Molecular Gradients Research Articles

Does It Compute?

Computational Biology in-article table of contents A discussion of computational biology has to start with a pioneer of the field, Alan Turing, especially in this centennial year of his birth. He introduced us to the digital computer and proposed that much biology could be described by mathematical equations—the number of spirals in a sunflower is a Fibonacci number and pattern formation in animal skins can be described by a reaction diffusion model. Turing lacked the data and the computing power to substantiate his models. Today, the availability of vast quantities of new data, together with striking advances in computing power, is promising to give us new insights into the mechanisms of life. This special section, together with related content in Science Signaling and Science Careers, highlights recent advances and outstanding challenges. Models that simulate biological processes can be characterized both by their level of biological detail and by their mathematical complexity. Mogilner et al. (p. [175][1]) describe these different classes of computer models, using the example of cell polarity mechanisms to show that diverse models are required to fit different experimental studies in an iterative loop of modeling and experimentation. In a News Focus, Pennisi (p. [172][2]) illustrates this loop, describing how researchers have combined modeling and experimentation to understand how lizards, turtles, and other animals cope with heat stress and potentially global warming (videos of some of these models can be found at ). ![Figure][3] CREDIT: SEITA MIYAZAWA/OSAKA UNIVERSITY Advances in sequencing technology have resulted in a barrage of genomic information. Zerbino et al. (p. [179][4]) review the development of computational methods and algorithms to efficiently analyze these data, from the initial genome reconstruction to their use in comparing individuals and organisms, reconstructing phylogenies, and tying genotype to phenotype. Munsky et al. (p. [183][5]) note that phenotypic variation can occur even in genetically identical cells. They discuss stochastic gene expression as the likely source of this variability and describe how the analysis of variability can give insight into the mechanisms of gene regulation. At the level of morphogenesis that so fascinated Turing, Morelli et al. (p. [187][6]) describe how a combination of theory and experiment is being used to investigate developmental processes. They describe how patterning can arise from molecular gradients, from coupled biological oscillations, or from mechanical deformations of cells and tissues. Underlying all of this analysis is computer code, and in a Policy Forum, Morin et al. (p. [159][7]) call for this code to be made widely available and suggest how this might be implemented. Turing not only sought mathematical rules that govern biology, as described in Perspectives by Hodges (p. [163][8]) and French (p. [164][9]); he also questioned whether there were fundamental differences between how machines and biological organisms compute. There is much more work to be done in exploring such questions, and we look forward to the many new insights that will be gained along the way. [1]: /lookup/volpage/336/175?iss=6078 [2]: /lookup/volpage/336/172?iss=6078 [3]: pending:yes [4]: /lookup/volpage/336/179?iss=6078 [5]: /lookup/volpage/336/183?iss=6078 [6]: /lookup/doi/10.1126/science.1215478 [7]: /lookup/doi/10.1126/science.1218263 [8]: /lookup/volpage/336/163?iss=6078 [9]: /lookup/doi/10.1126/science.1218350

Preparation of Parasagittal Slices for the Investigation of Dorsal-ventral Organization of the Rodent Medial Entorhinal Cortex

Computation in the brain relies on neurons responding appropriately to their synaptic inputs. Neurons differ in their complement and distribution of membrane ion channels that determine how they respond to synaptic inputs. However, the relationship between these cellular properties and neuronal function in behaving animals is not well understood. One approach to this problem is to investigate topographically organized neural circuits in which the position of individual neurons maps onto information they encode or computations they carry out. Experiments using this approach suggest principles for tuning of synaptic responses underlying information encoding in sensory and cognitive circuits. The topographical organization of spatial representations along the dorsal-ventral axis of the medial entorhinal cortex (MEC) provides an opportunity to establish relationships between cellular mechanisms and computations important for spatial cognition. Neurons in layer II of the rodent MEC encode location using grid-like firing fields. For neurons found at dorsal positions in the MEC the distance between the individual firing fields that form a grid is on the order of 30 cm, whereas for neurons at progressively more ventral positions this distance increases to greater than 1 m. Several studies have revealed cellular properties of neurons in layer II of the MEC that, like the spacing between grid firing fields, also differ according to their dorsal-ventral position, suggesting that these cellular properties are important for spatial computation. Here we describe procedures for preparation and electrophysiological recording from brain slices that maintain the dorsal-ventral extent of the MEC enabling investigation of the topographical organization of biophysical and anatomical properties of MEC neurons. The dorsal-ventral position of identified neurons relative to anatomical landmarks is difficult to establish accurately with protocols that use horizontal slices of MEC, as it is difficult to establish reference points for the exact dorsal-ventral location of the slice. The procedures we describe enable accurate and consistent measurement of location of recorded cells along the dorsal-ventral axis of the MEC as well as visualization of molecular gradients. The procedures have been developed for use with adult mice (> 28 days) and have been successfully employed with mice up to 1.5 years old. With adjustments they could be used with younger mice or other rodent species. A standardized system of preparation and measurement will aid systematic investigation of the cellular and microcircuit properties of this area.

Self-Diffusion of Chain Molecules in the Metal-Organic Framework IRMOF-1: Simulation and Experiment.

Metal-organic frameworks (MOFs) possess characteristics, such as tunable pore size and chemical functionality, that make them attractive candidates for separations, catalysis, gas storage, and sensing applications. The rate of diffusion of guest molecules in the pores is an important property for all of these potential applications. In this work, the self-diffusion of hydrocarbons in IRMOF-1 was studied as a function of chain length with a combination of molecular dynamics simulations and pulsed field gradient NMR experiments. Excellent agreement is seen between the experiments and simulations, and the self-diffusion coefficients in IRMOF-1 are on the same order as those in the bulk liquid. Additionally, the effect of concentration on diffusivity was found to be very small for low to moderate loadings. Molecular dynamics simulations also provided insights about the preferential diffusion pathways of these guests in IRMOF-1.

Positional information in neural map development: Lessons from the olfactory system

Positional information is fundamental in development. Although molecular gradients are thought to represent positional information in various systems, the molecular logic used to interpret these gradients remains controversial. In the nervous system, sensory maps are formed in the brain based on gradients of axon guidance molecules. However, it remains unclear how axons find their targets based on relative, not absolute, expression levels of axon guidance receptors. No model solely based on axon-target interactions explains this point. Recent studies in the olfactory system suggested that the neural map formation requires axon-axon interactions, which is known as axon sorting. This review discusses how axon-axon and axon-target interactions interpret molecular gradients and determine the axonal projection sites in neural map formation.

Rotating Cell Culture Systems for Human Cell Culture: Human Trophoblast Cells as a Model

The field of human trophoblast research aids in understanding the complex environment established during placentation. Due to the nature of these studies, human in vivo experimentation is impossible. A combination of primary cultures, explant cultures and trophoblast cell lines support our understanding of invasion of the uterine wall and remodeling of uterine spiral arteries by extravillous trophoblast cells (EVTs), which is required for successful establishment of pregnancy. Despite the wealth of knowledge gleaned from such models, it is accepted that in vitro cell culture models using EVT-like cell lines display altered cellular properties when compared to their in vivo counterparts. Cells cultured in the rotating cell culture system (RCCS) display morphological, phenotypic, and functional properties of EVT-like cell lines that more closely mimic differentiating in utero EVTs, with increased expression of genes mediating invasion (e.g. matrix metalloproteinases (MMPs)) and trophoblast differentiation. The Saint Georges Hospital Placental cell Line-4 (SGHPL-4) (kindly donated by Dr. Guy Whitley and Dr. Judith Cartwright) is an EVT-like cell line that was used for testing in the RCCS. The design of the RCCS culture vessel is based on the principle that organs and tissues function in a three-dimensional (3-D) environment. Due to the dynamic culture conditions in the vessel, including conditions of physiologically relevant shear, cells grown in three dimensions form aggregates based on natural cellular affinities and differentiate into organotypic tissue-like assemblies. The maintenance of a fluid orbit provides a low-shear, low-turbulence environment similar to conditions found in vivo. Sedimentation of the cultured cells is countered by adjusting the rotation speed of the RCCS to ensure a constant free-fall of cells. Gas exchange occurs through a permeable hydrophobic membrane located on the back of the bioreactor. Like their parental tissue in vivo, RCCS-grown cells are able to respond to chemical and molecular gradients in three dimensions (i.e. at their apical, basal, and lateral surfaces) because they are cultured on the surface of porous microcarrier beads. When grown as two-dimensional monolayers on impermeable surfaces like plastic, cells are deprived of this important communication at their basal surface. Consequently, the spatial constraints imposed by the environment profoundly affect how cells sense and decode signals from the surrounding microenvironment, thus implying an important role for the 3-D milieu. We have used the RCCS to engineer biologically meaningful 3-D models of various human epithelial tissues. Indeed, many previous reports have demonstrated that cells cultured in the RCCS can assume physiologically relevant phenotypes that have not been possible with other models. In summary, culture in the RCCS represents an easy, reproducible, high-throughput platform that provides large numbers of differentiated cells that are amenable to a variety of experimental manipulations. In the following protocol, using EVTs as an example, we clearly describe the steps required to three-dimensionally culture adherent cells in the RCCS.

Mapping Spatiotemporal Molecular Distributions Using a Microfluidic Array

The spatial and temporal distributions of an extensive number of diffusible molecules drive a variety of complex functions. These molecular distributions often possess length scales on the order of a millimeter or less; therefore, microfluidic devices have become a powerful tool to study the effects of these molecular distributions in both chemical and biological systems. Although there exist a number of studies utilizing microdevices for the creation of molecular gradients, there are few, if any, studies focusing on the measurement of spatial and temporal distributions of molecular species created within the study system itself. Here we present a microfluidic device capable of sampling multiple chemical messengers in a spatiotemporally resolved manner. This device operates through spatial segregation of nanoliter-sized volumes of liquid from a primary sample reservoir into a series of analysis microchannels, where fluid pumping is accomplished via a system of passive microfluidic pumps. Subsequent chemical analysis within each microchannel, achieved via optical or bioanalytical methods, yields quantitative data on the spatial and temporal information for any analytes of interest existing within the sample reservoir. These techniques provide a simple, cost-effective route to measure the spatiotemporal distributions of molecular analytes, where the system can be tailored to study both chemical and biological systems.

Microstructure and surface property of macroscopic gradient polymer initiated by polysiloxane benzophenone photoinitiators with different silicone chain lengths

This paper reported three kinds of polysiloxane benzophenone photoinitiators (HBP-Si-A/B/C) with different silicon contents, which were synthesized based on traditional photoinitiator 4-hydroxy benzophenone (HBP) and epoxy polysiloxane. The effect of silicon content in the photoinitiator molecule on its photopolymerization property, the ability to float up and surface morphology and the property of the gradient polymer film initiated by it was investigated. It is proved by UV absorption and gel permeation chromatography (GPC) measurements that HBP-Si-A/B/C with different silicon content had different abilities to float up. As a result, the gradient polymer with more significant molecular weight gradients could be obtained by using the polysiloxane benzophenone photoinitiator with higher silicon content, which had a better ability to float up caused by lower surface tension and energy, and the surface property was connected with the surface microstructure. The increase of silicon content in the polysiloxane-based photoinitiator could decrease the dispersion surface energy of gradient polymer film initiated by it and generate a more hydrophobic surface by a change of microstructure. In addition, the polysiloxane-based photoinitiator could also restrain the forming of wrinkling on the surface of the UV-curable film due to mitigation of oxygen inhibition in radical photopolymerization, and it may have potential in controlling patterned microstructures and surface property.

A compact microfluidic gradient generator using passive pumping

Creating and maintaining a precise molecular gradient which is stable in space and time are essential to studies of chemotaxis. This paper describes a simple, compact, and user-friendly microfluidic device using a passive pumping method to drive the liquid flow to generate a stable concentration gradient. A fluidic circuit is designed to offset the effects of the pressure imbalance between the two inlets. After loading approximately the same amount of culture media containing different concentrations of a certain chemotactic agent into the two inlet reservoirs, a linear concentration gradient will be automatically and quickly established at the downstream. Our device takes advantage of passive pumping and is compact enough to fit into a Petri dish, which is an attractive feature to biologists. Furthermore, this microfluidic gradient generator offers a platform for a facile way of long-term imaging and analysis using high resolution microscopy.

A disposable and multifunctional capsule for easy operation of microfluidic elastomer systems

The global lab-on-chip and microfluidic markets for cell-based assays have been predicted to grow considerably, as novel microfluidic systems enable cell biologists to perform in vitro experiments at an unprecedented level of experimental control. Nevertheless, microfluidic assays must, in order to compete with conventional assays, be made available at easily affordable costs, and in addition be made simple to operate for users having no previous experience with microfluidics. We have to this end developed a multifunctional microfluidic capsule that can be mass-produced at low cost in thermoplastic material. The capsule enables straightforward operation of elastomer inserts of optional design, here exemplified with insert designs for molecular gradient formation in microfluidic cell culture systems. The integrated macro–micro interface of the capsule ensures reliable connection of the elastomer fluidic structures to an external perfusion system. A separate compartment in the capsule filled with superabsorbent material is used for internal waste absorption. The capsule assembly process is made easy by integrated snap-fits, and samples within the closed capsule can be analyzed using both inverted and upright microscopes. Taken together, the capsule concept presented here could help accelerate the use of microfluidic-based biological assays in the life science sector.

Oxidative Damage Targets Complexes Containing DNA Methyltransferases, SIRT1, and Polycomb Members to Promoter CpG Islands

Cancer cells simultaneously harbor global losses and gains in DNA methylation. We demonstrate that inducing cellular oxidative stress by hydrogen peroxide treatment recruits DNA methyltransferase 1 (DNMT1) to damaged chromatin. DNMT1 becomes part of a complex(es) containing DNMT3B and members of the polycomb repressive complex 4. Hydrogen peroxide treatment causes relocalization of these proteins from non-GC-rich to GC-rich areas. Key components are similarly enriched at gene promoters in an invivo colitis model. Although high-expression genes enriched for members of the complex have histone mark and nascent transcription changes, CpG island-containing low-expression genes gain promoter DNA methylation. Thus, oxidative damage induces formation and relocalization of a silencing complex that may explain cancer-specific aberrant DNA methylation and transcriptional silencing.

Imaging Mass Spectrometry of Three-Dimensional Cell Culture Systems

Three-dimensional (3D) cell cultures have increased complexity compared to simple monolayer and suspension cultures, recapitulating the cellular architecture and molecular gradients in tissue. As such, they are popular for in vitro models in biological research. Classical imaging methodologies, like immunohistochemistry, are commonly used to examine the distribution of specific species within the spheroids. However, there is a need for an unbiased discovery-based methodology that would allow examination of protein/peptide distributions in 3D culture systems, without a need for prior knowledge of the analytes. We have developed a matrix-assisted laser desorption/ionization-mass spectrometry (MALDI-MS)-based imaging approach to examine protein distributions in 3D cell culture models. Using colon carcinoma cell lines, we detect changes in the spatial distribution of proteins across 3D culture structures. To identify the protein species present, we are combining results from the MS/MS capabilities of MALDI-MS to sequence peptides in a de novo fashion and nanoflow liquid chromatography-tandem mass spectrometry (nLC-MS/MS) of homogenized cultures. As a proof-of-principle, we have identified cytochrome C and Histone H4 as two of the predominant protein species in the 3D colon carcinoma cultures.

New Insights into the Biophysics of Cellular Polarization during Embryogenesis

New Insights into the Biophysics of Cellular Polarization during Embryogenesis

Cell adhesion and focal contact formation on linear RGD molecular gradients: study of non-linear concentration dependence effects

Cell adhesion onto bioengineered surfaces is affected by a number of variables, including the former substrate derivatization process. In this investigation, we studied the correlation between cell adhesion and cell–adhesive ligand surface concentration and organization due to substrate modification. For this purpose, Arg-Gly-Asp (RGD) gradient surfaces were created on poly(methyl methacrylate) substrates by continuous hydrolysis and were then grafted with biotin-PEG-RGD molecules. Cell culture showed that adhesion behavior changes in a nonlinear way in the narrow range of RGD surface densities assayed (2.8 to 4.4 pmol/cm2), with a threshold value of 4.0 pmol/cm2 for successful cell attachment and spreading. This nonlinear dependence may be explained by nonhomogeneous RGD surface distribution at the nanometre scale, conditioned by the stochastic nature of the hydrolysis process. Atomic force microscopy analysis of the gradient surface showed an evolution of surface morphology compatible with this hypothesis. From the Clinical EditorThe authors observed by AFM nonlinear dependence of cell adhesion on RGD gradient surfaces with different surface densities. The nonlinear characteristics may be explained by non-homogeneous RGD surface distribution at the nanometer scale, conditioned by the stochastic nature of the hydrolysis process.

Adsorption of Mixed Peptide/Thiol Adlayers on InAs: Assessment of Different Functionalization Strategies Using X-ray Photoelectron Spectroscopy

Mixed adlayers are commonly used to create surfaces with multiple functional groups or molecular gradients. The resulting surfaces are designed to have the combined effects of each adsorbed functional group. In this work, we combine the passivation ability of a thiol with the functionality of a peptide by assembling mixed peptide/thiol adlayers on InAs. Both sequential (insertion) and simultaneous (co-assembly) methods are used to functionalize InAs and are analyzed by contact angle measurements and X-ray photoelectron spectroscopy (XPS). Peptide coverage, thiol coverage, and oxide layer thicknesses are estimated from XPS data. For each method, oxide layer thicknesses were significantly lower than the oxide thicknesses for as-received samples. Surfaces functionalized using the insertion methods had lower oxide layer thicknesses than peptide only samples, indicating that the addition of the thiol helped block oxide regrowth. Functionalization with the thiol followed by the peptide yielded surfaces with the...

Gradients for configuration interaction energies with spin‐orbit coupling in a semiempirical framework

We present a method for the analytical evaluation of the molecular energy gradient for a semiempirical configuration interaction (CI) wavefunction, taking into account the spin-orbit coupling. We show how to proceed in the simplest case where all the wavefunctions belonging to the CI subspace considered are mixed by the spin-orbit interaction, and we develop an original procedure for the more complex case where only a limited number of CI eigenvectors of the spin-free Hamiltonian are mixed.

The clock and wavefront model revisited

The currently accepted interpretation of the clock and wavefront model of somitogenesis is that a posteriorly moving molecular gradient sequentially slows the rate of clock oscillations, resulting in a spatial readout of temporal oscillations. However, while molecular components of the clocks and wavefronts have now been identified in the pre-somitic mesoderm (PSM), there is not yet conclusive evidence demonstrating that the observed molecular wavefronts act to slow clock oscillations. Here we present an alternative formulation of the clock and wavefront model in which oscillator coupling, already known to play a key role in oscillator synchronisation, plays a fundamentally important role in the slowing of oscillations along the anterior–posterior (AP) axis. Our model has three parameters which can be determined, in any given species, by the measurement of three quantities: the clock period in the posterior PSM, somite length and the length of the PSM. A travelling wavefront, which slows oscillations along the AP axis, is an emergent feature of the model. Using the model we predict: (a) the distance between moving stripes of gene expression; (b) the number of moving stripes of gene expression and (c) the oscillator period profile along the AP axis. Predictions regarding the stripe data are verified using existing zebrafish data. We simulate a range of experimental perturbations and demonstrate how the model can be used to unambiguously define a reference frame along the AP axis. Comparing data from zebrafish, chick, mouse and snake, we demonstrate that: (a) variation in patterning profiles is accounted for by a single nondimensional parameter; the ratio of coupling strengths; and (b) the period profile along the AP axis is conserved across species. Thus the model is consistent with the idea that, although the genes involved in pattern propagation in the PSM vary, there is a conserved patterning mechanism across species.

Building molecular surface gradients with electron beam lithography

We present a strategy for patterning self-assembled monolayers with control of the area density of the molecules on the surface in a continuous and tunable fashion. Variation of the electron beam lithography parameters on patterning an amino-terminated silane layer on silicon allows control of the effective area density of the silane molecules. Gold nanoparticles are used as labels to visualize the area density of the amino groups in scanning electron microscopy images. The ability to continuously vary the density of functional molecules on surfaces and prepare molecular gradients is of wide interest in the fields of electronics, sensing and biology.

Image-based analysis of primary human neutrophil chemotaxis in an automated direct-viewing assay

Multi-well assays based on the Boyden chamber have enabled highly parallel studies of chemotaxis—the directional migration of cells in response to molecular gradients—while direct-viewing approaches have allowed more detailed questions to be asked at low throughput. Boyden-based plates provide a count of cells that pass through a membrane, but no information about cell appearance. In contrast, direct-viewing devices enable the observation of cells during chemotaxis, which allows measurement of many parameters including area, shape, and location. Here we show automated chemotaxis and cell morphology assays in a 96-unit direct-viewing plate. Using only 12 000 primary human neutrophils per datum, we measured dose-dependent stimulation and inhibition of chemotaxis and quantified the effects of inhibitors on cell area and elongation. With 60 parallel conditions we demonstrated 5-fold increase in throughput compared to previously reported direct-viewing approaches.

Influence of unlimited 3-membered ring cyclization on a multiscale dynamic Monte Carlo/continuum model of drying and curing in sol–gel silica films

The coating process of sol–gel silica films involves multiple length and time scales ranging from molecular to macroscopic. At the molecular scale, cyclization during polymerization is so extensive that it cannot be neglected or treated statistically. Here we present a multiscale model of a 1D sol–gel drying process coupled to a Monte Carlo polymerization model with unlimited cyclization. Because our model allows cyclic and cage–like siloxanes to form, it is better able to predict the silica gelation conversion than any other reported kinetic model. By studying the competition between molecular growth and cyclization, and the competition between mass transfer (drying) and reaction (gelation) on the drying process of the sol–gel silica film, we observe that cyclization delays the gelation, shrinks the molecular size, increases the likelihood of literal skinning, and leads to a molecular structure gradient inside the film. Although for simplicity our model just considers the possibility of forming 3-membered ring, it is the first multiscale model to couple unlimited cyclization in polycondensation with a continuum mass transfer process. Also it is the first model that can predict structure gradients caused by drying in sol–gel silica films.

Gradient immobilization of a cell adhesion RGD peptide on thermal responsive surface for regulating cell adhesion and detachment

Using surface initiated atomic transfer radical polymerization (ATRP) and an injection method, a poly(N-isopropylacrylamide)-b-poly(acrylic acid)-g-RGD (PNIPAAm-b-PAA-g-RGD) gradient surface was prepared. First, a thermoresponsive surface with a constant thickness of PNIPAAm was fabricated, onto which the AA monomers were block copolymerized using the PNIPAAm macromolecules as initiators. During this process, a continuous injection method was employed to yield a molecular weight gradient of PAA on the underlying uniform PNIPAAm layer. RGD peptide was finally covalently immobilized onto the PAA gradient by carbodiimide chemistry. In vitro culture of HepG2 cells showed that immobilization of the RGD peptide could accelerate cell attachment, while the thermoresponsive layer beneath could effectively release the cells by simply lowering temperature. Thus, the PNIPAAm-b-PAA-g-RGD gradient surface, combining the thermal response with cell affinity properties, can well regulate the cell adhesion and detachment, which may thus be useful for investigation of cell-substrate interactions with a smaller number of samples.