Plasma Lithography Surface Patterning for Creation of Cell Networks

Systematic manipulation of a cell microenvironment with micro- and nanoscale resolution is often required for deciphering various cellular and molecular phenomena. To address this requirement, we have developed a plasma lithography technique to manipulate the cellular microenvironment by creating a patterned surface with feature sizes ranging from 100 nm to millimeters. The goal of this technique is to be able to study, in a controlled way, the behaviors of individual cells as well as groups of cells and their interactions.This plasma lithography method is based on selective modification of the surface chemistry on a substrate by means of shielding the contact of low-temperature plasma with a physical mold. This selective shielding leaves a chemical pattern which can guide cell attachment and movement. This pattern, or surface template, can then be used to create networks of cells whose structure can mimic that found in nature and produces a controllable environment for experimental investigations. The technique is well suited to studying biological phenomenon as it produces stable surface patterns on transparent polymeric substrates in a biocompatible manner. The surface patterns last for weeks to months and can thus guide interaction with cells for long time periods which facilitates the study of long-term cellular processes, such as differentiation and adaption. The modification to the surface is primarily chemical in nature and thus does not introduce topographical or physical interference for interpretation of results. It also does not involve any harsh or toxic substances to achieve patterning and is compatible for tissue culture. Furthermore, it can be applied to modify various types of polymeric substrates, which due to the ability to tune their properties are ideal for and are widely used in biological applications. The resolution achievable is also beneficial, as isolation of specific processes such as migration, adhesion, or binding allows for discrete, clear observations at the single to multicell level.This method has been employed to form diverse networks of different cell types for investigations involving migration, signaling, tissue formation, and the behavior and interactions of neurons arraigned in a network.     

A Pre-pattern formation mechanism for animal coat markings

It is generally accepted that colour patterns in animals are genetically determined but the mechanism is not known. We suggest that a single mechanism which can exhibit an infinite variety of patterns is a candidate for it. We thus propose that a reaction-diffusion system which can be diffusively driven unstable could be responsible for the laying down of the pre-pattern for animal coat markings.For illustrative purposes only we consider a specific practical substrate inhibition reaction mechanism in detail and show that the geometry and scale of the domain, the relevant part of the integument, during the time of laying down plays a crucial role in the structural patterns which result. Patterns which exhibit a limited randomness are obtained for a selection of geometries and are specifically related to the coat colour distribution in the spotted felidae, zebra and other animals.     

FRAP analysis of membrane-associated proteins: lateral diffusion and membrane-cytoplasmic exchange

Obtaining quantitative kinetic parameters from fluorescence recovery after photobleaching (FRAP) experiments generally requires a theoretical analysis of protein mobility and appropriate solutions for FRAP recovery derived for a given geometry. Here we provide a treatment of FRAP recovery for a molecule undergoing a combined process of reversible membrane association and lateral diffusion on the plasma membrane for two commonly used bleach geometries: stripes, and boxes. Such analysis is complicated by the fact that diffusion of a molecule during photobleaching can lead to broadening of the bleach area, resulting in significant deviations of the actual bleach shape from the desired bleach geometry, which creates difficulty in accurately measuring kinetic parameters. Here we overcome the problem of deviations between actual and idealized bleach geometries by parameterizing, more accurately, the initial postbleach state. This allows for reconstruction of an accurate and analytically tractable approximation of the actual fluorescence distribution. Through simulated FRAP experiments, we demonstrate that this method can be used to accurately measure a broad range of combinations of diffusion constants and exchange rates. Use of this method to analyze the plextrin homology domain of PLC-δ1 in Caenorhabditis elegans results in quantitative agreement with prior analysis of this domain in other cells using other methods. Because of the flexibility, relative ease of implementation, and its use of standard, easily obtainable bleach geometries, this method should be broadly applicable to investigation of protein dynamics at the plasma membrane.     

Mechanical Cell–Cell Communication in Fibrous Networks: The Importance of Network Geometry

Cells contracting in extracellular matrix (ECM) can transmit stress over long distances, communicating their position and orientation to cells many tens of micrometres away. Such phenomena are not observed when cells are seeded on substrates with linear elastic properties, such as polyacrylamide (PA) gel. The ability for fibrous substrates to support far reaching stress and strain fields has implications for many physiological processes, while the mechanical properties of ECM are central to several pathological processes, including tumour invasion and fibrosis. Theoretical models have investigated the properties of ECM in a variety of network geometries. However, the effects of network architecture on mechanical cell–cell communication have received little attention. This work investigates the effects of geometry on network mechanics, and thus the ability for cells to communicate mechanically through different networks. Cell-derived displacement fields are quantified for various network geometries while controlling for network topology, cross-link density and micromechanical properties. We find that the heterogeneity of response, fibre alignment, and substrate displacement fields are sensitive to network choice. Further, we show that certain geometries support mechanical communication over longer distances than others. As such, we predict that the choice of network geometry is important in fundamental modelling of cell–cell interactions in fibrous substrates, as well as in experimental settings, where mechanical signalling at the cellular scale plays an important role. This work thus informs the construction of theoretical models for substrate mechanics and experimental explorations of mechanical cell–cell communication.     

A numerical simulation of neural fields on curved geometries

Despite the highly convoluted nature of the human brain, neural field models typically treat the cortex as a planar two-dimensional sheet of ne;urons. Here, we present an approach for solving neural field equations on surfaces more akin to the cortical geometries typically obtained from neuroimaging data. Our approach involves solving the integral form of the partial integro-differential equation directly using collocation techniques alongside efficient numerical procedures for determining geodesic distances between neural units. To illustrate our methods, we study localised activity patterns in a two-dimensional neural field equation posed on a periodic square domain, the curved surface of a torus, and the cortical surface of a rat brain, the latter of which is constructed using neuroimaging data. Our results are twofold: Firstly, we find that collocation techniques are able to replicate solutions obtained using more standard Fourier based methods on a flat, periodic domain, independent of the underlying mesh. This result is particularly significant given the highly irregular nature of the type of meshes derived from modern neuroimaging data. And secondly, by deploying efficient numerical schemes to compute geodesics, our approach is not only capable of modelling macroscopic pattern formation on realistic cortical geometries, but can also be extended to include cortical architectures of more physiological relevance. Importantly, such an approach provides a means by which to investigate the influence of cortical geometry upon the nucleation and propagation of spatially localised neural activity and beyond. It thus promises to provide model-based insights into disorders like epilepsy, or spreading depression, as well as healthy cognitive processes like working memory or attention.     

Morphological control of inositol-1,4,5-trisphosphate-dependent signals

Inositol-1,4,5-trisphosphate (InsP(3))-mediated calcium signals represent an important mechanism for transmitting external stimuli to the cell. However, information about intracellular spatial patterns of InsP(3) itself is not generally available. In particular, it has not been determined how the interplay of InsP(3) generation, diffusion, and degradation within complex cellular geometries can control the patterns of InsP(3) signaling. Here, we explore the spatial and temporal characteristics of [InsP(3)](cyt) during a bradykinin-induced calcium wave in a neuroblastoma cell. This is achieved by using a unique image-based computer modeling system, Virtual Cell, to integrate experimental data on the rates and spatial distributions of the key molecular components of the process. We conclude that the characteristic calcium dynamics requires rapid, high-amplitude production of [InsP(3)](cyt) in the neurite. This requisite InsP(3) spatiotemporal profile is provided, in turn, as an intrinsic consequence of the cell's morphology, demonstrating how geometry can locally and dramatically intensify cytosolic signals that originate at the plasma membrane. In addition, the model predicts, and experiments confirm, that stimulation of just the neurite, but not the soma or growth cone, is sufficient to generate a calcium response throughout the cell.     

Landscape as a model: the importance of geometry

In all models, but especially in those used to predict uncertain processes (e.g., climate change and nonnative species establishment), it is important to identify and remove any sources of bias that may confound results. This is critical in models designed to help support decisionmaking. The geometry used to represent virtual landscapes in spatially explicit models is a potential source of bias. The majority of spatial models use regular square geometry, although regular hexagonal landscapes have also been used. However, there are other ways in which space can be represented in spatially explicit models. For the first time, we explicitly compare the range of alternative geometries available to the modeller, and present a mechanism by which uncertainty in the representation of landscapes can be incorporated. We test how geometry can affect cell-to-cell movement across homogeneous virtual landscapes and compare regular geometries with a suite of irregular mosaics. We show that regular geometries have the potential to systematically bias the direction and distance of movement, whereas even individual instances of landscapes with irregular geometry do not. We also examine how geometry can affect the gross representation of real-world landscapes, and again show that individual instances of regular geometries will always create qualitative and quantitative errors. These can be reduced by the use of multiple randomized instances, though this still creates scale-dependent biases. In contrast, virtual landscapes formed using irregular geometries can represent complex real-world landscapes without error. We found that the potential for bias caused by regular geometries can be effectively eliminated by subdividing virtual landscapes using irregular geometry. The use of irregular geometry appears to offer spatial modellers other potential advantages, which are as yet underdeveloped. We recommend their use in all spatially explicit models, but especially for predictive models that are used in decisionmaking.     

The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing

BACKGROUND: Epithelial junctional networks assume packing geometries characterized by different cell shapes, neighbor number distributions and areas. The development of specific packing geometries is tightly controlled; in the Drosophila wing epithelium, cells convert from an irregular to a hexagonal array shortly before hair formation. Packing geometry is determined by developmental mechanisms that likely control the biophysical properties of cells and their interactions. RESULTS: To understand how physical cellular properties and proliferation determine cell-packing geometries, we use a vertex model for the epithelial junctional network in which cell packing geometries correspond to stable and stationary network configurations. The model takes into account cell elasticity and junctional forces arising from cortical contractility and adhesion. By numerically simulating proliferation, we generate different network morphologies that depend on physical parameters. These networks differ in polygon class distribution, cell area variation, and the rate of T1 and T2 transitions during growth. Comparing theoretical results to observed cell morphologies reveals regions of parameter space where calculated network morphologies match observed ones. We independently estimate parameter values by quantifying network deformations caused by laser ablating individual cell boundaries. CONCLUSIONS: The vertex model accounts qualitatively and quantitatively for the observed packing geometry in the wing disc and its response to perturbation by laser ablation. Epithelial packing geometry is a consequence of both physical cellular properties and the disordering influence of proliferation. The occurrence of T2 transitions during network growth suggests that elimination of cells from the proliferating disc epithelium may be the result of junctional force balances.     

Undirected motility of filamentous cyanobacteria produces reticulate mats

The roles of biology in the morphogenesis of microbial mats and stromatolites remain enigmatic due to the vast array of physical and chemical influences on morphology. However, certain microbial behaviors produce complex morphological features that can be directly attributed to motility patterns. Specifically, laboratory experiments with a strain of the cyanobacteria Pseudanabaena demonstrate that distinctive morphologies arise from the undirected gliding and colliding of filaments. When filamentous cells collide, they align and clump, producing intersecting ridges surrounding areas with low cell density, i.e. reticulate structures. Cell motility is essential for the development of reticulates and associated structures: filaments organize into reticulates faster than cell division and growth, and conditions that inhibit motility also inhibit reticulate formation. Cell density of the inoculum affects the frequency of cell–cell collisions, and thus the time required for biofilm organization into reticulate structures. This also affects the specific geometry of the reticulates. These patterns are propagated into larger structures as cyanobacterial cell numbers increase and cells remain motile. Thus, cell motility is important for templating and maintaining the morphology of these microbial communities, demonstrating a direct link between a microbial behavior and a community morphology. Reticulate geometries have been identified in natural microbial mats as well as in the fossil record, and these structures can be attributed to the motility of filamentous bacteria.     

The role of cell geometry and cell-cell communication in gradient sensing

Cells can measure shallow gradients of external signals to initiate and accomplish a migration or a morphogenetic process. Recently, starting from mathematical models like the local-excitation global-inhibition (LEGI) model and with the support of empirical evidence, it has been proposed that cellular communication improves the measurement of an external gradient. However, the mathematical models that have been used have over-simplified geometries (e.g., they are uni-dimensional) or assumptions about cellular communication, which limit the possibility to analyze the gradient sensing ability of more complex cellular systems. Here, we generalize the existing models to study the effects on gradient sensing of cell number, geometry and of long- versus short-range cellular communication in 2D systems representing epithelial tissues. We find that increasing the cell number can be detrimental for gradient sensing when the communication is weak and limited to nearest neighbour cells, while it is beneficial when there is long-range communication. We also find that, with long-range communication, the gradient sensing ability improves for tissues with more disordered geometries; on the other hand, an ordered structure with mostly hexagonal cells is advantageous with nearest neighbour communication. Our results considerably extend the current models of gradient sensing by epithelial tissues, making a step further toward predicting the mechanism of communication and its putative mediator in many biological processes.     

Divergence of interdomain geometry in two-domain proteins

For homologous protein chains composed of two domains, we have determined the extent to which they conserve (1) their interdomain geometry and (2) the molecular structure of the domain interface. This work was carried out on 128 unique two-domain architectures. Of the 128, we find 75 conserve their interdomain geometry and the structure of their domain interface; 5 conserve their interdomain geometry but not the structure of their interface; and 48 have variable geometries and divergent interface structure. We describe how different types of interface changes or the absence of an interface is responsible for these differences in geometry. Variable interdomain geometries can be found in homologous structures with high sequence identities (70%).     

Direct patterning of poly(acrylic acid) on polymer surfaces by ion beam lithography for the controlled adhesion of mammalian cells

Poly(acrylic acid) (PAA)-patterned polystyrene (PS) substrates were prepared by ion beam lithography to control cell behaviors of mouse fibroblasts and human embryonic kidney cells. Thin PAA films spin-coated on non-biological PS substrates were selectively irradiated with energetic proton ions through a pattern mask. The irradiated substrates were developed with deionized water to generate negative-type PAA patterns. The surface characteristics of the resulting PAA-patterned PS surface, such as surface morphology, chemical structure and composition and wettability, were investigated. Well-defined 100 μm PAA patterns were effectively formed on relatively hydrophobic PS substrates by ion beam lithography at higher fluences than 5 × 10¹⁴ ions/cm². Moreover, based on the in vitro cell culture test, cells were adhered and proliferated favorably onto hydrophilic PAA regions separated by hydrophobic PS regions on the PAA-patterned PS substrates, and thereby leading to the formation of well-defined cell patterns.     

Sequential induction of auxin efflux and influx carriers regulates lateral root emergence

In Arabidopsis, lateral roots originate from pericycle cells deep within the primary root. New lateral root primordia (LRP) have to emerge through several overlaying tissues. Here, we report that auxin produced in new LRP is transported towards the outer tissues where it triggers cell separation by inducing both the auxin influx carrier LAX3 and cell‐wall enzymes. LAX3 is expressed in just two cell files overlaying new LRP. To understand how this striking pattern of LAX3 expression is regulated, we developed a mathematical model that captures the network regulating its expression and auxin transport within realistic three‐dimensional cell and tissue geometries. Our model revealed that, for the LAX3 spatial expression to be robust to natural variations in root tissue geometry, an efflux carrier is required—later identified to be PIN3. To prevent LAX3 from being transiently expressed in multiple cell files, PIN3 and LAX3 must be induced consecutively, which we later demonstrated to be the case. Our study exemplifies how mathematical models can be used to direct experiments to elucidate complex developmental processes.     

Uncovering the Mechanism of Trapping and Cell Orientation during Neisseria gonorrhoeae Twitching Motility

Neisseria gonorrheae bacteria are the causative agent of the second most common sexually transmitted infection in the world. The bacteria move on a surface by means of twitching motility. Their movement is mediated by multiple long and flexible filaments, called type IV pili, that extend from the cell body, attach to the surface, and retract, thus generating a pulling force. Moving cells also use pili to aggregate and form microcolonies. However, the mechanism by which the pili surrounding the cell body work together to propel bacteria remains unclear. Understanding this process will help describe the motility of N. gonorrheae bacteria, and thus the dissemination of the disease which they cause. In this article we track individual twitching cells and observe that their trajectories consist of alternating moving and pausing intervals, while the cell body is preferably oriented with its wide side toward the direction of motion. Based on these data, we propose a model for the collective pili operation of N. gonorrheae bacteria that explains the experimentally observed behavior. Individual pili function independently but can lead to coordinated motion or pausing via the force balance. The geometry of the cell defines its orientation during motion. We show that by changing pili substrate interactions, the motility pattern can be altered in a predictable way. Although the model proposed is tangibly simple, it still has sufficient robustness to incorporate further advanced pili features and various cell geometries to describe other bacteria that employ pili to move on surfaces.     

Uncovering the Mechanism of Trapping and Cell Orientation during Neisseria gonorrhoeae Twitching Motility

Neisseria gonorrheae bacteria are the causative agent of the second most common sexually transmitted infection in the world. The bacteria move on a surface by means of twitching motility. Their movement is mediated by multiple long and flexible filaments, called type IV pili, that extend from the cell body, attach to the surface, and retract, thus generating a pulling force. Moving cells also use pili to aggregate and form microcolonies. However, the mechanism by which the pili surrounding the cell body work together to propel bacteria remains unclear. Understanding this process will help describe the motility of N. gonorrheae bacteria, and thus the dissemination of the disease which they cause. In this article we track individual twitching cells and observe that their trajectories consist of alternating moving and pausing intervals, while the cell body is preferably oriented with its wide side toward the direction of motion. Based on these data, we propose a model for the collective pili operation of N. gonorrheae bacteria that explains the experimentally observed behavior. Individual pili function independently but can lead to coordinated motion or pausing via the force balance. The geometry of the cell defines its orientation during motion. We show that by changing pili substrate interactions, the motility pattern can be altered in a predictable way. Although the model proposed is tangibly simple, it still has sufficient robustness to incorporate further advanced pili features and various cell geometries to describe other bacteria that employ pili to move on surfaces.     

Face mask application for calibration of respiratory inductive plethysmography in lambs

Respiratory inductive plethysmography is a non-invasive method of assessing breathing patterns that requires an airway connection for calibration. In previous studies an endotracheal tube was used to establish this connection. We employed a single position graphic calibration technique for gain calculation using a conical face mask in place of the endotracheal tube, thus eliminating the need for sedation and topical anaesthesia. Thirteen studies were completed on seven lambs. Validation of gains was performed by comparing volumes obtained simultaneously by respiratory inductive plethysmography and integrated pneumotachography. Total study time ranged between 5 and 10 min for each calibration procedure. Our results suggest that the conical mask can be used to perform accurate and time-efficient calibration of the respiratory inductive plethysmograph in the spontaneously breathing non-sedated lamb and eliminates the need for endotracheal intubation.     

A photo-electroactive surface strategy for immobilizing ligands in patterns and gradients for studies of cell polarization

We report a combined photochemical and electrochemical method to pattern ligands and cells in complex geometries and gradients on inert surfaces. This work demonstrates: (1) the control of density of immobilized ligands within overlapping photopatterns, and (2) the attached cell culture patterned onto ligand defined gradients for studies of directional cell polarity. Our approach is based on the photochemical activation of benzoquinonealkanethiols. Immobilization of aminooxy terminated ligands in selected region of the quinone monolayer resulted in patterns on the surface. This approach is unique in that the extent of photochemical deprotection, as well as ligand immobilization can be monitored and quantified by cyclic voltammetry in situ. Furthermore, complex photochemical patterns of single or multiple ligands can be routinely generated using photolithographic masks. Finally, this methodology is completely compatible with attached cell culture and we show how the subtle interplay between cell-cell interactions and underlying peptide gradient influences cell polarization. The combined use of photochemistry, electrochemistry and well defined surface chemistry provides molecular level control of patterned ligands and gradients on surfaces.     

Virtual glioblastoma: growth, migration and treatment in a three-dimensional mathematical model

Objectives:  Glioblastomas are aggressive primary brain cancers that are characterized by extensive infiltration into the brain and are highly resistant to treatment. Through mathematical modelling, we model the process of invasion and predict the relative importance of mechanisms contributing to malignant invasion. Clinically, we predict patterns of tumour recurrence following various modes of therapeutic intervention.
Materials and methods:  Our mathematical model uses a realistic three-dimensional brain geometry and considers migrating and proliferating cells as separate classes. Several mechanisms for infiltrative migration are considered. Methods are developed for simulating surgical resection, radiotherapy and chemotherapy.
Results:  The model provides clinically realistic predictions of tumour growth and recurrence following therapeutic intervention. Specific results include (i) invasiveness is governed largely by the ability of glioblastoma cells to degrade and migrate through the extracellular matrix and the ability of single migrating cells to form colonies; (ii) tumours originating deeper in the brain generally grow more quickly than those of superficial origin; (iii) upon surgery, the margins and geometry of resection significantly determine the extent and pattern of postoperative recurrence; (iv) radiotherapy works synergistically with greater resection margins to reduce recurrence; (v) simulations in both two- and three-dimensional geometries give qualitatively similar results; and (vi) in an actual clinical case comprising several surgical interventions, the model provides good qualitative agreement between the simulated and observed course of the disease.
Conclusions:  The model provides a useful initial framework by which biological mechanisms of invasion and efficacy of potential treatment regimens may be assessed.     

Geometry-induced inhomogeneity of distribution of cell adhesion molecules along branching processes

There is evidence that inhomogeneity of lateral distribution of cell adhesion molecules (CAM) in the plasma membrane is crucial for cell motility and growth. It is known that the cells move when the cell-substratum adhesiveness is within a certain critical range. We have carried out simulation studies of the factors governing inhomogeneous CAM distribution along uniform and branching cylinder-shaped cell processes on a flat substrate evenly covered with a ligand. Our model included the following mechanisms: intracellular transportation of CAM to an active (growing) part of the cell, installation in the plasma membrane, lateral diffusive redistribution of mobile CAM, formation and dissociation of CAM/ligand complexes, and CAM internalization by endocytosis. Since the rate of growth is two and one order of magnitude slower than the rate of trafficking and lateral diffusion, respectively, we analyzed steady distributions of CAM. We showed that interplay of the mechanisms included in the model may lead to the occurrence of CAM distributions with inhomogeneity, whose range is critical for translocation of an active part of the cell. It was shown that a difference in the diameters of asymmetric sister branches can cause different inhomogeneous distributions of CAM along these branches and thus can define conditions of their growth. Depending on the branching geometry, one or both sister branches may appear within this critical range, and a difference in the diameters may define a difference in the rate of growth and, correspondingly, in the length. This may constitute the basis for self-control of neurite outgrowth.