mitochondrial uncoupler or an electron transport chain inhibitor, but not a mitochondrial ATP synthase inhibitor, prevented the occurrence of transients and especially inhibited the oscillations. Knockdown of the mitochondrial Ca(2+) uniporter also inhibited the shear-induced [Ca(2+)]i transients/oscillations compared with controls. Hence, EC mitochondria, through Ca(2+) uptake/release, regulate the temporal profile of shear-induced ER Ca(2+) release. [Ca(2+)]i oscillation frequencies detected were within the range for activation of mechanoresponsive kinases and transcription factors, suggesting that dysfunctional EC mitochondria may contribute to cardiovascular disease by deregulating the shear-induced [Ca(2+)]i response.

Computational modeling of neurons: intensity-duration relationship of extracellular electrical stimulation for changes in intracellular calcium

In many instances of extensive nerve damage, the injured nerve never adequately heals, leaving lack of nerve function. Electrical stimulation (ES) has been shown to increase the rate and orient the direction of neurite growth, and is a promising therapy. However, the mechanism in which ES affects neuronal growth is not understood, making it difficult to compare existing ES protocols or to design and optimize new protocols. We hypothesize that ES acts by elevating intracellular calcium concentration ([Ca(2+)]i) via opening voltage-dependent Ca(2+) channels (VDCCs). In this work, we have created a computer model to estimate the ES Ca(2+) relationship. Using COMSOL Multiphysics, we modeled a small dorsal root ganglion (DRG) neuron that includes one Na(+) channel, two K(+) channels, and three VDCCs to estimate [Ca(2+)]i in the soma and growth cone. As expected, the results show that an ES that generates action potentials (APs) can efficiently raise the [Ca(2+)]i of neurons. More interestingly, our simulation results show that sub-AP ES can efficiently raise neuronal [Ca(2+)]i and that specific high-voltage ES can preferentially raise [Ca(2+)]i in the growth cone. The intensities and durations of ES on modeled growth cone calcium rise are consistent with directionality and orientation of growth cones experimentally shown by others. Finally, this model provides a basis to design experimental ES pulse parameters, including duration, intensity, pulse-train frequency, and pulse-train duration to efficiently raise [Ca(2+)]i in neuronal somas or growth cones.

Differential Regulation of Multiple Steps in Inositol 1,4,5-Trisphosphate Signaling by Protein Kinase C Shapes Hormone-stimulated Ca2+ Oscillations

How Ca(2+) oscillations are generated and fine-tuned to yield versatile downstream responses remains to be elucidated. In hepatocytes, G protein-coupled receptor-linked Ca(2+) oscillations report signal strength via frequency, whereas Ca(2+) spike amplitude and wave velocity remain constant. IP3 uncaging also triggers oscillatory Ca(2+) release, but, in contrast to hormones, Ca(2+) spike amplitude, width, and wave velocity were dependent on [IP3] and were not perturbed by phospholipase C (PLC) inhibition. These data indicate that oscillations elicited by IP3 uncaging are driven by the biphasic regulation of the IP3 receptor by Ca(2+), and, unlike hormone-dependent responses, do not require PLC. Removal of extracellular Ca(2+) did not perturb Ca(2+) oscillations elicited by IP3 uncaging, indicating that reloading of endoplasmic reticulum stores via plasma membrane Ca(2+) influx does not entrain the signal. Activation and inhibition of PKC attenuated hormone-induced Ca(2+) oscillations but had no effect on Ca(2+) increases induced by uncaging IP3. Importantly, PKC activation and inhibition differentially affected Ca(2+) spike frequencies and kinetics. PKC activation amplifies negative feedback loops at the level of G protein-coupled receptor PLC activity and/or IP3 metabolism to attenuate IP3 levels and suppress the generation of Ca(2+) oscillations. Inhibition of PKC relieves negative feedback regulation of IP3 accumulation and, thereby, shifts Ca(2+) oscillations toward sustained responses or dramatically prolonged spikes. PKC down-regulation attenuates phenylephrine-induced Ca(2+) wave velocity, whereas responses to IP3 uncaging are enhanced. The ability to assess Ca(2+) responses in the absence of PLC activity indicates that IP3 receptor modulation by PKC regulates Ca(2+) release and wave velocity.

The functional contribution of calcium ion flux heterogeneity in T cells

The role of intracellular calcium ion oscillations in T-cell physiology is being increasingly appreciated by studies that describe how unique temporal and spatial calcium ion signatures can control different signalling pathways. Within this review, we provide detailed mechanisms of calcium ion oscillations, and emphasise the pivotal role that calcium signalling plays in directing crucial events pertaining to T-cell functionality. We also describe methods of calcium ion quantification, and take the opportunity to discuss how a deeper understanding of calcium signalling combined with new detection and quantification methodologies can be used to better design immunotherapies targeting T-cell responses.

The interplay between plasma membrane and endoplasmic reticulum Ca(2+)ATPases in agonist-induced temporal Ca(2+) dynamics

A change in the intracellular free Ca(2+) concentration ([Ca(2+)]i) functions as a transmitter for signal transduction and shows a broad temporal pattern. Even genetically homogeneous cell types show different Ca(2+) response patterns under permanent agonist stimulation. In Ca(2+) signaling, the dynamics of the Ca(2+) release from the Ca(2+) channels during continuous agonist stimulation and the simultaneous effect of the pumps are unclear. In this study, the dynamic interaction of the Ca(2+) ATPases in the plasma membrane (PMCA) and the endoplasmic reticulum membrane (SERCA) during continuous ACh stimulation is monitored using Fluo-3 and Fura-2 loaded HEK 293 cells. We characterize Ca(2+) release patterns at the sub-maximal and maximal stimulation doses in the absence of extracellular Ca(2+). We analyze the responses regarding their types, oscillation frequency and response times. La(3+) (PMCA blocker) do not change the frequency and time courses in sub-maximal ACh treatment, while with the maximal stimulation oscillation frequency increase as oscillations superimpose on robust release, and response time of [Ca(2+)]i is elongated. A similar effect of La(3+) is observed in quantal Ca(2+) release phenomenon. In the presence of CPA, a SERCA blocker, oscillations are completely abolished, but response time does not change. We also observe that during continuous receptor stimulation, Ca(2+) release do not cease. These data may suggest that Ca(2+) release continues during agonist stimulation, but SERCA and PMCA form a new steady state and return [Ca(2+)]i to its physiological concentration.

Modeling the intracellular organization of calcium signaling

Calcium (Ca²⁺) is a key signaling ion that plays a fundamental role in many cellular processes in most types of tissues and organisms. The versatility of this signaling pathway is remarkable. Depending on the cell type and the stimulus, intracellular Ca²⁺ increases can last over different periods, as short spikes or more sustained signals. From a spatial point of view, they can be localized or invade the whole cell. Such a richness of behaviors is possible thanks to numerous exchange processes with the external medium or internal Ca²⁺ pools, mainly the endoplasmic or sarcoplasmic reticulum and mitochondria. These fluxes are also highly regulated. In order to get an accurate description of the spatiotemporal organization of Ca²⁺ signaling, it is useful to resort to modeling. Thus, each flux can be described by an appropriate kinetic expression. Ca²⁺ dynamics in a given cell type can then be simulated by a modular approach, consisting of the assembly of computational descriptions of the appropriate fluxes and regulations. Modeling can also be used to get insight into the mechanisms of decoding of the Ca²⁺ signals responsible for cellular responses. Cells can use frequency or amplitude coding, as well as take profit of Ca²⁺ oscillations to increase their sensitivity to small average Ca²⁺ increases.

Calcium-dependent regulation of glucose homeostasis in the liver

A major role of the liver is to integrate multiple signals to maintain normal blood glucose levels. The balance between glucose storage and mobilization is primarily regulated by the counteracting effects of insulin and glucagon. However, numerous signals converge in the liver to ensure energy demand matches the physiological status of the organism. Many circulating hormones regulate glycogenolysis, gluconeogenesis and mitochondrial metabolism by calcium-dependent signaling mechanisms that manifest as cytosolic Ca(2+) oscillations. Stimulus-strength is encoded in the Ca(2+) oscillation frequency, and also by the range of intercellular Ca(2+) wave propagation in the intact liver. In this article, we describe how Ca(2+) oscillations and waves can regulate glucose output and oxidative metabolism in the intact liver; how multiple stimuli are decoded though Ca(2+) signaling at the organ level, and the implications of Ca(2+) signal dysregulation in diseases such as metabolic syndrome and non-alcoholic fatty liver disease.

Functional inositol 1,4,5-trisphosphate receptors assembled from concatenated homo- and heteromeric subunits

Vertebrate genomes code for three subtypes of inositol 1,4,5-trisphosphate (IP3) receptors (IP3R1, -2, and -3). Individual IP3R monomers are assembled to form homo- and heterotetrameric channels that mediate Ca(2+) release from intracellular stores. IP3R subtypes are regulated differentially by IP3, Ca(2+), ATP, and various other cellular factors and events. IP3R subtypes are seldom expressed in isolation in individual cell types, and cells often express different complements of IP3R subtypes. When multiple subtypes of IP3R are co-expressed, the subunit composition of channels cannot be specifically defined. Thus, how the subunit composition of heterotetrameric IP3R channels contributes to shaping the spatio-temporal properties of IP3-mediated Ca(2+) signals has been difficult to evaluate. To address this question, we created concatenated IP3R linked by short flexible linkers. Dimeric constructs were expressed in DT40-3KO cells, an IP3R null cell line. The dimeric proteins were localized to membranes, ran as intact dimeric proteins on SDS-PAGE, and migrated as an ∼1100-kDa band on blue native gels exactly as wild type IP3R. Importantly, IP3R channels formed from concatenated dimers were fully functional as indicated by agonist-induced Ca(2+) release. Using single channel "on-nucleus" patch clamp, the channels assembled from homodimers were essentially indistinguishable from those formed by the wild type receptor. However, the activity of channels formed from concatenated IP3R1 and IP3R2 heterodimers was dominated by IP3R2 in terms of the characteristics of regulation by ATP. These studies provide the first insight into the regulation of heterotetrameric IP3R of defined composition. Importantly, the results indicate that the properties of these channels are not simply a blend of those of the constituent IP3R monomers.

Asymmetric distribution of dynamic calcium signals in the node of mouse embryo during left-right axis formation

In the node of mouse embryo, rotational movements of cilia generate an external liquid flow known as nodal flow, which determines left-right asymmetric gene expression. How nodal flow is converted into asymmetric gene expression is still controversial, but the increase of Ca(2+) levels in endodermal cells to the left of the node has been proposed to play a role. However, Ca(2+) signals inside the node itself have not yet been described. By our optimized Ca(2+) imaging method, we were able to observe dynamic Ca(2+) signals in the node in live mouse embryos. Pharmacological disruption of Ca(2+) signals did not affect ciliary movements or nodal flow, but did alter the expression patterns of the Nodal and Cerl-2 genes. Quantitative analyses of Ca(2+) signal frequencies and distributions showed that during left-right axis establishment, formerly symmetric Ca(2+) signals became biased to the left side. In iv/iv mutant embryos that showed randomized laterality due to ciliary immotility, Ca(2+) signals were found to be variously left-sided, right-sided, or bilateral, and thus symmetric on average. In Pkd2 mutant embryos, which lacked polycystin-2, a Ca(2+)-permeable cation channel necessary for left-right axis formation, the Ca(2+) signal frequency was lower than in wild-type embryos. Our data support a model in which dynamic Ca(2+) signals in the node are involved in left-right patterning.

Visualizing Ca(2+) signatures in plants

Ca(2+) is a key player in an astonishing variety of plant signal transduction pathways where transient, spiking or oscillatory changes in cytosolic Ca(2+) levels help to couple environmental or developmental cues to appropriate cellular responses. Understanding whether and how much Ca(2+) signaling contributes to defining stimulus-response specificity has long been a challenge, but recent work has provided strong evidence that specific information can indeed be encoded in the spatiotemporal characteristics of Ca(2+) signals. Identification of the Ca(2+) binding proteins that transduce Ca(2+) signals by regulating downstream effector proteins has revealed a complex network of Ca(2+) sensor families, of which some members show distinct patterns of expression and subcellular localization. By utilizing genetically encoded fluorescent Ca(2+) probes to monitor Ca(2+) changes at high spatiotemporal resolution, it is now possible to explore whether such spatial heterogeneities in Ca(2+) sensor distribution are coordinated with subcellular microdomains of Ca(2+) signaling. Such visualization of Ca(2+) signaling will also help to address which cellular compartments and transporters contribute to mobilizing and sequestering Ca(2+) and thus define stimulus-specific Ca(2+) signatures.

Modelling auxin efflux carrier phosphorylation and localization

Regulation of the activity and localization of PIN-FORMED (PIN) membrane proteins, which facilitate efflux of the plant hormone auxin from cells, is important for plants to respond to environmental stimuli and to develop new organs. The protein kinase PINOID (PID) is involved in regulating PIN phosphorylation, and this is thought to affect PIN localization by biasing recycling towards shootwards (apical) (rather than rootwards (basal)) membrane domains. PID has been observed to undergo transient internalization following auxin treatment, and it has been suggested that this may be a result of calcium-dependent sequestration of PID by the calcium-binding protein TOUCH3 (TCH3). We present a mathematical formulation of these processes and examine the resulting steady-state and time-dependent behaviours in response to transient increases in cytosolic calcium. We further combine this model with one for the recycling of PINs in polarized cells and also examine its behaviour. The results provide insight into the behaviour observed experimentally and provide the basis for subsequent studies of the tissue-level implications of these subcellular processes for phenomena such as gravitropism.

Spatial distribution and dose-response relationship for different operation modes in a reaction-diffusion model of the MAPK cascade

The mitogen-activated protein kinase (MAPK) cascade plays a critical role in the control of cell growth. Deregulation of this pathway contributes to the development of many cancers. To better understand its signal transduction, we constructed a reaction-diffusion model for the MAPK pathway. We modeled the three layers of phosphorylation-dephosphorylation reactions and diffusion processes from the cell membrane to the nucleus. Based on different types of feedback in the MAPK cascade, four operation modes are introduced. For each of the four modes, spatial distributions and dose-response curves of active kinases (i.e. ppMAPK) are explored by numerical simulation. The effects of propagation length, diffusion coefficient and feedback strength on the pathway dynamics are investigated. We found that intrinsic bistability in the MAPK cascade can generate a traveling wave of ppMAPK with constant amplitude when the propagation length is short. ppMAPK in this mode of intrinsic bistability decays more slowly than it does in all other modes as the propagation length increases. Moreover, we examined the global and local responses to Ras-GTP of these four modes, and demonstrated how the shapes of these dose-response curves change as the propagation length increases. Also, we found that larger diffusion constant gives a higher response level on the zero-order regime and makes the ppMAPK profiles flatter under strong Ras-GTP stimulus. Furthermore, we observed that spatial responses of ppMAPK are more sensitive to negative feedback than to positive feedback in the broader signal range. Finally, we showed how oscillatory signals pass through the kinase cascade, and found that high frequency signals are damped faster than low frequency ones.

Cumulated Ca2+ spike duration underlies Ca2+ oscillation frequency-regulated NFκB transcriptional activity

[Ca2+]i oscillations drive downstream events, like transcription, in a frequency-dependent manner. Why [Ca2+]i oscillation frequency regulates transcription has not been clearly revealed. A variation in [Ca2+]i oscillation frequency apparently leads to a variation in the time duration of cumulated [Ca2+]i elevations or cumulated [Ca2+]i spike duration. By manipulating [Ca2+]i spike duration, we generated a series of [Ca2+]i oscillations with the same frequency but different cumulated [Ca2+]i spike durations, as well as [Ca2+]i oscillations with the different frequencies but the same cumulated [Ca2+]i spike duration. Molecular assays demonstrated that, when generated in ‘artificial’ models alone, under physiologically simulated conditions or repetitive pulses of agonist exposure, [Ca2+]i oscillation regulates NFκB transcriptional activity, phosphorylation of IκBα and Ca2+-dependent gene expression all in a way actually dependent on cumulated [Ca2+]i spike duration whether or not frequency varies. This study underlines that [Ca2+]i oscillation frequency regulates NFκB transcriptional activity through cumulated [Ca2+]i spike-duration-mediated IκBα phosphorylation.

Microdomain organization and frequency-dependence of CREB-dependent transcriptional signaling in heart cells

Voltage-gated Ca(v)1.2 calcium channels couple membrane depolarization to cAMP response-element-binding protein (CREB)-dependent transcriptional activation. To investigate the spatial and temporal organization of CREB-dependent transcriptional nuclear microdomains, we combined perforated patch-clamp technique and FRET microscopy for monitoring CREB and CREB-binding protein interaction in the nuclei of live cells. The experimental approach to the quantitative assessment of CREB-dependent transcriptional signaling evoked by cAMP- and Ca(v)1.2-dependent mechanisms was devised in COS1 cells expressing recombinant Ca(v)1.2 calcium channels. Using continuous 2-dimensional wavelet transform and time series analyses, we found that nuclear CREB-dependent transcriptional signaling is organized differentially in spatially and temporally separated microdomains of 4 distinct types. In rat neonatal cardiomyocytes, CREB-dependent transcription is mediated by the cAMP-initiated CaMKII-sensitive and Ca(v)1.2-initiated CaMKII-insensitive mechanisms. The latter microdomains show a tendency to exhibit periodic behavior correlated with spontaneous contraction of myocytes suggestive of frequency-dependent CREB-dependent transcriptional regulation in the heart.

Derivation of Ca2+ signals from puff properties reveals that pathway function is robust against cell variability but sensitive for control

Ca(2+) is a universal second messenger in eukaryotic cells transmitting information through sequences of concentration spikes. A prominent mechanism to generate these spikes involves Ca(2+) release from the endoplasmic reticulum Ca(2+) store via inositol 1,4,5-trisphosphate (IP(3))-sensitive channels. Puffs are elemental events of IP(3)-induced Ca(2+) release through single clusters of channels. Intracellular Ca(2+) dynamics are a stochastic system, but a complete stochastic theory has not been developed yet. We formulate the theory in terms of interpuff interval and puff duration distributions because, unlike the properties of individual channels, they can be measured in vivo. Our theory reproduces the typical spectrum of Ca(2+) signals like puffs, spiking, and bursting in analytically treatable test cases as well as in more realistic simulations. We find conditions for spiking and calculate interspike interval (ISI) distributions. Signal form, average ISI and ISI distributions depend sensitively on the details of cluster properties and their spatial arrangement. In contrast to that, the relation between the average and the standard deviation of ISIs does not depend on cluster properties and cluster arrangement and is robust with respect to cell variability. It is controlled by the global feedback processes in the Ca(2+) signaling pathway (e.g., via IP(3)-3-kinase or endoplasmic reticulum depletion). That relation is essential for pathway function because it ensures frequency encoding despite the randomness of ISIs and determines the maximal spike train information content. Hence, we find a division of tasks between global feedbacks and local cluster properties that guarantees robustness of function while maintaining sensitivity of control of the average ISI.

Understanding the temporal codes of intra-cellular signals

The health of organisms and cells depends on appropriate responses to diverse internal and external cues, stimuli, or challenges, such as changes in hormone or cytokine levels, or exposure to a pathogen. Cellular responses must be tailored to the identity and intensity of the stimulus and therefore intra-cellular signals must carry information about both. However, signaling mediators often form intricate networks that react to multiple stimuli yet manage to produce stimulus-specific responses. The multi-functionality ('functional pleiotropism') of signaling nodes suggests that biological networks have evolved ways of passing physiologically relevant stimulus information through shared channels. Increasing evidence supports the notion that this is achieved in part through temporal regulation of signaling mediators' activities. The present challenge is to identify the features of temporal activity profile that represent information about a given stimulus and understand how cells read the temporal codes to control their responses.

Using Jensen's inequality to explain the role of regular calcium oscillations in protein activation

Oscillations of cytosolic Ca(2 +) are very important for cellular signalling in excitable and non-excitable cells. The information of various extracellular stimuli is encoded into oscillating patterns of Ca(2 +) that subsequently lead to the activation of different Ca(2 +)-sensitive target proteins in the cell. The question remains, however, why this information is transmitted by means of an oscillating rather than a constant signal. Here we show that, in fact, Ca(2 +) oscillations can achieve a better activation of target proteins than a comparable constant signal with the same amount of Ca(2 +) used. For this we use Jensen's inequality that describes the relation between the function value of the average of a set of argument values and the average of the function values of the arguments from that set. We analyse the role of the cooperativity of the binding of Ca(2 +) and of zero-order ultrasensitivity, which are two properties that are often observed in experiments on the activation of Ca(2 +)-sensitive target proteins. Our results apply to arbitrary oscillation shapes and a very general decoding model, thus generalizing the observations of several previous studies. We compare our results with data from experimental studies investigating the activation of nuclear factor of activated T cells (NFAT) and Ras by oscillatory and constant signals. Although we are restricted to specific approximations due to the lack of detailed kinetic data, we find good qualitative agreement with our theoretical predictions.

Design and analysis of molecular relay channels: an information theoretic approach

In this paper, we consider a molecular relay channel in which signal molecules are transmitted by a sender of communication, propagated, amplified, removed in the channel, and sensed by the receiver of communication that decodes the signal molecules. To understand and characterize the communication capacity of the molecular relay channel, we develop an information communication model that consists of the transmitter, channel, and receiver. Mutual information is used to quantify the amount of information that is transfered from the transmitter through the channel to the receiver. The method employed and results presented in this paper may help elucidate design principles of biological systems as well as help in the design and engineering of synthetic biological systems from the perspective of information theory.