Phase-locked signals elucidate circuit architecture of an oscillatory pathway

Modeling of Endothelial Calcium Responses within a Microfluidic Generator of Spatio-Temporal ATP and Shear Stress Signals

Intracellular calcium dynamics play essential roles in the proper functioning of cellular activities. It is a well known important chemosensing and mechanosensing process regulated by the spatio-temporal microenvironment. Nevertheless, how spatio-temporal biochemical and biomechanical stimuli affect calcium dynamics is not fully understood and the underlying regulation mechanism remains missing. Herein, based on a developed microfluidic generator of biochemical and biomechanical signals, we theoretically analyzed the generation of spatio-temporal ATP and shear stress signals within the microfluidic platform and investigated the effect of spatial combination of ATP and shear stress stimuli on the intracellular calcium dynamics. The simulation results demonstrate the capacity and flexibility of the microfluidic system in generating spatio-temporal ATP and shear stress. Along the transverse direction of the microchannel, dynamic ATP signals of distinct amplitudes coupled with identical shear stress are created, which induce the spatio-temporal diversity in calcium responses. Interestingly, to the multiple combinations of stimuli, the intracellular calcium dynamics reveal two main modes: unimodal and oscillatory modes, showing significant dependence on the features of the spatio-temporal ATP and shear stress stimuli. The present study provides essential information for controlling calcium dynamics by regulating spatio-temporal biochemical and biomechanical stimuli, which shows the potential in directing cellular activities and understanding the occurrence and development of disease.

A review on microfluidics manipulation of the extracellular chemical microenvironment and its emerging application to cell analysis

Spatiotemporal manipulation of extracellular chemical environments with simultaneous monitoring of cellular responses plays an essential role in exploring fundamental biological processes and expands our understanding of underlying mechanisms. Despite the rapid progress and promising successes in manipulation strategies, many challenges remain due to the small size of cells and the rapid diffusion of chemical molecules. Fortunately, emerging microfluidic technology has become a powerful approach for precisely controlling the extracellular chemical microenvironment, which benefits from its integration capacity, automation, and high-throughput capability, as well as its high resolution down to submicron. Here, we summarize recent advances in microfluidics manipulation of the extracellular chemical microenvironment, including the following aspects: i) Spatial manipulation of chemical microenvironments realized by convection flow-, diffusion-, and droplet-based microfluidics, and surface chemical modification; ii) Temporal manipulation of chemical microenvironments enabled by flow switching/shifting, moving/flowing cells across laminar flows, integrated microvalves/pumps, and droplet manipulation; iii) Spatiotemporal manipulation of chemical microenvironments implemented by a coupling strategy and open-space microfluidics; and iv) High-throughput manipulation of chemical microenvironments. Finally, we briefly present typical applications of the above-mentioned technical advances in cell-based analyses including cell migration, cell signaling, cell differentiation, multicellular analysis, and drug screening. We further discuss the future improvement of microfluidics manipulation of extracellular chemical microenvironments to fulfill the needs of biological and biomedical research and applications.

Synchronization of pancreatic islets by periodic or non-periodic muscarinic agonist pulse trains

Pulsatile insulin secretion into the portal vein from the many pancreatic islets of Langerhans is critical for efficient glucose homeostasis. The islets are themselves endogenous oscillators, but since they are not physically coupled it is not obvious how their oscillations are synchronized across the pancreas. It has been proposed that synchronization of islets is achieved through periodic activity of intrapancreatic ganglia, and indeed there are data supporting this proposal. Postganglionic nerves are cholinergic, and their product, acetylcholine, can influence islet β-cells through actions on M₃ muscarinic receptors which are coupled to G_q type G-proteins. In addition, the neurons secrete several peptide hormones that act on β-cell receptors. The data supporting synchronization via intrapancreatic ganglia are, however, limited. In particular, it has not been shown that trains of muscarinic pulses are effective at synchronizing islets in vitro. Also, if as has been suggested, there is a ganglionic pacemaker driving islets to a preferred frequency, no neural circuitry for this pacemaker has been identified. In this study, both points are addressed using a microfluidic system that allows for the pulsed application of the muscarinic agonist carbachol. We find that murine islets are entrained and synchronized over a wide range of frequencies when the carbachol pulsing is periodic, adding support to the hypothesis that ganglia can synchronize islets in vivo. We also find that islet synchronization is very effective even if the carbachol pulses are applied at random times. This suggests that a neural pacemaker is not needed; all that is required is that islets receive occasional coordinated input from postganglionic neurons. The endogenous rhythmic activity of the islets then sets the frequency of the islet population rhythm, while the input from ganglia acts only to keep the islet oscillators in phase.

A Two-Pulse Cellular Stimulation Test Elucidates Variability and Mechanisms in Signaling Pathways

Mammalian cells respond in a variable manner when provided with physiological pulses of ligand, such as low concentrations of acetylcholine present for just tens of seconds or TNFα for just tens of minutes. For a two-pulse stimulation, some cells respond to both pulses, some do not respond, and yet others respond to only one or the other pulse. Are these different response patterns the result of the small number of ligands being able to only stochastically activate the pathway at random times or an output pattern from a deterministic algorithm responding differently to different stimulation intervals? If the response is deterministic in nature, what parameters determine whether a response is generated or skipped? To answer these questions, we developed a two-pulse test that utilizes different rest periods between stimulation pulses. This "rest-period test" revealed that cells skip responses predictably as the rest period is shortened. By combining these experimental results with a mathematical model of the pathway, we further obtained mechanistic insight into potential sources of response variability. Our analysis indicates that in both intracellular calcium and NFκB signaling, response variability is consistent with extrinsic noise (cell-to-cell variability in protein levels), a short-term memory of stimulation, and high Hill coefficient processes. Furthermore, these results support recent works that have emphasized the role of deterministic processes for explaining apparently stochastic cellular response variability and indicate that even weak stimulations likely guide mammalian cells to appropriate fates rather than leaving outcomes to chance. We envision that the rest-period test can be applied to other signaling pathways to extract mechanistic insight.

A sharp-edge-based acoustofluidic chemical signal generator

Resolving the temporal dynamics of cell signaling pathways is essential for regulating numerous downstream functions, from gene expression to cellular responses. Mapping these signaling pathways requires the exposure of cells to time-varying chemical signals; these are difficult to generate and control over a wide temporal range. Herein, we present an acoustofluidic chemical signal generator based on a sharp-edge-based micromixing strategy. The device, simply by modulating the driving signals of an acoustic transducer including the ON/OFF switching frequency, actuation time and duty cycle, is capable of generating both single-pulse and periodic chemical signals that are temporally controllable in terms of stimulation period, stimulation duration and duty cycle. We also demonstrate the device's applicability and versatility for cell signaling studies by probing the calcium (Ca2+) release dynamics of three different types of cells stimulated by ionomycin signals of different shapes. Upon short single-pulse ionomycin stimulation (∼100 ms) generated by our device, we discover that cells tend to dynamically adjust the intracellular level of Ca2+ through constantly releasing and accepting Ca2+ to the cytoplasm and from the extracellular environment, respectively. With advantages such as simple fabrication and operation, compact device design, and reliability and versatility, our device will enable decoding of the temporal characteristics of signaling dynamics for various physiological processes.

Capacitive coupling synchronizes autonomous microfluidic oscillators

Even identically designed autonomous microfluidic oscillators have device-to-device oscillation variability that arises due to inconsistencies in fabrication, materials, and operation conditions. This work demonstrates, experimentally and theoretically, that with appropriate capacitive coupling these microfluidic oscillators can be synchronized. The size and characteristics of the capacitive coupling needed and the range of input flow rate differences that can be synchronized are also characterized. In addition to device-to-device variability, there is also within-device oscillation noise that arises. An additional advantage of coupling multiple fluidic oscillators together is that the oscillation noise decreases. The ability to synchronize multiple autonomous oscillators is also a first step towards enhancing their usefulness as tools for biochemical research applications where multiplicate experiments with identical temporal-stimulation conditions are required.

VEGFR1 promotes cell migration and proliferation through PLCγ and PI3K pathways

The ability to control vascular endothelial growth factor (VEGF) signaling offers promising therapeutic potential for vascular diseases and cancer. Despite this promise, VEGF-targeted therapies are not clinically effective for many pathologies, such as breast cancer. VEGFR1 has recently emerged as a predictive biomarker for anti-VEGF efficacy, implying a functional VEGFR1 role beyond its classically defined decoy receptor status. Here we introduce a computational approach that accurately predicts cellular responses elicited via VEGFR1 signaling. Aligned with our model prediction, we show empirically that VEGFR1 promotes macrophage migration through PLCγ and PI3K pathways and promotes macrophage proliferation through a PLCγ pathway. These results provide new insight into the basic function of VEGFR1 signaling while offering a computational platform to quantify signaling of any receptor.

Temporal Bias: Time-Encoded Dynamic GPCR Signaling

Evidence suggests that cells can time-encode signals for secure transport and perception of information, and it appears that this dynamic signaling is a common principle of nature to code information in time. G-protein-coupled receptor (GPCR) signaling networks are no exception as their composition and signal transduction appear temporally flexible. In this review, we discuss the potential mechanisms by which GPCRs code biological information in time to create 'temporal bias.' We highlight dynamic signaling patterns from the second messenger to the receptor-ligand level and shed light on the dynamics of G-protein cycles, the kinetics of ligand-receptor interaction, and the occurrence of distinct signaling waves within the cell. A dynamic feature such as temporal bias adds to the complexity of GPCR signaling bias and gives rise to the question whether this trait could be exploited to gain control over time-encoded cell physiology.

New insights into mammalian signaling pathways using microfluidic pulsatile inputs and mathematical modeling

Temporally modulated input mimics physiology. This chemical communication strategy filters the biochemical noise through entrainment and phase-locking. Under laboratory conditions, it also expands the observability space for downstream responses. A combined approach involving microfluidic pulsatile stimulation and mathematical modeling has led to deciphering of hidden/unknown temporal motifs in several mammalian signaling pathways and has provided mechanistic insights, including how these motifs combine to form distinct band-pass filters and govern fate regulation under dynamic microenvironment. This approach can be utilized to understand signaling circuit architectures and to gain mechanistic insights for several other signaling systems. Potential applications include synthetic biology and biotechnology, in developing pharmaceutical interventions, and in developing lab-on-chip models.

Cellular Interrogation: Exploiting Cell-to-Cell Variability to Discriminate Regulatory Mechanisms in Oscillatory Signalling

The molecular complexity within a cell may be seen as an evolutionary response to the external complexity of the cell’s environment. This suggests that the external environment may be harnessed to interrogate the cell’s internal molecular architecture. Cells, however, are not only nonlinear and non-stationary, but also exhibit heterogeneous responses within a clonal, isogenic population. In effect, each cell undertakes its own experiment. Here, we develop a method of cellular interrogation using programmable microfluidic devices which exploits the additional information present in cell-to-cell variation, without requiring model parameters to be fitted to data. We focussed on Ca²⁺ signalling in response to hormone stimulation, which exhibits oscillatory spiking in many cell types and chose eight models of Ca²⁺ signalling networks which exhibit similar behaviour in simulation. We developed a nonlinear frequency analysis for non-stationary responses, which could classify models into groups under parameter variation, but found that this question alone was unable to distinguish critical feedback loops. We further developed a nonlinear amplitude analysis and found that the combination of both questions ruled out six of the models as inconsistent with the experimentally-observed dynamics and heterogeneity. The two models that survived the double interrogation were mathematically different but schematically identical and yielded the same unexpected predictions that we confirmed experimentally. Further analysis showed that subtle mathematical details can markedly influence non-stationary responses under parameter variation, emphasising the difficulty of finding a “correct” model. By developing questions for the pathway being studied, and designing more versatile microfluidics, cellular interrogation holds promise as a systematic strategy that can complement direct intervention by genetics or pharmacology.

We have developed a cellular interrogation methodology that combines programmable microfluidics, fluorescence microscopy and mathematical analysis and have used it to discriminate between models of repetitive Ca²⁺ spiking in HeLa cells. Our approach exploits the natural variability in response of individual cells in a clonal population and the non-steady state behavior of the response in each cell, thereby providing more powerful discrimination. Interrogation consists of steps or pulses of histamine of fixed concentration and width but varying frequency. Eight mathematical models of repetitive Ca²⁺ spiking were chosen from the literature and methods of nonlinear frequency and nonlinear amplitude analysis were developed which ruled out all but two of the models, without having to fit the models to the data. Further analysis of the remaining models yielded predictions that were experimentally confirmed. Cellular interrogation offers a general approach to ruling out competing hypotheses about molecular mechanisms, which is complementary to traditional methods of genetics and biochemistry.

Band-pass processing in a GPCR signaling pathway selects for NFAT transcription factor activation

Many biological processes are rhythmic and proper timing is increasingly appreciated as being critical for development and maintenance of physiological functions. To understand how temporal modulation of an input signal influences downstream responses, we employ microfluidic pulsatile stimulation of a G-protein coupled receptor, the muscarinic M3 receptor, in single cells with simultaneous real-time imaging of both intracellular calcium and NFAT nuclear localization. Interestingly, we find that reduced stimulation with pulses of ligand can give more efficient transcription factor activation, if stimuli are timed appropriately. Our experiments and computational analyses show that M3 receptor-induced calcium oscillations form a low pass filter while calcium-induced NFAT translocation forms a high pass filter. The combination acts as a band-pass filter optimized for intermediate frequencies of stimulation. We demonstrate that receptor desensitization and NFAT translocation rates determine critical features of the band-pass filter and that the band-pass may be shifted for different receptors or NFAT dynamics. As an example, we show that the two NFAT isoforms (NFAT4 and NFAT1) have shifted band-pass windows for the same receptor. While we focus specifically on the M3 muscarinic receptor and NFAT translocation, band-pass processing is expected to be a general theme that applies to multiple signaling pathways.

A G-protein subunit translocation embedded network motif underlies GPCR regulation of calcium oscillations

G-protein βγ subunits translocate reversibly from the plasma membrane to internal membranes on receptor activation. Translocation rates differ depending on the γ subunit type. There is limited understanding of the role of the differential rates of Gβγ translocation in modulating signaling dynamics in a cell. Bifurcation analysis of the calcium oscillatory network structure predicts that the translocation rate of a signaling protein can regulate the damping of system oscillation. Here, we examined whether the Gβγ translocation rate regulates calcium oscillations induced by G-protein-coupled receptor activation. Oscillations in HeLa cells expressing γ subunit types with different translocation rates were imaged and quantitated. The results show that differential Gβγ translocation rates can underlie the diversity in damping characteristics of calcium oscillations among cells. Mathematical modeling shows that a translocation embedded motif regulates damping of G-protein-mediated calcium oscillations consistent with experimental data. The current study indicates that such a motif may act as a tuning mechanism to design oscillations with varying damping patterns by using intracellular translocation of a signaling component.

Measurement of the entrainment window of islets of Langerhans by microfluidic delivery of a chirped glucose waveform

Within single islets of Langerhans, the endocrine portion of the pancreas, intracellular metabolites, as well as insulin secretion, oscillate with a period of ∼5 min. In vivo, pulsatile insulin oscillations are also observed with periods ranging from 5-15 minutes. In order for oscillations of insulin to be observed in vivo, the majority of islets in the pancreas must synchronize their output. It is known that populations of islets can be synchronized via entrainment of the individual islets to low amplitude glucose oscillations that have periods close to islets' natural period. However, the range of glucose periods and amplitudes that can entrain islets has not been rigorously examined. To find the range of glucose periods that can entrain islets, a microfluidic system was utilized to produce and deliver a chirped glucose waveform to populations of islets while their individual intracellular [Ca(2+)] ([Ca(2+)]i) oscillations were imaged. Waveforms with amplitudes of 0.5, 1, and 1.5 mM above a median value of 11 mM were applied while the period was swept from 20-2 min. Oscillations of [Ca(2+)]i resonated the strongest when the period of the glucose wave was within 2 min of the natural period of the islets, typically close to 5 min. Some examples of 1 : 2 and 2 : 1 entrainment were observed during exposure to long and short glucose periods, respectively. These results shed light on the dynamic nature of islet behavior and may help to understand dynamics observed in vivo.

Integrated perfusion and separation systems for entrainment of insulin secretion from islets of Langerhans

A microfluidic system was developed to investigate the entrainment of insulin secretion from islets of Langerhans to oscillatory glucose levels. A gravity-driven perfusion system was integrated with a microfluidic system to deliver sinusoidal glucose waveforms to the islet chamber. Automated manipulation of the height of the perfusion syringes allowed precise control of the ratio of two perfusion solutions into a chamber containing 1-10 islets. Insulin levels in the perfusate were measured using an online competitive electrophoretic immunoassay with a sampling period of 10 s. The insulin immunoassay had a detection limit of 3 nM with RSDs of calibration points ranging from 2-8%. At 11 mM glucose, insulin secretion from single islets was oscillatory with a period ranging from 3-6 min. Application of a small amplitude sinusoidal wave of glucose with a period of 5 or 10 min, shifted the period of the insulin oscillations to this forcing period. Exposing groups of 6-10 islets to a sinusoidal glucose wave synchronized their behavior, producing a coherent pulsatile insulin response from the population. These results demonstrate the feasibility of the developed system for the study of oscillatory insulin secretion and can be easily modified for investigating the dynamic nature of other hormones released from different cell types.

The structure of dynamic GPCR signaling networks

G-protein-coupled receptors (GPCRs) stimulate signaling networks that control a variety of critical physiological processes. Static information on the map of interacting signaling molecules at the basis of many cellular processes exists, but little is known about the dynamic operation of these networks. Here we focus on two questions. First, Is the network architecture underlying GPCR-activated cellular processes unique in comparison with others such as transcriptional networks? We discuss how spatially localized GPCR signaling requires uniquely organized networks to execute polarized cell responses. Second, What approaches overcome challenges in deciphering spatiotemporally dynamic networks that govern cell behavior? We focus on recently developed microfluidic and optical approaches that allow GPCR signaling pathways to be triggered and perturbed with spatially and temporally variant input while simultaneously visualizing molecular and cellular responses. When integrated with mathematical modeling, these approaches can help identify design principles that govern cell responses to extracellular signals. We outline why optical approaches that allow the behavior of a selected cell to be orchestrated continually are particularly well suited for probing network organization in single cells.

Entrainment to periodic initiation and transition rates in a computational model for gene translation

Periodic oscillations play an important role in many biomedical systems. Proper functioning of biological systems that respond to periodic signals requires the ability to synchronize with the periodic excitation. For example, the sleep/wake cycle is a manifestation of an internal timing system that synchronizes to the solar day. In the terminology of systems theory, the biological system must entrain or phase-lock to the periodic excitation. Entrainment is also important in synthetic biology. For example, connecting several artificial biological systems that entrain to a common clock may lead to a well-functioning modular system. The cell-cycle is a periodic program that regulates DNA synthesis and cell division. Recent biological studies suggest that cell-cycle related genes entrain to this periodic program at the gene translation level, leading to periodically-varying protein levels of these genes. The ribosome flow model (RFM) is a deterministic model obtained via a mean-field approximation of a stochastic model from statistical physics that has been used to model numerous processes including ribosome flow along the mRNA. Here we analyze the RFM under the assumption that the initiation and/or transition rates vary periodically with a common period . We show that the ribosome distribution profile in the RFM entrains to this periodic excitation. In particular, the protein synthesis pattern converges to a unique periodic solution with period . To the best of our knowledge, this is the first proof of entrainment in a mathematical model for translation that encapsulates aspects such as initiation and termination rates, ribosomal movement and interactions, and non-homogeneous elongation speeds along the mRNA. Our results support the conjecture that periodic oscillations in tRNA levels and other factors related to the translation process can induce periodic oscillations in protein levels, and may suggest a new approach for re-engineering genetic systems to obtain a desired, periodic, protein synthesis rate.

Maintaining Stimulant Waveforms in Large Volume Microfluidic Cell Chambers

Stimulation of cells with temporal waveforms can be used to observe the frequency-dependent nature of cellular responses. The ability to produce and maintain the temporal waveforms in spite of the broadening processes that occur as the wave travels through the microfluidic system is critical for observing dynamic behaviors. Broadening of waves in microfluidic channels has been examined, but the effect that large-volume cell chambers have on the waves has not. In this report, a sinusoidal glucose wave delivered to a 1 mm diameter cell chamber using various microfluidic channel structures was simulated by finite element analysis with the goal of minimizing the broadening of the waveform in the chamber and maximizing the homogeneity of the concentration in the chamber at any given time. Simulation results indicated that increasing the flow rate was the most effective means to achieve these goals, but at a given volumetric flow rate, geometries that deliver the waveform to multiple regions in the chamber while maintaining a high linear velocity produced sufficient results. A 4-inlet geometry with a 220 μm channel width gave the best result in the simulation and was used to deliver glucose waveforms to a population of pancreatic islets of Langerhans. The result was a stronger and more robust synchronization of the islet population as compared to when a non-optimized chamber was used. This general strategy will be useful in other microfluidic systems examining the frequency-dependence nature of cellular behavior.

Microfluidic interrogation and mathematical modeling of multi-regime calcium signaling dynamics

Through microfluidic interrogation we analyzed real-time calcium responses of HEK293 cells stimulated with short pulses of the M3 muscarinic receptor ligand carbachol in two different concentration regimes. Lower ligand concentrations elicit oscillatory calcium signals while higher concentrations trigger a rapid rise that eventually settles down at a steady-state slightly above pre-stimulus levels, referred to as an acute signal. Cells were periodically pulsed with carbachol at these two concentration regimes using a custom-made microfluidic platform, and the resulting calcium signals were measured with a single fluorescent readout. Pulsed stimulations at these two concentration regimes resulted in multiple types of response patterns that each delivered complementary information about the M3 muscarinic receptor signaling pathway. These multiple types of calcium response patterns enabled development of a comprehensive mathematical model of multi-regime calcium signaling. The resulting model suggests that dephosphorylation of deactivated receptors is rate limiting for recovery of calcium signals in the acute regime (high ligand concentration), while calcium replenishment and IP3 production determine signal recovery in the oscillatory regime (low ligand concentration). This study not only provides mechanistic insight into multi-regime signaling of the M3 muscarinic receptor pathway, but also provides a general strategy for analyzing multi-regime pathways using only one fluorescent readout.

Microfluidic oscillators with widely tunable periods

We present experiments and theory of a constant flow-driven microfluidic oscillator with widely tunable oscillation periods. This oscillator converts two constant input-flows from a syringe pump into an alternating, periodic output-flow with oscillation periods that can be adjusted to between 0.3 s to 4.1 h by tuning an external membrane capacitor. This capacitor allows multiple adjustable periods at a given input flow-rate, thus providing great flexibility in device operation. Also, we show that a sufficiently large external capacitance, relative to the internal capacitance of the microfluidic valve itself, is a critical requirement for oscillation. These widely tunable microfluidic oscillators are envisioned to be broadly useful for the study of biological rhythms, as on-chip timing sources for microfluidic logic circuits, and other applications that require variation in timed flow switching.

Silibinin (Milk Thistle) potentiates ethanol-dependent hepatocellular carcinoma progression in male mice

Hepatocellular carcinoma (HCC) is a global health burden with limited treatment options and poor prognosis. Silibinin, an antioxidant derived from the Milk Thistle plant (Silybum marianum), is reported to exert hepatoprotective and antitumorigenic effects in vitro and in vivo by suppressing oxidative stress and proliferation. Using a DEN-initiated mouse model of HCC, this study examined the effects of dietary silibinin supplementation alone, or in combination with chronic ethanol consumption on HCC progression. Our data demonstrate silibinin exerted marginal hepatoprotective effects in early stages of hepatocarcinogenesis but, when co-administered with ethanol, exacerbated the promotional effects of ethanol in HCC bearing mice, but only in males.

Phase resetting reveals network dynamics underlying a bacterial cell cycle

Genomic and proteomic methods yield networks of biological regulatory interactions but do not provide direct insight into how those interactions are organized into functional modules, or how information flows from one module to another. In this work we introduce an approach that provides this complementary information and apply it to the bacterium Caulobacter crescentus, a paradigm for cell-cycle control. Operationally, we use an inducible promoter to express the essential transcriptional regulatory gene ctrA in a periodic, pulsed fashion. This chemical perturbation causes the population of cells to divide synchronously, and we use the resulting advance or delay of the division times of single cells to construct a phase resetting curve. We find that delay is strongly favored over advance. This finding is surprising since it does not follow from the temporal expression profile of CtrA and, in turn, simulations of existing network models. We propose a phenomenological model that suggests that the cell-cycle network comprises two distinct functional modules that oscillate autonomously and couple in a highly asymmetric fashion. These features collectively provide a new mechanism for tight temporal control of the cell cycle in C. crescentus. We discuss how the procedure can serve as the basis for a general approach for probing network dynamics, which we term chemical perturbation spectroscopy (CPS).

During the cell cycle, the cell progresses through a series of stages that are associated with various cell cycle events such as replication of genetic materials. Genetic and molecular dissections have revealed that the cell cycle is regulated by a network of interacting molecules that produces oscillatory dynamics. The major cell cycle regulators have been identified previously in different species and the activity of these regulators oscillates. However, the question of how cell cycle regulators coordinate different cell cycle events during the cell cycle remains controversial. Here, we investigate this question in a model bacterial system for cell cycle, Caulobacter crescentus. We perturb the expression of the master cell cycle regulator ctrA in a pulsatile fashion and quantify the response of the cell cycle to such perturbations. The measured response is contradictory to the existing mechanism of Caulobacter cell cycle control, which views the cell cycle progression as a sequential activation/inhibition process. We propose a new model that involves coupling of multiple oscillators and show the quantitative agreement between this new model and our measurements. We expect this procedure to be generalized and applied to a broad range of systems to obtain information that complements that obtained from other methods.

Extending the IP3 receptor model to include competition with partial agonists

The inositol 1,4,5-trisphosphate (IP(3)) receptor is a Ca(2+) channel located in the endoplasmic reticulum and is regulated by IP(3) and Ca(2+). This channel is critical to calcium signaling in cell types as varied as neurons and pancreatic beta cells to mast cells. De Young and Keizer (1992) created an eight-state, nine-variable model of the IP(3) receptor. In their model, they accounted for three binding sites, a site for IP(3), activating Ca(2+), and deactivating Ca(2+). The receptor is only open if IP(3) and activating Ca(2+) is bound. Li and Rinzel followed up this paper in 1994 by introducing a reduction that made it into a two variable system. A recent publication by Rossi et al. (2009) studied the effect of introducing IP(3)-like molecules, referred to as partial agonists (PA), into the cell to determine the structure-function relationship between IP(3) and its receptor. Initial results suggest a competitive model, where IP(3) and PA fight for the same binding site. We extend the original eight-state model to a 12-state model in order to illustrate this competition, and perform a similar reduction to that of Li and Rinzel in the first modeling study we are aware of considering PA effect on an IP(3) receptor. Using this reduction we solve for the equilibrium open probability for calcium release in the model. We replicate graphs provided by the Rossi paper, and find that optimizing the subunit affinities for IP(3) and PA yields a good fit to the data. We plug our extended reduced model into a full cell model, in order to analyze the effects PA have on whole cell properties specifically the propagation of calcium waves in two dimensions. We conclude that PA creates qualitatively different calcium dynamics than would simply reducing IP(3), but that effectively PA can act as an IP(3) knockdown.

Temporal gradients in microfluidic systems to probe cellular dynamics: a review

Microfluidic devices have found a unique place in cellular studies due to the ease of fabrication, their ability to provide long-term culture, or the seamless integration of downstream measurements into the devices. The accurate and precise control of fluid flows also allows unique stimulant profiles to be applied to cells that have been difficult to perform with conventional devices. In this review, we describe and provide examples of microfluidic systems that have been used to generate temporal gradients of stimulants, such as waveforms or pulses, and how these profiles have been used to produce biological insights into mammalian cells that are not typically revealed under static concentration gradients. We also discuss the inherent analytical challenges associated with producing and maintaining temporal gradients in these devices.

Linear conversion of pressure into concentration, rapid switching of concentration, and generation of linear ramps of concentration in a microfluidic device

Mixing of liquids to produce solutions with different concentrations is one of the basic functionalities of microfluidic devices. Generation of specific temporal patterns of concentration in microfluidic devices is an important technique to study responses of cells and model organisms to variations in the chemical composition of their environment. Here, we present a simple microfluidic network that linearly converts pressure at an inlet into concentration of a soluble reagent in an observation region and also enables independent concurrent linear control of concentrations of two reagents. The microfluidic device has an integrated mixer channel with chaotic three-dimensional flow that facilitates rapid switching of concentrations in a continuous range. A simple pneumatic setup generating linear ramps of pressure is used to produce smooth linear ramps and triangular waves of concentration with different slopes. The use of chaotic vs. laminar mixers is discussed in the context of microfluidic devices providing rapid switching and generating temporal waves of concentration.

Precisely targeted delivery of cells and biomolecules within microchannels using aqueous two-phase systems

Laminar and pulsatile flow of aqueous solutions in microfluidic channels can be useful for controlled delivery of cells and molecules. Dispersion effects resulting from diffusion and convective disturbances, however, result in reagent delivery profiles becoming blurred over the length of the channels. This issue is addressed partially by using oil-in-water phase systems. However, there are limitations in terms of the biocompatibility of these systems for adherent cell culture. Here we present a fully biocompatible aqueous two-phase flow system that can be used to pattern cells within simple microfluidic channel designs, as well as to deliver biochemical treatments to cells according to discrete boundaries. We demonstrate that aqueous two-phase systems are capable of precisely delivering cells as laminar patterns, or as islands by way of forced droplet formation. We also demonstrate that these systems can be used to precisely control chemical delivery to preformed monolayers of cells growing within channels. Treatments containing trypsin were localized more reliably using aqueous two-phase delivery than using conventional delivery in aqueous medium.

Constant flow-driven microfluidic oscillator for different duty cycles

This paper presents microfluidic devices that autonomously convert two constant flow inputs into an alternating oscillatory flow output. We accomplish this hardware embedded self-control programming using normally closed membrane valves that have an inlet, an outlet, and a membrane-pressurization chamber connected to a third terminal. Adjustment of threshold opening pressures in these 3-terminal flow switching valves enabled adjustment of oscillation periods to between 57 and 360 s with duty cycles of 0.2-0.5. These values are in relatively good agreement with theoretical values, providing the way for rational design of an even wider range of different waveform oscillations. We also demonstrate the ability to use these oscillators to perform temporally patterned delivery of chemicals to living cells. The device only needs a syringe pump, thus removing the use of complex, expensive external actuators. These tunable waveform microfluidic oscillators are envisioned to facilitate cell-based studies that require temporal stimulation.

Hi-Fi transmission of periodic signals amid cell-to-cell variability

Since information in intracellular calcium signaling is often frequency encoded, it is physiologically critical and experimentally useful to have reliable, convenient, and non-invasive methods to entrain it. Because of cell-to-cell variability, synchronization of intracellular signaling across a population of genetically identical cells can still be difficult to achieve. For intrinsically oscillatory signaling pathways, such as calcium, upon continuous stimulation, cell-to-cell variability is manifested as differences in intracellular response frequencies. Even with entrainment using periodic stimulation, cell-to-cell variability is manifested as differences in the fidelity with which extracellular inputs are converted into intracellular signals. Here we present a combined theoretical and experimental analysis that shows how to appropriately balance stimulation strength, duration, and rest intervals to achieve entrainment with high fidelity stimulation-to-response ratios for G-protein-coupled receptor-triggered intracellular calcium oscillations. We further demonstrate that stimulation parameters that give high fidelity entrainment are significantly altered upon changes in intracellular enzyme levels and cell surface receptor levels. Theoretical analysis suggests that, at key threshold values, even small changes in these protein concentrations or activities can result in precipitous changes in entrainment fidelity, with implications for pathophysiology.