Chemotactic cell trapping in controlled alternating gradient fields

The MAPK/ERK channel capacity exceeds 6 bit/hour

Living cells utilize signaling pathways to sense, transduce, and process information. As the extracellular stimulation often has rich temporal characteristics which may govern dynamic cellular responses, it is important to quantify the rate of information flow through the signaling pathways. In this study, we used an epithelial cell line expressing a light-activatable FGF receptor and an ERK activity reporter to assess the ability of the MAPK/ERK pathway to transduce signal encoded in a sequence of pulses. By stimulating the cells with random light pulse trains, we demonstrated that the MAPK/ERK channel capacity is at least 6 bits per hour. The input reconstruction algorithm detects the light pulses with 1-min accuracy 5 min after their occurrence. The high information transmission rate may enable the pathway to coordinate multiple processes including cell movement and respond to rapidly varying stimuli such as chemoattracting gradients created by other cells.

Short-time diffusive fluxes over membrane receptors yields the direction of a signalling source

An essential ability of many cell types is to detect stimuli in the form of shallow chemical gradients. Such cues may indicate the direction that new growth should occur, or the location of a mate. Amplification of these faint signals is due to intra-cellular mechanisms, while the cue itself is generated by the noisy arrival of signalling molecules to surface bound membrane receptors. We employ a new hybrid numerical-asymptotic technique coupling matched asymptotic analysis and numerical inverse Laplace transform to rapidly and accurately solve the parabolic exterior problem describing the dynamic diffusive fluxes to receptors. We observe that equilibration occurs on long timescales, potentially limiting the usefulness of steady-state quantities for localization at practical biological timescales. We demonstrate that directional information is encoded primarily in early arrivals to the receptors, while equilibrium quantities inform on source distance. We develop a new homogenization result showing that complex receptor configurations can be replaced by a uniform effective condition. In the extreme scenario where the cell adopts the angular direction of the first impact, we show this estimate to be surprisingly accurate.

On-demand microfluidic mixing by actuating integrated magnetic microwalls

Various types of passive and active micromixers have been successfully developed to address the problem of mixing in microfluidic devices. However, many applications do not need fluids to be mixed at all times, or indeed require mixing to be turned on and off at will. Achieving such on-demand mixing is not feasible for passive mixers, particularly when the flow rate cannot be used as a control parameter. On the other hand, active mixers are usually not designed to be able to turn mixing off completely, and they often have complicated fabrication processes and special operation requirements, limiting the range of applications. In this work, we demonstrate an on-demand micromixer based on the actuation of magnetic microwalls. These are made by replica micromoulding and can be easily integrated within commercial microfluidic devices, such as the ibidi® 3-in-1 μ-Slide. Using a simple magnet, the microwalls can be actuated between a fully upright 'on' state, which turns on mixing by creating a meandering path in the main channel, and a fully collapsed 'off' state, which completely turns off mixing by opening up the channel leaving it unobstructed. Besides the increase in path length when the microwalls are activated, inertia effects also play a significant role for mixing due to the tight bends in the meandering flow path. We quantify the mixing effect using coloured fluids of different viscosities and at different flow rates, and we show that the microwalls can effectively enhance mixing across a wide range of operational conditions.

Coupling cell shape and velocity leads to oscillation and circling in keratocyte galvanotaxis

During wound healing, fish keratocyte cells undergo galvanotaxis where they follow a wound-induced electric field. In addition to their stereotypical persistent motion, keratocytes can develop circular motion without a field or oscillate while crawling in the field direction. We developed a coarse-grained phenomenological model that captures these keratocyte behaviors. We fit this model to experimental data on keratocyte response to an electric field being turned on. A critical element of our model is a tendency for cells to turn toward their long axis, arising from a coupling between cell shape and velocity, which gives rise to oscillatory and circular motion. Galvanotaxis is influenced not only by the field-dependent responses, but also cell speed and cell shape relaxation rate. When the cell reacts to an electric field being turned on, our model predicts that stiff, slow cells react slowly but follow the signal reliably. Cells that polarize and align to the field at a faster rate react more quickly and follow the signal more reliably. When cells are exposed to a field that switches direction rapidly, cells follow the average of field directions, while if the field is switched more slowly, cells follow a "staircase" pattern. Our study indicated that a simple phenomenological model coupling cell speed and shape is sufficient to reproduce a broad variety of different keratocyte behaviors, ranging from circling to oscillation to galvanotactic response, by only varying a few parameters.

Covalent transfer of chemical gradients onto a graphenic surface with 2D and 3D control

Control over the functionalization of graphenic materials is key to enable their full application in electronic and optical technologies. Covalent functionalization strategies have been proposed as an approach to tailor the interfaces' structure and properties. However, to date, none of the proposed methods allow for a covalent functionalization with control over the grafting density, layer thickness and/or morphology, which are key aspects for fine-tuning the processability and performance of graphenic materials. Here, we show that the no-slip boundary condition at the walls of a continuous flow microfluidic device offers a way to generate controlled chemical gradients onto a graphenic material with 2D and 3D control, a possibility that will allow the sophisticated functionalization of these technologically-relevant materials.

Understanding the Cell's Response to Chemical Signals: Utilisation of Microfluidic Technology in Studies of Cellular and Dictyostelium discoideum Chemotaxis

Cellular chemotaxis has been the subject of a variety of studies due to its relevance in physiological processes, disease pathogenesis, and systems biology, among others. The migration of cells towards a chemical source remains a closely studied topic, with the Boyden chamber being one of the earlier techniques that has successfully studied cell chemotaxis. Despite its success, diffusion chambers such as these presented a number of problems, such as the quantification of many aspects of cell behaviour, the reproducibility of procedures, and measurement accuracy. The advent of microfluidic technology prompted more advanced studies of cell chemotaxis, usually involving the social amoeba Dictyostelium discoideum (D. discoideum) as a model organism because of its tendency to aggregate towards chemotactic agents and its similarities to higher eukaryotes. Microfluidic technology has made it possible for studies to look at chemotactic properties that would have been difficult to observe using classic diffusion chambers. Its flexibility and its ability to generate consistent concentration gradients remain some of its defining aspects, which will surely lead to an even better understanding of cell migratory behaviour and therefore many of its related biological processes. This paper first dives into a brief introduction of D. discoideum as a social organism and classical chemotaxis studies. It then moves to discuss early microfluidic devices, before diving into more recent and advanced microfluidic devices and their use with D. discoideum. The paper then closes with brief opinions about research progress in the field and where it will possibly lead in the future.

Generation of Dynamic Concentration Profile Using A Microfluidic Device Integrating Pneumatic Microvalves

Generating and maintaining the concentration dilutions of diffusible molecules in microchannels is critical for high-throughput chemical and biological analysis. Conventional serial network microfluidic technologies can generate high orders of arbitrary concentrations by a predefined microchannel network. However, a previous design requires a large occupancy area and is unable to dynamically generate different profiles in the same chip, limiting its applications. This study developed a microfluidic device enabling dynamic variations of both the concentration in the same channel and the concentration distribution in multiple channels by adjusting the flow resistance using programmable pneumatic microvalves. The key component (the pneumatic microvalve) allowed dynamic adjustment of the concentration profile but occupied a tiny space. Additionally, a Matlab program was developed to calculate the flow rates and flow resistance of various sections of the device, which provided theoretical guidance for dimension design. In silico investigations were conducted to evaluate the microvalve deformation with widths from 100 to 300 µm and membrane thicknesses of 20 and 30 µm under the activation pressures between 0 and 2000 mbar. The flow resistance of the deformed valve was studied both numerically and experimentally and an empirical model for valve flow resistance with the form of Rh=aebP was proposed. Afterward, the fluid flow in the valve region was characterized using Micro PIV to further demonstrate the adjustment mechanism of the flow resistance. Then, the herringbone structures were employed for fast mixing to allow both quick variation of concentration and minor space usage of the channel network. Finally, an empirical formula-supported computational program was developed to provide the activation pressures required for the specific concentration profile. Both linear (Ck = -0.2k + 1) and nonlinear (Ck = (110)k) concentration distribution in four channels were varied using the same device by adjusting microvalves. The device demonstrated the capability to control the concentration profile dynamically in a small space, offering superior application potentials in analytical chemistry, drug screening, and cell biology research.

Generation of droplets with adjustable chemical concentrations based on fixed potential induced-charge electro-osmosis

The effective control of the sample concentration within droplets is essential in a broad range of assays in chemistry and biochemistry. Here we provide an electrical method for producing batches of aqueous droplets with various chemical concentrations by exploiting fixed-potential induced-charge electroosmosis (ICEO) flow around a bipolar electrode. By applying an AC electric signal to the bipolar electrode and changing the zeta potential on it, the bipolar electrode acts as a gate electrode for generating asymmetric ICEO flow. The ICEO flow induced transverse vortexes interact with two parallel laminar streams with different chemical compositions. Controlled mixing of the aqueous solutions can be achieved by adjusting the shape and size of the asymmetric vortexes via altering the electric signal applied to the gate electrode. The mixed streams are split at a bifurcation, and one of the streams with a desired controlled concentration is pumped into a flow-focusing geometry to generate droplets with adjustable chemical concentrations. The in-droplet concentration increases in the range of 0.412-1.404 mM, as the applied voltage increases in the range of 0-70 mV at 15 kHz. This approach offers a promising method for on-chip control of chemical concentrations within droplets without labor-intensive dilutions while minimizing the sample consumption, showing great potential for next generation droplet-based applications.

Critical role of lipid membranes in polarization and migration of cells: a biophysical view

Cell migration plays vital roles in many biologically relevant processes such as tissue morphogenesis and cancer metastasis, and it has fascinated biophysicists over the past several decades. However, despite an increasing number of studies highlighting the orchestration of proteins involved in different signaling pathways, the functional roles of lipid membranes have been essentially overlooked. Lipid membranes are generally considered to be a functionless two-dimensional matrix of proteins, although many proteins regulating cell migration gain functions only after they are recruited to the membrane surface and self-organize their functional domains. In this review, we summarize how the logistical recruitment and release of proteins to and from lipid membranes coordinates complex spatiotemporal molecular processes. As predicted from the classical framework of the Smoluchowski equation of diffusion, lipid/protein membranes serve as a 2D reaction hub that contributes to the effective and robust regulation of polarization and migration of cells involving several competing pathways.

Bridging from single to collective cell migration: A review of models and links to experiments

Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.

Acoustofluidic generation of droplets with tunable chemical concentrations

The dynamic control of the chemical concentration within droplets is required in numerous droplet microfluidic applications. Here, we propose an acoustofluidic method for the generation of a library of aqueous droplets with the desired chemical concentrations in a continuous oil phase. Surface acoustic waves produced by a focused interdigital transducer interact with two parallel laminar streams with different chemical compositions. Coupling the acoustic waves with the flow streams results in the controlled acoustofluidic mixing of the aqueous solutions through the formation of acoustic streaming flow-induced microvortices. The mixed streams are split at a bifurcation, and one of the streams with a precisely controlled chemical concentration is fed into a T-junction to produce droplets with tunable chemical concentrations. The periodic acoustofluidic mixing of the aqueous streams enables the generation of a droplet library with a well-defined inter-droplet concentration gradient. The proposed method is a promising tool for the on-chip dynamic control of in-droplet chemical concentrations and for next-generation droplet microfluidic applications.

Heterogeneities Shape Passive Intracellular Transport

A living cell's interior is one of the most complex and intrinsically dynamic systems, providing an elaborate interplay between cytosolic crowding and ATP-driven motion that controls cellular functionality. Here, we investigated two distinct fundamental features of the merely passive, non-biomotor-shuttled material transport within the cytoplasm of Dictyostelium discoideum cells: the anomalous non-linear scaling of the mean-squared displacement of a 150-nm-diameter particle and non-Gaussian distribution of increments. Relying on single-particle tracking data of 320,000 data points, we performed a systematic analysis of four possible origins for non-Gaussian transport: 1) sample-based variability, 2) rarely occurring strong motion events, 3) ergodicity breaking/aging, and 4) spatiotemporal heterogeneities of the intracellular medium. After excluding the first three reasons, we investigated the remaining hypothesis of a heterogeneous cytoplasm as cause for non-Gaussian transport. A, to our knowledge, novel fit model with randomly distributed diffusivities implementing medium heterogeneities suits the experimental data. Strikingly, the non-Gaussian feature is independent of the cytoskeleton condition and lag time. This reveals that efficiency and consistency of passive intracellular transport and the related anomalous scaling of the mean-squared displacement are regulated by cytoskeleton components, whereas cytoplasmic heterogeneities are responsible for the generic, non-Gaussian distribution of increments.

Screening by changes in stereotypical behavior during cell motility

Stereotyped behaviors are series of postures that show very little variability between repeats. They have been used to classify the dynamics of individuals, groups and species without reference to the lower-level mechanisms that drive them. Stereotypes are easily identified in animals due to strong constraints on the number, shape, and relative positions of anatomical features, such as limbs, that may be used as landmarks for posture identification. In contrast, the identification of stereotypes in single cells poses a significant challenge as the cell lacks these landmark features, and finding constraints on cell shape is a non-trivial task. Here, we use the maximum caliber variational method to build a minimal model of cell behavior during migration. Without reference to biochemical details, we are able to make behavioral predictions over timescales of minutes using only changes in cell shape over timescales of seconds. We use drug treatment and genetics to demonstrate that maximum caliber descriptors can discriminate between healthy and aberrant migration, thereby showing potential applications for maximum caliber methods in automated disease screening, for example in the identification of behaviors associated with cancer metastasis.

Diffusing wave paradox of phototactic particles in traveling light pulses

Cells navigate through complex surroundings by following cues from their environment. A prominent example is Dictyostelium, which is directed by chemotaxis towards regions with higher concentrations. In the presence of traveling chemical waves, however, amoebae migrate counter to the running wave. Such behavior, referred to as diffusing wave paradox, suggests the existence of adaptation and directional memory. Here we experimentally investigate the response of phototactic self-propelled microparticles to traveling light-pulses. Despite their entirely memory-less (i.e., strictly local) response to the environment, we observe the same phenomenological behavior, i.e., particle motion counter to the pulse direction. Our findings are supported by a minimal model which considers active particle reorientations within local light gradients. The complex and robust behavior of synthetic active particles to spatially and temporally varying stimuli enables new strategies for achieving collective behavior and can be used for the design of micro-robotic systems with limited signal-processing capabilities.

Ultraflexible Nanowire Array for Label- and Distortion-Free Cellular Force Tracking

Living cells interact with their immediate environment by exerting mechanical forces, which regulate important cell functions. Elucidation of such force patterns yields deep insights into the physics of life. Here we present a top-down nanostructured, ultraflexible nanowire array biosensor capable of probing cell-induced forces. Its universal building block, an inverted conical semiconductor nanowire, greatly enhances both the functionality and the sensitivity of the device. In contrast to existing cellular force sensing architectures, microscopy is performed on the nanowire heads while cells deflecting the nanowires are confined within the array. This separation between the optical path and the cells under investigation excludes optical distortions caused by cell-induced refraction, which can give rise to feigned displacements on the 100 nm scale. The undistorted nanowire displacements are converted into cellular forces via the nanowire spring constant. The resulting distortion-free cellular force transducer realizes a high-resolution and label-free biosenor based on optical microscopy. Its performance is demonstrated in a proof-of-principle experiment with living Dictyostelium discoideum cells migrating through the nanowire array. Cell-induced forces are probed with a resolution of 50 piconewton, while the most flexible nanowires promise to enter the 100 femtonewton realm.

Dynamic seesaw model for rapid signaling responses in eukaryotic chemotaxis

Directed movement of eukaryotic cells toward spatiotemporally varied chemotactic stimuli enables rapid intracellular signaling responses. While macroscopic cellular manifestation is shaped by balancing external stimuli strength with finite internal delays, the organizing principles of the underlying molecular mechanisms remain to be clarified. Here, we developed a novel modeling framework based on a simple seesaw mechanism to elucidate how cells repeatedly reverse polarity. As a key feature of the modeling, the bottom module of bidirectional molecular transport is successively controlled by three upstream modules of signal reception, initial signal processing, and Rho GTPase regulation. Our simulations indicated that an isotropic cell is polarized in response to a graded input signal. By applying a reversal gradient to a chemoattractant signal, lamellipod-specific molecules (i.e. PIP₃ and PI3K) disappear, first from the cell front, and then they redistribute at the opposite side, whereas functional molecules at the rear of the cell (i.e. PIP₂ and PTEN) act oppositely. In particular, the model cell exhibits a seesaw-like spatiotemporal pattern for the establishment of front and rear and interconversion, consistent with those related experimental observations. Increasing the switching frequency of the chemotactic gradient causes the cell to stay in a trapped state, further supporting the proposed dynamics of eukaryotic chemotaxis with the underlying cytoskeletal remodeling.

Hydrodynamics in Cell Studies

Hydrodynamic phenomena are ubiquitous in living organisms and can be used to manipulate cells or emulate physiological microenvironments experienced in vivo. Hydrodynamic effects influence multiple cellular properties and processes, including cell morphology, intracellular processes, cell–cell signaling cascades and reaction kinetics, and play an important role at the single-cell, multicellular, and organ level. Selected hydrodynamic effects can also be leveraged to control mechanical stresses, analyte transport, as well as local temperature within cellular microenvironments. With a better understanding of fluid mechanics at the micrometer-length scale and the advent of microfluidic technologies, a new generation of experimental tools that provide control over cellular microenvironments and emulate physiological conditions with exquisite accuracy is now emerging. Accordingly, we believe that it is timely to assess the concepts underlying hydrodynamic control of cellular microenvironments and their applications and provide some perspective on the future of such tools in in vitro cell-culture models. Generally, we describe the interplay between living cells, hydrodynamic stressors, and fluid flow-induced effects imposed on the cells. This interplay results in a broad range of chemical, biological, and physical phenomena in and around cells. More specifically, we describe and formulate the underlying physics of hydrodynamic phenomena affecting both adhered and suspended cells. Moreover, we provide an overview of representative studies that leverage hydrodynamic effects in the context of single-cell studies within microfluidic systems.

Acoustic Actuation of in situ Fabricated Artificial Cilia

We present on-chip acoustic actuation of in situ fabricated artificial cilia. Arrays of cilia structures are UV polymerized inside a microfluidic channel using a photocurable polyethylene glycol (PEG) polymer solution and photomasks. During polymerization, cilia structures are attached to a silane treated glass surface inside the microchannel. Then, the cilia structures are actuated using acoustic vibrations at 4.6 kHz generated by piezo transducers. As a demonstration of a practical application, DI water and fluorescein dye solutions are mixed inside a microfluidic channel. Using pulses of acoustic excitations, and locally fabricated cilia structures within a certain region of the microchannel, a waveform of mixing behavior is obtained. This result illustrates one potential application wherein researchers can achieve spatiotemporal control of biological microenvironments in cell stimulation studies. These acoustically actuated, in situ fabricated, cilia structures can be used in many on-chip applications in biological, chemical and engineering studies.

Mathematics of Experimentally Generated Chemoattractant Gradients

Many eukaryotic cells move in the direction of a chemical gradient. Several assays have been developed to measure this chemotactic response, but no complete mathematical models of the spatial and temporal gradients are available to describe the fundamental principles of chemotaxis. Here we provide analytical solutions for the gradients formed by release of chemoattractant from a point source by passive diffusion or forced flow (micropipettes) and gradients formed by laminar diffusion in a Zigmond chamber. The results show that gradients delivered with a micropipette are formed nearly instantaneously, are very steep close to the pipette, and have a steepness that is strongly dependent on the distance from the pipette. In contrast, gradients in a Zigmond chamber are formed more slowly, are nearly independent of the distance from the source, and resemble the temporal and spatial properties of the natural cAMP wave that Dictyostelium cells experience during cell aggregation.

Dissecting Spatial and Temporal Sensing in Dictyostelium Chemotaxis Using a Wave Gradient Generator

External cues that dictate the direction of cell migration are likely dynamic during many biological processes such as embryonic development and wound healing. Until recently, how cells integrate spatial and temporal information to determine the direction of migration has remained elusive. In Dictyostelium discoideum, the chemoattractant cAMP that directs cell aggregation propagates as periodic waves. In light of the fact that any temporally evolving complex signals, in principle, can be expressed as a sum of sinusoidal functions with various frequencies, the Dictyostelium system serves as a minimal example, where the dynamic signal is in the simplest form of near sinusoidal wave with one dominant frequency. Here, we describe a method to emulate the traveling waves in a fluidics device. The text provides step-by-step instructions on the device setup and describes ways to analyze the acquired data. These include quantification of membrane translocation of fluorescently labeled proteins in individual Dictyostelium cells and estimation of exogenous cAMP profiles. The described approach has already helped decipher spatial and temporal aspects of chemotactic sensing in Dictyostelium. More specifically, it allowed one to discriminate the temporal and the spatial sensing aspects of directional sensing. With some modifications, one should be able to implement similar analysis in other cell types.

Nanostructured surfaces of biodegradable silica fibers enhance directed amoeboid cell migration in a microtubule-dependent process

This study reveals significantly enhanced amoeboid cell migration on biodegradable silica fibers in comparison to plain glass surfaces.

The microfluidic lighthouse: an omnidirectional gradient generator

Studies of chemotactic cell migration rely heavily on various assay systems designed to evaluate the ability of cells to move in response to attractant molecules. In particular, the development of microfluidics-based devices in recent years has made it possible to spatially distribute attractant molecules in graded profiles that are sufficiently stable and precise to test theoretical predictions regarding the accuracy and efficiency of chemotaxis and the underlying mechanism of stimulus perception. However, because the gradient is fixed in a direction orthogonal to the laminar flow and thus the chamber geometry, conventional devices are limited for the study of cell re-orientation to gradients that move or change directions. Here, we describe the development of a simple radially symmetric microfluidics device that can deliver laminar flow in 360°. A stimulant introduced either from the central inlet or by photo uncaging is focused into the laminar flow in a direction determined by the relative rate of regulated flow from multiple side channels. Schemes for flow regulation and an extended duplexed device were designed to generate and move gradients in desired orientations and speed, and then tested to steer cell migration of Dictyostelium and neutrophil-like HL60 cells. The device provided a high degree of freedom in the positioning and orientation of attractant gradients, and thus may serve as a versatile platform for studying cell migration, re-orientation, and steering.

Challenges in tissue engineering - towards cell control inside artificial scaffolds

Control of living cells is vital for the survival of organisms. Each cell inside an organism is exposed to diverse external mechano-chemical cues, all coordinated in a spatio-temporal pattern triggering individual cell functions. This complex interplay between external chemical cues and mechanical 3D environments is translated into intracellular signaling loops. Here, we describe how external mechano-chemical cues control cell functions, especially cell migration, and influence intracellular information transport. In particular, this work focuses on the quantitative analysis of (1) intracellular vesicle transport to understand intracellular state changes in response to external cues, (2) cellular sensing of external chemotactic cues, and (3) the cells' ability to migrate in 3D structured environments, artificially fabricated to mimic the 3D environment of tissue in the human body.

Simultaneous or Sequential Orthogonal Gradient Formation in a 3D Cell Culture Microfluidic Platform

Biochemical gradients are ubiquitous in biology. At the tissue level, they dictate differentiation patterning or cell migration. Recapitulating in vitro the complexity of such concentration profiles with great spatial and dynamic control is crucial in order to understand the underlying mechanisms of biological phenomena. Here, a microfluidic design capable of generating diffusion-driven, simultaneous or sequential, orthogonal linear concentration gradients in a 3D cell-embedded scaffold is described. Formation and stability of the orthogonal gradients are demonstrated by computational and fluorescent dextran-based characterizations. Then, system utility is explored in two biological systems. First, stem cells are subjected to orthogonal gradients of morphogens in order to mimic the localized differentiation of motor neurons in the neural tube. Similarly to in vivo, motor neurons preferentially differentiate in regions of high concentration of retinoic acid and smoothened agonist (acting as sonic hedgehog), in a concentration-dependent fashion. Then, a rotating gradient is applied to HT1080 cancer cells and the change in migration direction is investigated as the cells adapt to a new chemical environment. The response time of ≈4 h is reported. These two examples demonstrate the versatility of this new design that can also prove useful in many applications including tissue engineering and drug screening.

A spatiotemporally controllable chemical gradient generator via acoustically oscillating sharp-edge structures

The ability to generate stable, spatiotemporally controllable concentration gradients is critical for resolving the dynamics of cellular response to a chemical microenvironment. Here we demonstrate an acoustofluidic gradient generator based on acoustically oscillating sharp-edge structures, which facilitates in a step-wise fashion the rapid mixing of fluids to generate tunable, dynamic chemical gradients. By controlling the driving voltage of a piezoelectric transducer, we demonstrated that the chemical gradient profiles can be conveniently altered (spatially controllable). By adjusting the actuation time of the piezoelectric transducer, moreover, we generated pulsatile chemical gradients (temporally controllable). With these two characteristics combined, we have developed a spatiotemporally controllable gradient generator. The applicability and biocompatibility of our acoustofluidic gradient generator are validated by demonstrating the migration of human dermal microvascular endothelial cells (HMVEC-d) in response to a generated vascular endothelial growth factor (VEGF) gradient, and by preserving the viability of HMVEC-d cells after long-term exposure to an acoustic field. Our device features advantages such as simple fabrication and operation, compact and biocompatible device, and generation of spatiotemporally tunable gradients.

Recovering a stochastic process from super-resolution noisy ensembles of single-particle trajectories

Recovering a stochastic process from noisy ensembles of single-particle trajectories is resolved here using the coarse-grained Langevin equation as a model. The massive redundancy contained in single-particle tracking data allows recovering local parameters of the underlying physical model. We use several parametric and nonparametric estimators to compute the first and second moments of the process, to recover the local drift, its derivative, and the diffusion tensor, and to deconvolve the instrumental from the physical noise. We use numerical simulations to also explore the range of validity for these estimators. The present analysis allows defining what can exactly be recovered from statistics of super-resolution microscopy trajectories used for characterizing molecular trafficking underlying cellular functions.

How actin/myosin crosstalks guide the adhesion, locomotion and polarization of cells

Cell-tissue-tissue interaction is determined by specific short range forces between cell adhesion molecules (CAMs) and ligands of the tissue, long range repulsion forces mediated by cell surface grafted macromolecules and adhesion-induced elastic stresses in the cell envelope. This interplay of forces triggers the rapid random clustering of tightly coupled linkers. By coupling of actin gel patches to the intracellular domains of the CAMs, these clusters can grow in a secondary process resulting in the formation of functional adhesion microdomains (ADs). The ADs can act as biochemical steering centers by recruiting and activating functional proteins, such as GTPases and associated regulating proteins, through electrostatic-hydrophobic forces with cationic lipid domains that act as attractive centers. First, I summarize physical concepts of cell adhesion revealed by studies of biomimetic systems. Then I describe the role of the adhesion domains as biochemical signaling platforms and force transmission centers promoting cellular protrusions, in terms of a shell string model of cells. Protrusion forces are generated by actin gelation triggered by molecular machines (focal adhesion kinase (FAK), Src-kinases and associated adaptors) which assemble around newly formed integrin clusters. They recruit and activate the GTPases Rac-1 and actin gelation promoters to charged membrane domains via electrostatic-hydrophobic forces. The cell front is pushed forward in a cyclic and stepwise manner and the step-width is determined by the dynamics antagonistic interplay between Rac-1 and RhoA. The global cell polarization in the direction of motion is mediated by the actin-microtubule (MT) crosstalk at adhesion domains. Supramolecular actin-MT assemblies at the front help to promote actin polymerization. At the rear they regulate the dismantling of the ADs through the Ca(++)-mediated activation of the protease calpain and trigger their disruption by RhoA mediated contraction via stress fibers. This article is part of a Special Issue entitled: Mechanobiology.

Extracellular and intracellular factors regulating the migration direction of a chemotactic cell in traveling-wave chemotaxis

This report presents a simple model that describes the motion of a single Dictyostelium discoideum cell exposed to a traveling wave of cyclic adenosine monophosphate (cAMP). The model incorporates two types of responses to stimulation by cAMP: the changes in the polarity and motility of the cell. The periodic change in motility is assumed to be induced by periodic cAMP stimulation on the basis of previous experimental studies. Consequently, the net migration of the cell occurs in a particular direction with respect to wave propagation, which explains the migration of D. discoideum cells in aggregation. The wave period and the difference between the two response times are important parameters that determine the direction of migration. The theoretical prediction compared with experiments presented in another study. The transition from the single-cell state of the population of D. discoideum cells to the aggregation state is understood to be a specific example of spontaneous breakage of symmetry in biology.

Microfluidic static droplet array for analyzing microbial communication on a population gradient

Quorum sensing (QS) is a type of cell-cell communication using signal molecules that are released and detected by cells, which respond to changes in their population density. A few studies explain that QS may operate in a density-dependent manner; however, due to experimental challenges, this fundamental hypothesis has never been investigated. Here, we present a microfluidic static droplet array (SDA) that combines a droplet generator with hydrodynamic traps to independently generate a bacterial population gradient into a parallel series of droplets under complete chemical and physical isolation. The SDA independently manipulates both a chemical concentration gradient and a bacterial population density. In addition, the bacterial population gradient in the SDA can be tuned by a simple change in the number of sample plug loading. Finally, the method allows the direct analysis of complicated biological events in an addressable droplet to enable the characterization of bacterial communication in response to the ratio of two microbial populations, including two genetically engineered QS circuits, such as the signal sender for acyl-homoserine lactone (AHL) production and the signal receiver bacteria for green fluorescent protein (GFP) expression induced by AHL. For the first time, we found that the population ratio of the signal sender and receiver indicates a significant and potentially interesting partnership between microbial communities. Therefore, we envision that this simple SDA could be a useful platform in various research fields, including analytical chemistry, combinatorial chemistry, synthetic biology, microbiology, and molecular biology.

Acoustofluidic chemical waveform generator and switch

Eliciting a cellular response to a changing chemical microenvironment is central to many biological processes including gene expression, cell migration, differentiation, apoptosis, and intercellular signaling. The nature and scope of the response is highly dependent upon the spatiotemporal characteristics of the stimulus. To date, studies that investigate this phenomenon have been limited to digital (or step) chemical stimulation with little control over the temporal counterparts. Here, we demonstrate an acoustofluidic (i.e., fusion of acoustics and microfluidics) approach for generating programmable chemical waveforms that permits continuous modulation of the signal characteristics including the amplitude (i.e., sample concentration), shape, frequency, and duty cycle, with frequencies reaching up to 30 Hz. Furthermore, we show fast switching between multiple distinct stimuli, wherein the waveform of each stimulus is independently controlled. Using our device, we characterized the frequency-dependent activation and internalization of the β2-adrenergic receptor (β2-AR), a prototypic G-protein coupled receptor (GPCR), using epinephrine. The acoustofluidic-based programmable chemical waveform generation and switching method presented herein is expected to be a powerful tool for the investigation and characterization of the kinetics and other dynamic properties of many biological and biochemical processes.

Rectified directional sensing in long-range cell migration

How spatial and temporal information are integrated to determine the direction of cell migration remains poorly understood. Here, by precise microfluidics emulation of dynamic chemoattractant waves, we demonstrate that, in Dictyostelium, directional movement as well as activation of small guanosine triphosphatase Ras at the leading edge is suppressed when the chemoattractant concentration is decreasing over time. This 'rectification' of directional sensing occurs only at an intermediate range of wave speed and does not require phosphoinositide-3-kinase or F-actin. From modelling analysis, we show that rectification arises naturally in a single-layered incoherent feedforward circuit with zero-order ultrasensitivity. The required stimulus time-window predicts ~5 s transient for directional sensing response close to Ras activation and inhibitor diffusion typical for protein in the cytosol. We suggest that the ability of Dictyostelium cells to move only in the wavefront is closely associated with rectification of adaptive response combined with local activation and global inhibition.

Cellular memory in eukaryotic chemotaxis

Natural chemical gradients to which cells respond chemotactically are often dynamic, with both spatial and temporal components. A primary example is the social amoeba Dictyostelium, which migrates to the source of traveling waves of chemoattractant as part of a self-organized aggregation process. Despite its physiological importance, little is known about how cells migrate directionally in response to traveling waves. The classic back-of-the-wave problem is how cells chemotax toward the wave source, even though the spatial gradient reverses direction in the back of the wave. Here, we address this problem by using microfluidics to expose cells to traveling waves of chemoattractant with varying periods. We find that cells exhibit memory and maintain directed motion toward the wave source in the back of the wave for the natural period of 6 min, but increasingly reverse direction for longer wave periods. Further insights into cellular memory are provided by experiments quantifying cell motion and localization of a directional-sensing marker after rapid gradient switches. The results can be explained by a model that couples adaptive directional sensing to bistable cellular memory. Our study shows how spatiotemporal cues can guide cell migration over large distances.

Persistent cellular motion control and trapping using mechanotactic signaling

Chemotactic signaling and the associated directed cell migration have been extensively studied owing to their importance in emergent processes of cellular aggregation. In contrast, mechanotactic signaling has been relatively overlooked despite its potential for unique ways to artificially signal cells with the aim to effectively gain control over their motile behavior. The possibility of mimicking cellular mechanotactic signals offers a fascinating novel strategy to achieve targeted cell delivery for in vitro tissue growth if proven to be effective with mammalian cells. Using (i) optimal level of extracellular calcium ([Ca²⁺ ]_ext mM) we found, (ii) controllable fluid shear stress of low magnitude (), and (iii) the ability to swiftly reverse flow direction (within one second), we are able to successfully signal Dictyostelium discoideum amoebae and trigger migratory responses with heretofore unreported control and precision. Specifically, we are able to systematically determine the mechanical input signal required to achieve any predetermined sequences of steps including straightforward motion, reversal and trapping. The mechanotactic cellular trapping is achieved for the first time and is associated with a stalling frequency of Hz for a reversing direction mechanostimulus, above which the cells are effectively trapped while maintaining a high level of directional sensing. The value of this frequency is very close to the stalling frequency recently reported for chemotactic cell trapping [Meier B, et al. (2011) Proc Natl Acad Sci USA 108:11417–11422], suggesting that the limiting factor may be the slowness of the internal chemically-based motility apparatus.

Polymer brushes patterned with micrometer-scale chemical gradients using laminar co-flow

We present a facile microfluidic method for forming narrow chemical gradients in polymer brushes. Co-flow of an alkylating agent solution and a neat solvent in a microfluidic channel forms a diffusion-driven concentration gradient, and thus a gradient in reaction rate at the interface of the two flows, leading to a quaternization gradient in the underlying poly(2-(dimethylamino)ethyl methacrylate) polymer brush. The spatial distribution of the quaternized polymer brush is characterized by confocal Raman microscopy. The quaternization gradient length in the polymer brush can be varied with the injection flow rate and the distance from the co-flow junction. A chemical gradient in the polymer brush as narrow as 5 μm was created by controlling these parameters. The chemical gradient by laminar co-flow is compared with numerical calculations that include only one adjustable parameter: the reaction rate constant of the polymer brush quaternization. The calculated chemical gradient agrees with the experimental data, which validates the numerical procedures established in this study. Flow of multiple laminar streams of reactive agent solutions enables single-run fabrication of brush gradients with more than one chemical property. As one example, four laminar streams-neat solvent/benzyl bromide solution/propargyl bromide solution/neat solvent-generate multistep gradients of aromatic and alkyne groups. Because the alkyne functional group is a click-reaction available site, the alkyne gradient could allow small gradient formation with a wide variety of chemical properties in a polymer brush.

Automated single cell microbioreactor for monitoring intracellular dynamics and cell growth in free solution

We report an automated microfluidic-based platform for single cell analysis that allows for cell culture in free solution with the ability to control the cell growth environment. Using this approach, cells are confined by the sole action of gentle fluid flow, thereby enabling non-perturbative analysis of cell growth away from solid boundaries. In addition, the single cell microbioreactor allows for precise and time-dependent control over cell culture media, with the combined ability to observe the dynamics of non-adherent cells over long time scales. As a proof-of-principle demonstration, we used the platform to observe dynamic cell growth, gene expression, and intracellular diffusion of repressor proteins while precisely tuning the cell growth environment. Overall, this microfluidic approach enables the direct observation of cellular dynamics with exquisite control over environmental conditions, which will be useful for quantifying the behaviour of single cells in well-defined media.

Modeling self-organized spatio-temporal patterns of PIP₃ and PTEN during spontaneous cell polarization

During spontaneous cell polarization of Dictyostelium discoideum cells, phosphatidylinositol (3,4,5)-triphoshpate (PIP3) and PTEN (phosphatase tensin homolog) have been identified as key signaling molecules which govern the process of polarization in a self-organized manner. Recent experiments have quantified the spatio-temporal dynamics of these signaling components. Surprisingly, it was found that membrane-bound PTEN can be either in a high or low state, that PIP3 waves were initiated in areas lacking PTEN through an excitable mechanism, and that PIP3 was degraded even though the PTEN concentration remained low. Here we develop a reaction-diffusion model that aims to explain these experimental findings. Our model contains bistable dynamics for PTEN, excitable dynamics for PIP3, and postulates the existence of two species of PTEN with different dephosphorylation rates. We show that our model is able to produce results that are in good qualitative agreement with the experiments, suggesting that our reaction-diffusion model underlies the self-organized spatio-temporal patterns observed in experiments.

Memory improves precision of cell sensing in fluctuating environments

Biological cells are often found to sense their chemical environment near the single-molecule detection limit. Surprisingly, this precision is higher than simple estimates of the fundamental physical limit, hinting towards active sensing strategies. In this work, we analyse the effect of cell memory, e.g. from slow biochemical processes, on the precision of sensing by cell-surface receptors. We derive analytical formulas, which show that memory significantly improves sensing in weakly fluctuating environments. However, surprisingly when memory is adjusted dynamically, the precision is always improved, even in strongly fluctuating environments. In support of this prediction we quantify the directional biases in chemotactic Dictyostelium discoideum cells in a flow chamber with alternating chemical gradients. The strong similarities between cell sensing and control engineering suggest universal problem-solving strategies of living matter.

Distinct cell shapes determine accurate chemotaxis

The behaviour of an organism often reflects a strategy for coping with its environment. Such behaviour in higher organisms can often be reduced to a few stereotyped modes of movement due to physiological limitations, but finding such modes in amoeboid cells is more difficult as they lack these constraints. Here, we examine cell shape and movement in starved Dictyostelium amoebae during migration toward a chemoattractant in a microfluidic chamber. We show that the incredible variety in amoeboid shape across a population can be reduced to a few modes of variation. Interestingly, cells use distinct modes depending on the applied chemical gradient, with specific cell shapes associated with shallow, difficult-to-sense gradients. Modelling and drug treatment reveals that these behaviours are intrinsically linked with accurate sensing at the physical limit. Since similar behaviours are observed in a diverse range of cell types, we propose that cell shape and behaviour are conserved traits.

Using microfluidic chip to form brain-derived neurotrophic factor concentration gradient for studying neuron axon guidance

Molecular gradients play a significant role in regulating biological and pathological processes. Although conventional gradient-generators have been used for studying chemotaxis and axon guidance, there are still many limitations, including the inability to maintain stable tempo-spatial gradients and the lack of the cell monitoring in a real-time manner. To overcome these shortcomings, microfluidic devices have been developed. In this study, we developed a microfluidic gradient device for regulating neuron axon guidance. A microfluidic device enables the generation of Brain-derived neurotrophic factor (BDNF) gradient profiles in a temporal and spatial manner. We test the effect of the gradient profiles on axon guidance, in the BDNF concentration gradient axon towards the high concentration gradient. This microfluidic gradient device could be used as a powerful tool for cell biology research.

Reactivity mapping with electrochemical gradients for monitoring reactivity at surfaces in space and time

Studying and controlling reactions at surfaces is of great fundamental and applied interest in, among others, biology, electronics and catalysis. Because reaction kinetics is different at surfaces compared with solution, frequently, solution-characterization techniques cannot be used. Here we report solution gradients, prepared by electrochemical means, for controlling and monitoring reactivity at surfaces in space and time. As a proof of principle, electrochemically derived gradients of a reaction parameter (pH) and of a catalyst (Cu(I)) have been employed to make surface gradients on the micron scale and to study the kinetics of the (surface-confined) imine hydrolysis and the copper(I)-catalysed azide-alkyne 1,3-dipolar cycloaddition, respectively. For both systems, the kinetic data were spatially visualized in a two-dimensional reactivity map. In the case of the copper(I)-catalysed azide-alkyne 1,3-dipolar cycloaddition, the reaction order (2) was deduced from it.

Recent developments in microfluidics-based chemotaxis studies

Microfluidic devices can better control cellular microenvironments compared to conventional cell migration assays. Over the past few years, microfluidics-based chemotaxis studies showed a rapid growth. New strategies were developed to explore cell migration in manipulated chemical gradients. In addition to expanding the use of microfluidic devices for a broader range of cell types, microfluidic devices were used to study cell migration and chemotaxis in complex environments. Furthermore, high-throughput microfluidic chemotaxis devices and integrated microfluidic chemotaxis systems were developed for medical and commercial applications. In this article, we review recent developments in microfluidics-based chemotaxis studies and discuss the new trends in this field observed over the past few years.

Excitable behavior in amoeboid chemotaxis

Chemotaxis, the directed motion of cells in response to chemical gradients, is a fundamental process. Eukaryotic cells detect spatial differences in chemoattractant receptor occupancy with high precision and use these differences to bias the location of actin-rich protrusions to guide their movement. Research into chemotaxis has benefitted greatly from a systems biology approach that combines novel experimental and computational tools to pose and test hypotheses. Recently, one such hypothesis has been postulated proposing that chemotaxis in eukaryotic cells is mediated by locally biasing the activity of an underlying excitable system. The excitable system hypothesis can account for a number of cellular behaviors related to chemotaxis, including the stochastic nature of the movement of unstimulated cells, the directional bias imposed by chemoattractant gradients, and the observed spatial and temporal distribution of signaling and cytoskeleton proteins.

Theoretical model for cell migration with gradient sensing and shape deformation

Amoeboid cells take various shapes during migration, depending on the cell type and its environment. Deformability of the cell shape can then affect the migrating behavior. In this article, we introduce a theoretical model of chemotactic cell migration with elliptical shape deformation. Based on the model, we calculate the stationary distributions of the migration directions analytically. As a result, we find that the distributions show different characteristics depending on the difference in the interdependence of the internal polarity, cell morphology and gradient sensing.

Actin cytoskeleton of chemotactic amoebae operates close to the onset of oscillations

The rapid reorganization of the actin cytoskeleton in response to external stimuli is an essential property of many motile eukaryotic cells. Here, we report evidence that the actin machinery of chemotactic Dictyostelium cells operates close to an oscillatory instability. When averaging the actin response of many cells to a short pulse of the chemoattractant cAMP, we observed a transient accumulation of cortical actin reminiscent of a damped oscillation. At the single-cell level, however, the response dynamics ranged from short, strongly damped responses to slowly decaying, weakly damped oscillations. Furthermore, in a small subpopulation, we observed self-sustained oscillations in the cortical F-actin concentration. To substantiate that an oscillatory mechanism governs the actin dynamics in these cells, we systematically exposed a large number of cells to periodic pulse trains of different frequencies. Our results indicate a resonance peak at a stimulation period of around 20 s. We propose a delayed feedback model that explains our experimental findings based on a time-delay in the regulatory network of the actin system. To test the model, we performed stimulation experiments with cells that express GFP-tagged fusion proteins of Coronin and actin-interacting protein 1, as well as knockout mutants that lack Coronin and actin-interacting protein 1. These actin-binding proteins enhance the disassembly of actin filaments and thus allow us to estimate the delay time in the regulatory feedback loop. Based on this independent estimate, our model predicts an intrinsic period of 20 s, which agrees with the resonance observed in our periodic stimulation experiments.

Tunable, pulsatile chemical gradient generation via acoustically driven oscillating bubbles

We present a novel concept of generating both static and pulsatile chemical gradients using acoustically activated bubbles designed in a ladder-like arrangement. Furthermore, by regulating the amplitude of the bubble oscillation, we demonstrate that the chemical gradient profiles can be effectively tuned.

Fluorescent reporters and methods to analyze fluorescent signals

The use of fluorescent reporters and the development of new imaging technologies have revolutionized studies in cell biology. During recent years the number of fluorescent proteins offering the ability to visualize the distribution of proteins, organelles, and cells has increased tremendously. In parallel, the imaging tools available were refined rapidly enabling now the use of a huge spectrum of specialized methods to explore the cellular and subcellular localization and dynamics of fluorescently tagged markers. This chapter presents an overview of fluorescent reporters and methods available, and describes a selection of those that are routinely applicable in imaging studies using Dictyostelium discoideum.

Synthetic spatially graded Rac activation drives cell polarization and movement

Migrating cells possess intracellular gradients of active Rho GTPases, which serve as central hubs in transducing signals from extracellular receptors to cytoskeletal and adhesive machinery. However, it is unknown whether shallow exogenously induced intracellular gradients of Rho GTPases are sufficient to drive cell polarity and motility. Here, we use microfluidic control to generate gradients of a small molecule and thereby directly induce linear gradients of active, endogenous Rac without activation of chemotactic receptors. Gradients as low as 15% were sufficient not only to trigger cell migration up the chemical gradient but to induce both cell polarization and repolarization. Cellular response times were inversely proportional to the steepness of Rac inducer gradient in agreement with a mathematical model, suggesting a function for chemoattractant gradient amplification upstream of Rac. Increases in activated Rac levels beyond a well-defined threshold augmented polarization and decreased sensitivity to the imposed gradient. The threshold was governed by initial cell polarity and PI3K activity, supporting a role for both in defining responsiveness to Rac activation. Our results reveal that Rac can serve as a starting point in defining cell polarity. Furthermore, our methodology may serve as a template to investigate processes regulated by intracellular signaling gradients.