Controlled Initiation of Enzymatic Reactions in Micrometer-Sized Biomimetic Compartments

Physicochemical considerations for bottom-up synthetic biology

The bottom-up construction of synthetic cells from molecular components is arguably one of the most challenging areas of research in the life sciences. We review the impact of confining biological systems in synthetic vesicles. Complex cell-like systems require control of the internal pH, ionic strength, (macro)molecular crowding, redox state and metabolic energy conservation. These physicochemical parameters influence protein activity and need to be maintained within limits to ensure the system remains in steady-state. We present the physicochemical considerations for building synthetic cells with dimensions ranging from the smallest prokaryotes to eukaryotic cells.

Protein synthesis in artificial cells: using compartmentalisation for spatial organisation in vesicle bioreactors

Spatially segregated in vitro protein expression in a vesicle-based artificial cell, with different proteins synthesised in defined vesicle regions.

Composition based strategies for controlling radii in lipid nanotubes

Nature routinely carries out small-scale chemistry within lipid bound cells and organelles. Liposome-lipid nanotube networks are being developed by many researchers in attempt to imitate these membrane enclosed environments, with the goal to perform small-scale chemical studies. These systems are well characterized in terms of the diameter of the giant unilamellar vesicles they are constructed from and the length of the nanotubes connecting them. Here we evaluate two methods based on intrinsic curvature for adjusting the diameter of the nanotube, an aspect of the network that has not previously been controllable. This was done by altering the lipid composition of the network membrane with two different approaches. In the first, the composition of the membrane was altered via lipid incubation of exogenous lipids; either with the addition of the low intrinsic curvature lipid soy phosphatidylcholine (soy-PC) or the high intrinsic curvature lipid soy phosphatidylethanolamine (soy-PE). In the second approach, exogenous lipids were added to the total lipid composition during liposome formation. Here we show that for both lipid augmentation methods, we observed a decrease in nanotube diameter following soy-PE additions but no significant change in size following the addition of soy-PC. Our results demonstrate that the effect of soy-PE on nanotube diameter is independent of the method of addition and suggests that high curvature soy-PE molecules facilitate tube membrane curvature.

Probing enzymatic activity inside single cells

We report a novel approach for determining the enzymatic activity within a single suspended cell. Using a steady-state microfluidic delivery device and timed exposure to the pore-forming agent digitonin, we controlled the plasma membrane permeation of individual NG108-15 cells. Mildly permeabilized cells (~100 pores) were exposed to a series of concentrations of fluorescein diphosphate (FDP), a fluorogenic alkaline phosphatase substrate, with and without levamisole, an alkaline phosphatase inhibitor. We generated quantitative estimates for intracellular enzyme activity and were able to construct both dose-response and dose-inhibition curves at the single-cell level, resulting in an apparent Michaelis contant Km of 15.3 μM ± 1.02 (mean ± standard error of the mean (SEM), n = 16) and an inhibition constant Ki of 0.59 mM ± 0.07 (mean ± SEM, n = 14). Enzymatic activity could be monitored just 40 s after permeabilization, and five point dose-inhibition curves could be obtained within 150 s. This rapid approach offers a new methodology for characterizing enzyme activity within single cells.

Exploration of the shapes of double-walled vesicles with a confined inner membrane

We investigate double-walled vesicles as a simple model system for multi-vesicular structures, where the inner membrane is confined within the outer membrane. Various shapes of double-walled vesicles in two dimensions are obtained by means of our recently-developed discrete space variation method, and the shapes of each layer are found to be interdependent. Confined within the outer membrane, an inner membrane with a larger surface area always shows a cristae shape. As previous simulations and theoretical analyses of a single-walled vesicle have been done before, the geometric properties of double-walled vesicles, including the mean square radius of gyration and volume within the vesicle membrane, are studied in detail as functions of the pressure and surface area. It is found that due to the inter-space restriction of each layer, double-walled vesicles exhibit different behaviors compared with the previously-observed scaling laws of single-walled vesicles. It is straightforward to extend this study to more complicated and realistic biological systems, such as those including electrostatic interactions between membranes and solvent, phase separation, and cooperative interactions between multicomponent membranes.

Generation of phospholipid vesicle-nanotube networks and transport of molecules therein

We describe micromanipulation and microinjection procedures for the fabrication of soft-matter networks consisting of lipid bilayer nanotubes and surface-immobilized vesicles. These biomimetic membrane systems feature unique structural flexibility and expandability and, unlike solid-state microfluidic and nanofluidic devices prepared by top-down fabrication, they allow network designs with dynamic control over individual containers and interconnecting conduits. The fabrication is founded on self-assembly of phospholipid molecules, followed by micromanipulation operations, such as membrane electroporation and microinjection, to effect shape transformations of the membrane and create a series of interconnected compartments. Size and geometry of the network can be chosen according to its desired function. Membrane composition is controlled mainly during the self-assembly step, whereas the interior contents of individual containers is defined through a sequence of microneedle injections. Networks cannot be fabricated with other currently available methods of giant unilamellar vesicle preparation (large unilamellar vesicle fusion or electroformation). Described in detail are also three transport modes, which are suitable for moving water-soluble or membrane-bound small molecules, polymers, DNA, proteins and nanoparticles within the networks. The fabrication protocol requires ∼90 min, provided all necessary preparations are made in advance. The transport studies require an additional 60-120 min, depending on the transport regime.

Liposome and lipid bilayer arrays towards biosensing applications

Sensitive and selective biosensors for high-throughput screening are having an increasing impact in modern medical care. The establishment of robust protein biosensing platforms however remains challenging, especially when membrane proteins are involved. Although this type of proteins is of enormous relevance since they are considered in >60% of the pharmaceutical drug targets, their fragile nature (i.e., the requirement to preserve their natural lipid environment to avoid denaturation and loss of function) puts strong additional prerequisites onto a successful biochip. In this review, the leading approaches to create lipid membrane-based arrays towards the creation of membrane protein biosensing platforms are described. Liposomes assembled in micro- and nanoarrays and the successful set-ups containing functional membrane proteins, as well as the use of liposomes in networks, are discussed in the first part. Then, the complementary approaches to create cell-mimicking supported membrane patches on a substrate in an array format will be addressed. Finally, the progress in assembling free-standing (functional) lipid bilayers over nanopore arrays for ion channel sensing will be reported. This review illustrates the rapid pace by which advances are being made towards the creation of a heterogeneous biochip for the high-throughput screening of membrane proteins for diagnostics, drug screening, or drug discovery purposes.

Direct access and control of the intracellular solution environment in single cells

Methods that can control and vary the solution environment around single cells are abundant. In contrast, methods that offer direct access to the intracellular proteome and genome in single cells with the control, flexibility, and convenience given by microfluidic methods are both scarce and in great demand. Here, we present such a method based on using a microfluidic device mounted on a programmable scanning stage and cells on-chip permeabilized by the pore-forming glycoside digitonin. We characterized the on-chip digitonin poration, as well as the solution exchange within cells. Intracellular solution exchange times vary with the dose of exposure to digitonin from less than a second to tens of seconds. Also, the degree of permeabilization obtained for cells treated with the same dose varies considerably, especially for low doses of digitonin exposure and low permeabilities. With the use of the presented setup, the degree of permeabilization can be measured during the permeabilization process, which allows for "on-line" optimization of the digitonin exposure time. Using this calibrated permeabilization method, we demonstrate the generation of intracellular oscillations, intracellular gradients, and the delivery of substrate to initiate enzymatic reactions in situ. This method holds the potential to screen and titrate intracellular receptors or enzymes or to generate intracellular oscillations, useful in the study of signaling pathways and oscillation decoding among other applications.

Steady-state electrochemical determination of lipidic nanotube diameter utilizing an artificial cell model

By exploiting the capabilities of steady-state electrochemical measurements, we have measured the inner diameter of a lipid nanotube using Fick's first law of diffusion in conjunction with an imposed linear concentration gradient of electroactive molecules over the length of the nanotube. Fick's law has been used in this way to provide a direct relationship between the nanotube diameter and the measurable experimental parameters Deltai (change in current) and nanotube length. Catechol was used to determine the Deltai attributed to its flux out of the nanotube. Comparing the nanotube diameter as a function of nanotube length revealed that membrane elastic energy was playing an important role in determining the size of the nanotube and was different when the tube was connected to either end of two vesicles or to a vesicle on one end and a pipet tip on the other. We assume that repulsive interaction between neck regions can be used to explain the trends observed. This theoretical approach based on elastic energy considerations provides a qualitative description consistent with experimental data.

Development and fabrication of nanoporous silicon-based bioreactors within a microfluidic chip

Multi-scale lithography and cryogenic deep reactive ion etching techniques were used to create ensembles of nanoporous, picolitre volume, reaction vessels within a microfluidic system. The fabrication of these vessels is described and how this process can be used to tailor vessel porosity by controlling the width of slits that constitute the vessel pores is demonstrated. Control of pore size allows the containment of nucleic acids and enzymes that are the foundation of biochemical reaction systems, while allowing smaller reaction constituents to traverse the container membrane and continuously supply the reaction. In this work, a 5.4 kb DNA plasmid was retained within the reaction vessels and labeled under microfluidic control with ethidium bromide as an initial proof-of-principle. Subsequently, a coupled enzyme reaction, in which glucose oxidase (GOX) and horseradish peroxidase (HRP) were contained and fed with a substrate solution of glucose and Amplex Red to produce fluorescent resorufin, was carried out under microfluidic control and monitored using fluorescent microscopy. The fabrication techniques presented are broadly applicable and can be adapted to produce devices in which a variety of high aspect ratio, nanoporous silicon structures can be integrated within a microfluidic network. The devices shown here are amenable to being scaled in number and organized to implement more complex reaction systems for applications in sensing and actuation as well as fundamental studies of biological reaction systems.

Microcompartmentation in artificial cells: pH-induced conformational changes alter protein localization

We report artificial cells in which protein localization in a primitive synthetic model for the cytoplasm is controlled by pH. Our model cells are giant lipid vesicles (GVs, ca. 5-30 microm diameter) with two coexisting aqueous compartments generated by phase separation of an encapsulated poly(ethylene glycol) (PEG) and dextran solution. Proteins are localized to a microcompartment by partitioning between the phases. We quantified the local concentration of fluorescently labeled human serum albumin (HSA) via confocal fluorescence microscopy. At pH 6.5, the labeled HSA was more concentrated in the dextran-rich phase, but at partially/fully denaturing pH (4.1 or 12) it was localized in the PEG-rich phase. This partitioning behavior is consistent with a more expanded, hydrophobic conformation at low and high pH. Labeled HSA could be relocalized from the PEG-rich into the dextran-rich phase domain by increasing the pH from 4.1 to 6.5 to renature the protein. This approach to controlling protein localization does not require extensive reorganization of the vesicle interior; coexisting PEG-rich and dextran-rich compartments are maintained throughout the experiments. It is also quite general; we demonstrated that several other proteins varying in size and isoelectric point also relocalized within compartmentalized artificial cells in response to external pH change. This work presents stimulus-responsive protein relocalization between compartments in an artificial cell; such experimental models can provide a framework for investigating the consequences of protein localization in cell biology.

Thermodynamics and dynamics of the formation of spherical lipid vesicles

We propose a free energy expression accounting for the formation of spherical vesicles from planar lipid membranes and derive a Fokker-Planck equation for the probability distribution describing the dynamics of vesicle formation. We find that formation may occur as an activated process for small membranes and as a transport process for sufficiently large membranes. We give explicit expressions for the transition rates and the characteristic time of vesicle formation in terms of the relevant physical parameters.

The multiple faces of self-assembled lipidic systems

Lipids, the building blocks of cells, common to every living organisms, have the propensity to self-assemble into well-defined structures over short and long-range spatial scales. The driving forces have their roots mainly in the hydrophobic effect and electrostatic interactions. Membranes in lamellar phase are ubiquitous in cellular compartments and can phase-separate upon mixing lipids in different liquid-crystalline states. Hexagonal phases and especially cubic phases can be synthesized and observed in vivo as well. Membrane often closes up into a vesicle whose shape is determined by the interplay of curvature, area difference elasticity and line tension energies, and can adopt the form of a sphere, a tube, a prolate, a starfish and many more. Complexes made of lipids and polyelectrolytes or inorganic materials exhibit a rich diversity of structural morphologies due to additional interactions which become increasingly hard to track without the aid of suitable computer models. From the plasma membrane of archaebacteria to gene delivery, self-assembled lipidic systems have left their mark in cell biology and nanobiotechnology; however, the underlying physics is yet to be fully unraveled.PACS Codes: 87.14.Cc, 82.70.Uv.

Macromolecular crowding improves polymer encapsulation within giant lipid vesicles

We report the effect of macromolecular crowding on encapsulation efficiency of fluorescently labeled poly(ethylene glycol) (PEG) and dextran polymers within individual giant lipid vesicles (GVs). Low concentrations of the fluorescently labeled polymers (82 nM to 186 pM) were mixed with varying concentrations of nonfluorescent polymers that served as crowding agents during vesicle formation by gentle hydration. Encapsulation efficiency of the fluorescently labeled polymers in individual GVs (EEind) was determined via confocal fluorescence microscopy. EEind for high molecular weight polymers (e.g., fluorescein isothiocyanate (FITC)-dextran 500 and 2000 kDa) increased substantially in the presence of several weight percent unlabeled PEG or dextran. For example, when 0.24 microM FITC dextran 500 kDa was encapsulated, addition of 3% PEG 8 kDa improved the mean concentration in the GVs from 0.14 microM (+/-50%) to 0.24 microM (+/-12%). Light scattering data indicate reduced hydrodynamic radii for polymers as a function of increasing polymer concentration, suggesting that the improvements in EEind result from polymer condensation due to macromolecular crowding. Polymeric cosolutes did not significantly impact EEind for lower molecular weight polymers (e.g., Alexa Fluor 488-PEG 20 kDa), which already encapsulated efficiently (EEind to approximately 1). However, for both the higher and lower molecular weight labeled polymers, cosolutes led to improved uniformity in EEind for vesicles within a batch. Methods for improving the value and homogeneity of EEind for polymeric solutes in lipid vesicles are important in a variety of applications, including the use of vesicles as microreactors and as vehicles for drug delivery.

Shape optimization in lipid nanotube networks

Starting from a high surface free-energy state, lipid nanotube networks are capable to self-organize into tree-like structures with particular geometrical features. In this work we analyze the process of self-organization in such networks, and report a strong similarity to the Euclidian Steiner Tree Problem (ESTP). ESTP is a well-known NP-hard optimization problem of finding a network connecting a given set of terminal points on a plane, allowing addition of auxiliary points, with the overall objective to minimize the total network length. The present study shows that aggregate lipid structures self-organize into geometries that correspond to locally optimal solutions to such problems.

Injection and transport of bacteria in nanotube-vesicle networks

The microinjection of bacteria (the MG1655 strain of E. coli) into unilamellar lipid vesicles contained in surface-immobilized nanotube-vesicle networks is demonstrated. The density of bacteria can be controlled from a single bacterium up to several thousands of bacteria per injected vesicle. The bacteria retain flagellar motion and propulsion. The bacteria (approximately 2 × 0.8 μm) cannot escape from one vesicle to another as the size of the nanotubes is too small (∼200 nm in diameter) to allow for entry. Bacteria can, however, be moved from one vesicle to another in a nanotube-vesicle network by using Marangoni flows. Thus, single or several species can be transferred to a neighboring vesicle at will. The technique offers new possibilities for live matter functionalization into synthetic host networks, and may provide means for studying the effect of compartmentalization and perfusion of chemical species on a single bacterium. Furthermore, it may serve as an experimental model to study how vesicle-encapsulated bacteria evade destruction in macrophages or how bacteria surf along thin membrane nanotubes toward connected macrophage cell bodies.

Liposomes: technologies and analytical applications

Liposomes are structurally and functionally some of the most versatile supramolecular assemblies in existence. Since the beginning of active research on lipid vesicles in 1965, the field has progressed enormously and applications are well established in several areas, such as drug and gene delivery. In the analytical sciences, liposomes serve a dual purpose: Either they are analytes, typically in quality-assessment procedures of liposome preparations, or they are functional components in a variety of new analytical systems. Liposome immunoassays, for example, benefit greatly from the amplification provided by encapsulated markers, and nanotube-interconnected liposome networks have emerged as ultrasmall-scale analytical devices. This review provides information about new developments in some of the most actively researched liposome-related topics.

Model membrane systems and their applications

The complexity of biological membranes has motivated the development of a wide variety of simpler model systems whose size, geometry, and composition can be tailored with great precision. Approaches highlighted in this review are illustrated in Figure 1 including vesicles, supported bilayers, and hybrid membrane systems. These have been used to study problems ranging from phase behavior to membrane fusion. Experimental membrane models continue to advance in complexity with respect to architecture, size, and composition, as do computer simulations of their properties and dynamics. Analytical techniques such as imaging secondary ion mass spectrometry have also been developed and refined to give increasing spatial resolution and information content on membrane composition and dynamics.

Using giant unilamellar lipid vesicle micro-patterns as ultrasmall reaction containers to observe reversible ATP synthesis/hydrolysis of F0F1-ATPase directly

F(0)F(1)-ATPase within chromatophores, which was labeled with pH-sensitive quantum dots, was encapsulated in large unilamellar lipid vesicles (LUVs) through reverse-phase evaporation. Then a microarray of chromatophore-containing LUVs was created using a micro-contact printing (mu-CP) technique. Through controlled dehydration-rehydration of the lipid patterns, a microarray of single chromatophore-containing giant unilamellar lipid vesicles (GUVs) was formed with desired size and uniform shape. The reversible ATP synthesis/hydrolysis of F(0)F(1)-ATPase in GUVs was directly observed by fluorescence microscopy through the fluorescence intensity increase/decrease in the pH-sensitive quantum dots labeled on the outer surface of the chromatophore. To the best of our knowledge, this is the first direct observation of the reversible behavior of F(0)F(1)-ATPase at the bulk scale.

Polymer encapsulation within giant lipid vesicles

We report encapsulation of polymers and small molecules within individual giant lipid vesicles (GVs; 3-80 microm), as determined by confocal fluorescence microscopy. Polymer-bound or free dyes were encapsulated within GVs by including these molecules in the aqueous solution during vesicle formation via gentle hydration. Encapsulation efficiencies of individual GVs (EE(ind)) were determined from the fluorescence intensity ratio inside vs outside the vesicle. EE(ind) varied considerably from vesicle to vesicle, with interior solute concentrations for GVs within the same batch ranging from much less than to slightly more than the initial concentration. The majority of GVs had high internal concentrations of polymer or small-molecule encapsulants equal to or slightly greater than the external concentration. EE(ind) decreased for high molecular weight polymers (e.g., dextran 500 000), but was relatively insensitive to the GV diameter, membrane composition, or incubation temperature in our experiments. Knowledge of EE(ind) is important for quantitative evaluation of reactions occurring within GVs (e.g., enzymatic processes) and for optimizing encapsulation conditions.

Tunable filtering of chemical signals in a simple nanoscale reaction-diffusion network

We study numerically the filtering capabilities of a nanoscale network of two micrometer-sized containers joined by a nanotube, one of which hosts an enzymatic chemical reaction. Spatiotemporal chemical signals of substrate molecules are injected into the network. The substrate propagates by diffusion and reacts with enzymes distributed in the network prior to the injections. The dimensions of the network are tailored in a way that the transport and enzymatic reaction rates are comparable in size, a situation in which the overall behavior is highly influenced by the geometry and topology of the network. This property is crucial for the functionality of the filter developed in here. It is demonstrated that input signals can be classified in a crude way using a simple setup (a two-container network) and that the classification can be tuned by changing the geometry of the network (the length of the tube connecting the two containers). The filter device we investigate can also be viewed as a primitive chemistry-based computational element in the sense that the information encoded in the signals is processed using chemical reactions. In particular, it is demonstrated that the two-container device may filter out signals based on the average injection frequency.

Solid supported lipid bilayers: From biophysical studies to sensor design

The lipid bilayer is one of the most eloquent and important self-assembled structures in nature. It not only provides a protective container for cells and sub-cellular compartments, but also hosts much of the machinery for cellular communication and transport across the cell membrane. Solid supported lipid bilayers provide an excellent model system for studying the surface chemistry of the cell. Moreover, they are accessible to a wide variety of surface-specific analytical techniques. This makes it possible to investigate processes such as cell signaling, ligand-receptor interactions, enzymatic reactions occurring at the cell surface, as well as pathogen attack. In this review, the following membrane systems are discussed: black lipid membranes, solid supported lipid bilayers, hybrid lipid bilayers, and polymer cushioned lipid bilayers. Examples of how supported lipid membrane technology is interfaced with array based systems by photolithographic patterning, spatial addressing, microcontact printing, and microfluidic patterning are explored. Also, the use of supported lipid bilayers in microfluidic devices for the development of lab-on-a-chip based platforms is examined. Finally, the utility of lipid bilayers in nanotechnology and future directions in this area are discussed.

Zipper dynamics of surfactant nanotube Y junctions

We investigate the formation of Y junctions in surfactant nanotubes connecting vesicles. Based on experimental observations of the surfactant flow on the nanotubes, we conclude that a Y junction propagates with a zipperlike mechanism. The surfactants from two nanotube branches undergo 1:1 mixing at the junction, and spontaneously form the extension of the third nanotube branch. Taking into account the tension driven surfactant flow, we develop a model for the Y junction dynamics that is in quantitative agreement with the experimental data.

Direct reconstitution of plasma membrane lipids and proteins in nanotube-vesicle networks

We demonstrate here that nanotube-vesicle networks can be constructed directly from plasma membranes of cultured cells. We used a combination of dithiothreitol (DTT) and formaldehyde to produce micron-sized plasma membrane vesicles that were subsequently shaped into networks using micromanipulation methods previously used on purely synthetic systems. Only a single cell is required to derive material sufficient to build a small network. This protocol covers the advantages of reconstitution in vesicles, such as full control over the solution environment, while keeping the proteins in their original surroundings with the proper orientation. Furthermore, control of membrane protein and lipid content in the networks is achievable by employing different cell types, for example, by overexpression of a desired protein or the use of specialized cell-types as sources for rare proteins and lipids. In general, the method provides simple accessibility for functional studies of plasma membrane constituents. Specifically, it provides a direct means to functionalize nanotube-vesicle networks with desired proteins and lipids for studies of transport activity both across membranes (protein-mediated) and across nanotubes (diffusion), and substrate conversion down to the single-molecule limit. Nanotube-vesicle networks can adopt different geometries and topologies and undergo shape changes at will, providing a flexible system for changing the physical and chemical environment around, for example, a membrane protein. Furthermore, the method offers unique possibilities for extracting membrane and protein material for nanotechnological sensor and analytical devices based on lipid membrane networks.

Proton Permeation into Single Vesicles Occurs via a Sequential Two-Step Mechanism and Is Heterogeneous

This article describes the first single-vesicle study of proton permeability across the lipid membrane of small (approximately 100 nm) uni- and multilamellar vesicles, which were composed of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC). To follow proton permeation into the internal volume of each vesicle, we encapsulated carboxyfluorescein, a pH-sensitive dye whose fluorescence was quenched in the presence of excess protons. A microfluidic platform was used for easy exchange of high- and low-pH solutions, and fluorescence quenching of single vesicles was detected with single-molecule total internal reflection fluorescence (TIRF) microscopy. Upon solution exchange and acidification of the extravesicular solution (from pH 9 to 3.5), we observed for each vesicle a biphasic decay in fluorescence. Through single-vesicle analysis, we found that rate constants for the first decay followed a Poisson distribution, whereas rate constants for the second decay followed a normal distribution. We propose that proton permeation into each vesicle first arose from formation of transient pores and then transitioned into the second decay phase, which occurred by the solubility-diffusion mechanism. Furthermore, for the bulk population of vesicles, the decay rate constant and vesicle intensity (dependent on size) correlated to give an average permeability coefficient; however, for individual vesicles, we found little correlation, which suggested that proton permeability among single vesicles was heterogeneous in our experiments.

Nanoscale pipetting for controlled chemistry in small arrayed water droplets using a double-barrel pipet

We present a new methodology which provides for the miniaturization of one of the most common tools in use in chemistry and biology laboratories today-the micropipet. We have used glass-fabricated double-barrel nanopipets to controllably produce arrayed water droplets with volumes as small as a few attoliters under an organic layer. We have addressed individual droplets and added controlled amounts of either additional volume or reagents from one of the barrels of the pipet. We demonstrate that this method can be used for miniaturized cell-free protein expression.

Controlling enzymatic reactions by geometry in a biomimetic nanoscale network

We demonstrate that a transition from a compact geometry (sphere) to a structured geometry (several spheres connected by nanoconduits) in nanotube-vesicle networks (NVNs) induces an ordinary enzyme-catalyzed reaction to display wavelike properties. The reaction dynamics can be controlled directly by the geometry of the network, and such networks can be used to generate wavelike patterns in product formation. The results have bearing for understanding catalytic reactions in biological systems as well as for designing emerging wet chemical nanotechnological devices.

Biofabrication with Chitosan

The traditional motivation for integrating biological components into microfabricated devices has been to create biosensors that meld the molecular recognition capabilities of biology with the signal processing capabilities of electronic devices. However, a different motivation is emerging; biological components are being explored to radically change how fabrication is achieved at the micro- and nanoscales. Here we review biofabrication, the use of biological materials for fabrication, and focus on three specific biofabrication approaches: directed assembly, where localized external stimuli are employed to guide assembly; enzymatic assembly, where selective biocatalysts are enlisted to build macromolecular structure; and self-assembly, where information internal to the biological material guides its own assembly. Also reviewed are recent results with the aminopolysaccharide chitosan, a material that offers a combination of properties uniquely suited for biofabrication. In particular, chitosan can be directed to assemble in response to locally applied electrical signals, and the chitosan backbone provides sites that can be employed for the assembly of proteins, nucleic acids, and virus particles.

Diffusive transport in networks built of containers and tubes

We have developed analytical and numerical methods to study the transport of noninteracting particles in large networks consisting of M d -dimensional containers C1,...,C(M) with radii R(i) linked together by tubes of length l(ij) and radii a(ij) where i,j = 1,2,...,M. Tubes may join directly with each other, forming junctions. It is possible that some links are absent. Instead of solving the diffusion equation for the full problem we formulated an approach that is computationally more efficient. We derived a set of rate equations that govern the time dependence of the number of particles in each container, N1(t), N2(t),...,N(M)(t). In such a way the complicated transport problem is reduced to a set of M first-order integro-differential equations in time, which can be solved efficiently by the algorithm presented here. The workings of the method have been demonstrated on a couple of examples: networks involving three, four, and seven containers and one network with a three-point junction. Already simple networks with relatively few containers exhibit interesting transport behavior. For example, we showed that it is possible to adjust the geometry of the networks so that the particle concentration varies in time in a wave-like manner. Such behavior deviates from simple exponential growth and decay occurring in the two-container system.