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Quantitative transcription regulation studies in vivo and in vitro often make use of reporter proteins. Here we show that using Broccoli aptamers, quantitative study of transcription in various regulatory scenarios is possible without a translational step. To explore the method we studied several regulatory scenarios that we analyzed using thermodynamic occupancy-based models, and found excellent agreement with previous studies. In the next step we show that non-coding DNA can have a dramatic effect on the level of transcription, similar to the influence of the lac repressor with a strong affinity to operator sites. Finally, we point out the limitations of the method in terms of delay times coupled to the folding of the aptamer. We conclude that the Broccoli aptamer is suitable for quantitative transcription measurements., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 van der Sijs et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Poorly water-soluble iron-containing compounds are promising iron fortificants. However, ensuring high bioaccessibility and low reactivity of iron is challenging. We present the potential application of ferrous pyrophosphate (Fe(II)PP) and Fe(II)-containing M 2(1- x ) Fe 2 x P 2 O 7 salts (0 < x < 1, M = Ca, Zn, or Mn) for delivery of iron and a second essential mineral (M). After preparation by a facile and environment-friendly coprecipitation method, the salts were investigated for their composition, pH-dependent dissolution, iron-mediated discoloration of a black tea solution, and oxidation of vitamin C. Our results suggest that these salts are possible dual-fortificants with tunable composition that compared to Fe(II)PP (i) show lower (<0.5 mM) and enhanced (to 5 mM) iron dissolution in moderate and gastric pH, respectively, (ii) exhibit less discoloration and dissolved iron in tea when x = 0.470 for M = Ca or Zn and x = 0.086 for M = Mn, and (iii) do not increase the oxidation extent of vitamin C over 48 h when x = 0.06, 0.086, or 0.053 for M = Ca, Zn, or Mn, respectively., Competing Interests: The authors declare no competing financial interest., (© 2024 The Authors. Published by American Chemical Society.)

Hypothesis: Oil-water interfaces that are created by confining a certain amount of oil in a square shaped pixel (∼200 x 200 μm 2 with a height of ∼10 μm) topped by a layer of water, have a curvature that depends on the amount of oil that happens to be present in the confining area. Under the application of an electric field normal to the interface, the interface will deform due to inhomogeneities in the electric field. These inhomogeneities are expected to arise from the initial curvature of the meniscus, from fringe fields that emerge at the confining pixel walls and, if applicable, from interfacially adsorbed particles., Modeling and Experiments: We model the shape of the confined oil-water interface invoking capillarity and electrostatics. Furthermore, we measure the initial curvature by tracking the position of interfacially adsorbed particles depending on sample tilt., Findings: We found that the pixels exhibited meniscus curvature radii ranging from 0.6-7 mm. The corresponding model based minimum oil film thicknesses range between 0.7 and 9 μm. Furthermore, the model shows that the initial meniscus curvature can increase up to 76 percent relative to the initial curvature by the electric field before the oil film becomes unstable. The pixel wall and particles are shown to have minimal impact on the interface deformation., Competing Interests: Declaration of Competing Interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Faranaaz Rogier reports financial support was provided by Dutch Research Council (TOPPUNT Grant)., (Copyright © 2023 The Author(s). Published by Elsevier Inc. All rights reserved.)

Genetic feedback loops can be used by cells to regulate internal processes or to keep track of time. It is often thought that, for a genetic circuit to display self-sustained oscillations, a degree of cooperativity is needed in the binding and unbinding of actor species. This cooperativity is usually modeled using a Hill function, regardless of the actual promoter architecture. Furthermore, genetic circuits do not operate in isolation and often transcription factors are shared between different promoters. In this work we show how mathematical modelling of genetic feedback loops can be facilitated with a mechanistic fold-change function that takes into account the titration effect caused by competing binding sites for transcription factors. The model shows how the titration effect facilitates self-sustained oscillations in a minimal genetic feedback loop: a gene that produces its own repressor directly without cooperative transcription factor binding. The use of delay-differential equations leads to a stability contour that predicts whether a genetic feedback loop will show self-sustained oscillations, even when taking the bursty nature of transcription into account., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Landman et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Mixed pyrophosphate salts with the general formula Ca 2(1-x) Fe 4x (P 2 O 7 ) (1+2x) potentially possess less iron-phenolic reactivity compared to ferric pyrophosphate (FePP), due to decreased soluble Fe in the food-relevant pH range 3-7. We investigated reactivity (i.e., complexation, oxidation, and surface interaction) of FePP and mixed salts (with x = 0.14, 0.15, 0.18, and 0.35) in presence of structurally diverse phenolics. At pH 5-7, increased soluble iron from all salts was observed in presence of water-soluble phenolics. XPS confirmed that water-soluble phenolics solubilize iron after coordination at the salt surface, resulting in increased discoloration. However, color changes for mixed salts with x ≤ 0.18 remained acceptable for slightly water-soluble and insoluble phenolics. Furthermore, phenolic oxidation in presence of mixed salts was significantly reduced compared to FePP at pH 6. In conclusion, these mixed Ca-Fe(III) pyrophosphate salts with x ≤ 0.18 can potentially be used in designing iron-fortified foods containing slightly water-soluble and/or insoluble phenolics., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

What measurable physical properties allow one to distinguish surfactant-stabilised from Pickering emulsions? Whereas surfactants influence oil/water interfaces by lowering the oil/water interfacial tension, particles are assumed to have little effect on the interfacial tension. Here we perform interfacial tension (IFT) measurements on three different systems: (1) soybean oil and water with ethyl cellulose nanoparticles (ECNPs), (2) silicone oil and water with the globular protein bovine serum albumin (BSA), and (3) sodium dodecyl sulfate (SDS) solutions and air. The first two systems contain particles, while the third system contains surfactant molecules. We observe a significant decrease in interfacial tension with increasing particle/molecule concentration in all three systems. We analyse the surface tension data using the Gibbs adsorption isotherm and the Langmuir equation of state for the surface, resulting in surprisingly high adsorption densities for the particle-based systems. These seem to behave very much like the surfactant system: the decrease in tension is due to the presence of many particles at the interface, each with an adsorption energy of a few k B T . Dynamic interfacial tension measurements show that the systems are in equilibrium, and that the characteristic time scale for adsorption is much longer for particle-based systems than for surfactants, in line with their size difference. In addition, the particle-based emulsion is shown to be less stable against coalescence than the surfactant-stabilised emulsion. This leaves us with the conclusion that we are not able to make a clear distinction between the surfactant-stabilised and Pickering emulsions.

Hydrophobic polyelectrolytes (HPEs) can solubilize bilayer membranes, form micelles, or can reversibly aggregate as a function of pH. The transitions are often remarkably sharp. We show that these cooperative transitions occur by a competition between two or more conformational states and can be explained within the framework of Monod-Wymann-Changeux (MWC) theory that was originally formulated for allosteric interactions. Here, we focus on the pH-dependent destabilization and permeation of bilayer membranes by HPEs. We formulate the general conditions that lead to sharp conformational transitions involving simple macromolecules mediated by concentration variations of molecular ligands. That opens up potential applications ranging from medicine to the development of switchable materials.

Hypothesis: Well-defined two-dimensional colloidal crystal monolayers (CCM) have numerous applications, such as photonic crystal, sensors, and masks for colloidal lithography. Therefore, significant effort was devoted to the preparation of preparing CCM. However, the fabrication of CCM that can float in the continuous phase and readily transfer to other substrate remains an elusive challenge., Experiments: In this article a facile approach to prepare floating CCM from polymeric colloids as building blocks is reported. The key to obtain floating CCM is the selection of an appropriate solvent to release the formed CCM from the substrate. There are two steps involved in the preparation of floating CCM: formation and peeling off., Findings: First, colloids are dispersed in a solvent. Evaporation of this solvent results in the formation of a meniscus structure of the air-liquid interface between the colloids that are on the substrate. The deformation of the meniscus gives rise to capillary attraction, driving the colloids together in a dense monolayer. Once a crystallization nucleus is formed, a convective flow containing additional colloids sets in, resulting in the formation of CCM on the substrate. Second, the remaining bulk dispersion is replaced by an extracting solvent that wets the substrate and peels the formed CCM off. The influence of the several solvents, the substrate materials, and the types of colloids on the CCM formation are investigated systematically. The robustness of the approach facilitates the preparation of CCM. Furthermore, the floating feature of the CCM in principle makes transfer of the CCM to other substrates possible, which broadens its applications., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier Inc. All rights reserved.)

Mimicking the locomotive abilities of living organisms on the microscale, where the downsizing of rigid parts and circuitry presents inherent problems, is a complex feat. In nature, many soft-bodied organisms (inchworm, leech) have evolved simple, yet efficient locomotion strategies in which reciprocal actuation cycles synchronize with spatiotemporal modulation of friction between their bodies and environment. We developed microscopic (∼100 μm) hydrogel crawlers that move in aqueous environment through spatiotemporal modulation of the friction between their bodies and the substrate. Thermo-responsive poly-n-isopropyl acrylamide hydrogels loaded with gold nanoparticles shrink locally and reversibly when heated photothermally with laser light. The out-of-equilibrium collapse and reswelling of the hydrogel is responsible for asymmetric changes in the friction between the actuating section of the crawler and the substrate. This friction hysteresis, together with off-centered irradiation, results in directional motion of the crawler. We developed a model that predicts the order of magnitude of the crawler motion (within 50%) and agrees with the observed experimental trends. Crawler trajectories can be controlled enabling applications of the crawler as micromanipulator that can push small cargo along a surface.

Hypothesis: Self-assembly using anisotropic colloidal building blocks may lead to superstructures similar to those found in molecular systems yet can have unique optical, electronic, and structural properties. To widen the spectrum of achievable superstructures and related properties, significant effort was devoted to the synthesis of new types of colloidal particles. Despite these efforts, the preparation of anisotropic colloids carrying chemically orthogonal anchor groups on distinct surface patches remains an elusive challenge., Experiments: We report a simple yet effective method for synthesizing patchy particles via seed-mediated heterogeneous nucleation. Key to this procedure is the use of 3-(trimethoxysilyl)propyl methacrylate (TPM) or 3-(trimethoxysilyl)propyl acrylate (TMSPA), which can form patches on a variety of functional polymer seeds via a nucleation and growth mechanism., Findings: A family of anisotropic colloids with tunable numbers of patches and patch arrangements were prepared. By continuously feeding TPM or TMSPA the geometry of the colloids could be adjusted accurately. Furthermore, the patches could be reshaped by selectively polymerizing and/or solvating the individual colloidal compartments. Relying on the chemically distinct properties of the TPM/TMSPA and seed-derived domains, both types of patches could be functionalized independently. Combining detailed control over the patch chemistry and geometry opens new avenues for colloidal self-assembly., Competing Interests: Declaration of Competing Interest The authors declared that there is no conflict of interest., (Copyright © 2020 The Author(s). Published by Elsevier Inc. All rights reserved.)

Chemotactic interactions are ubiquitous in nature and can lead to non-reciprocal and complex emergent behaviour in multibody systems. However, developing synthetic, inanimate embodiments of a chemomechanical framework to generate non-reciprocal interactions of tunable strength and directionality has been challenging. Here we show how chemotactic signalling between microscale oil droplets of different chemistries in micellar surfactant solutions can result in predator-prey-like non-reciprocal chasing interactions. The interactions and dynamic self-organization result from the net directional, micelle-mediated transport of oil between emulsion droplets of differing composition and are powered by the free energy of mixing. We systematically elucidated chemical design rules to tune the interactions between droplets by varying the oil and surfactant chemical structure and concentration. Through the integration of experiment and simulation, we also investigated the active behaviour and dynamic reorganization of multidroplet clusters. Our findings demonstrate how chemically minimal systems can be designed with controllable, non-reciprocal chemotactic interactions to generate emergent self-organization and collective behaviours reminiscent of biological systems.

Transient assembled structures play an indispensable role in a wide variety of processes fundamental to living organisms including cellular transport, cell motility, and proliferation. Typically, the formation of these transient structures is driven by the consumption of molecular fuels via dissipative reaction networks. In these networks, building blocks are converted from inactive precursor states to active (assembling) states by (a set of) irreversible chemical reactions. Since the activated state is intrinsically unstable and can be maintained only in the presence of sufficient fuel, fuel depletion results in the spontaneous disintegration of the formed superstructures. Consequently, the properties and behavior of these assembled structures are governed by the kinetics of fuel consumption rather than by their thermodynamic stability. This fuel dependency endows biological systems with unprecedented spatiotemporal adaptability and inherent self-healing capabilities. Fascinated by these unique material characteristics, coupling the assembly behavior to molecular fuel or light-driven reaction networks was recently implemented in synthetic (supra)molecular systems. In this invited feature article, we discuss recent studies demonstrating that dissipative assembly is not limited to the molecular world but can also be translated to building blocks of colloidal dimensions. We highlight crucial guiding principles for the successful design of dissipative colloidal systems and illustrate these with the current state of the art. Finally, we present our vision on the future of the field and how marrying nonequilibrium self-assembly with the functional properties associated with colloidal building blocks presents a promising route for the development of next-generation materials.

Pickering stabilizers are typically considered to be perfectly smooth and chemically homogeneous. The use of rough and heterogeneous colloids is expected to fundamentally alter the properties of emulsions. In particular, we investigate the role of surface structuring in the emulsification and catastrophic phase inversion of Pickering emulsions. To gain deeper fundamental insights into this topic, we fabricate in a controlled and simple manner patchy rough particles with a polystyrene core and organosilicate asperities. As a consequence of the synthesis, the surface roughness and chemical heterogeneity are coupled, namely the chemical heterogeneity is directly connected with the surface patchiness. The synthesis is robust, scalable and leads to the production of grams in less than a day. The geometrical roughness is characterized with AFM, while the chemical composition is extracted from oxidative mass loss upon combustion. Wetting studies are empirically carried out using a gel trapping technique and the results are compared with the theoretically derived contact angles of particles. Systematic variations in the emulsification shear rate, oil/water ratio and particle type reveal the influence of particle heterogeneity on the formation and formulation of emulsions. This work paves the way for a deeper understanding of the behavior of Pickering emulsions, where non-ideal, heterogeneous particles are present.

There is a large debate on the destabilization mechanism of emulsions. We present a simple technique using mechanical compression to destabilize oil-in-water emulsions. Upon compression of the emulsion, the continuous aqueous phase is squeezed out, while the dispersed oil phase progressively deforms from circular to honeycomb-like shapes. The films that separate the oil droplets are observed to thin and break at a critical oil/water ratio, leading to coalescence events. Electrostatic interactions and local droplet rearrangements do not determine film rupture. Instead, the destabilization occurs like an avalanche propagating through the system, starting at areas where the film thickness is smallest.

We report the (spontaneous) formation of colloidal strings, Bernal spiral-like, and tubular clusters comprising spherical, isotropically functionalized colloidal particles in an aqueous environment. The formation of colloidal strings and Bernal spiral-like clusters is guided by an interplay between short-ranged hydrophobic attraction and relatively longer-ranged electrostatic repulsion acting between the colloids. When a dispersion of these colloids is densified via centrifugation, well-defined tubular aggregates were observed.

Bifunctional Janus particles with patches carrying orthogonal surface functionalities that can be independently modified are widely seen as promising building blocks for the bottom-up assembly of functional materials due to their full compositional and geometrical programmability. However, synthesis of these colloids remains an elusive task as current scalable procedures are generally limited to monofunctional particles only. Herein, a scalable bulk wet-chemical synthetic method for fabricating bifunctional Janus particles following a two-step dispersion polymerization is developed. Patch formation on these colloids is driven by the spontaneous phase separation between a brominated outer shell and poly(propargyl acrylate) (p(PA)), formed after the seed particles were swollen with the corresponding monomer. The size ratio between the two patches is readily tunable by controlling the volumetric ratio between the feeding monomers. The distinct patches of these Janus particles carry chemical handles facilitating independent and orthogonal surface modification using Atom Transfer Radical Polymerization (ATRP) and thiol-yne Click chemistry for the brominated and alkyne-containing patches, respectively. The presented route toward bifunctional patchy spheres provides a versatile starting point for the development of bifunctional colloidal particles with tailored directional properties.

Dimple colloids with well-defined cavities were synthesized by a modified dispersion polymerization. The key step in the procedure is the delayed addition of cross-linkers into the reaction mixture. By systematically studying the effect of the delayed addition time and the concentration of the cross-linker on the resulting particle morphology, we identified the dominating driving force that underlies dimple formation. The delayed addition of cross-linkers results in colloids with a core-shell morphology consisting of a core rich in linear polymers and a cross-linked shell. This morphology was confirmed by selectively etching non-cross-linked material using dimethylformamide. With polymerization proceeding, consumption of monomers present in the swollen particles leads to contraction of the particles, which is larger for the core composed of linear polymers compared to the stiffer cross-linked shell. To accommodate this decrease in volume, the outer cross-linked shell has to buckle, resulting in a well-defined dimple. Furthermore, we extended the procedure to incorporate functional monomers, yielding chemically modifiable dimple particles. Subsequently, we showed that by leveraging the core-shell structure, these dimple particles can be used to prepare dumbbell-shaped colloids with one hollow and one solid lobe. These partially hollow anisotropic particles assemble into strings with well-defined orientations in an alternating current electric field., Competing Interests: The authors declare no competing financial interest.

There are limitations in establishing a direct link between fungal exposure and health effects due to the methodology used, among other reasons. Culture methods ignore the nonviable/uncultivable fraction of airborne fungi. Molecular methods allow for a better understanding of the environmental health impacts of microbial communities. However, there are challenges when applying these techniques to bioaerosols, particularly to fungal cells. This study reveals that there is a loss of fungal cells when samples are recovered from air using wet samplers and aimed to create and test an improved protocol for concentrating mold spores via filtration prior to DNA extraction. Results obtained using the new technique showed that up to 3 orders of magnitude more fungal DNA was retrieved from the samples using quantitative PCR. A sequencing approach with MiSeq revealed a different diversity profile depending on the methodology used. Specifically, 8 fungal families out of 19 families tested were highlighted to be differentially abundant in centrifuged and filtered samples. An experiment using laboratory settings showed the same spore loss during centrifugation for Aspergillus niger and Penicillium roquefortii strains. We believe that this work helped identify and address fungal cell loss during processing of air samples, including centrifugation steps, and propose an alternative method for a more accurate evaluation of fungal exposure and diversity. IMPORTANCE This work shed light on a significant issue regarding the loss of fungal spores when recovered from air samples using liquid medium and centrifugation to concentrate air particles before DNA extraction. We provide proof that the loss affects the overall fungal diversity of aerosols and that some taxa are differentially more affected than others. Furthermore, a laboratory experiment confirmed the environmental results obtained during field sampling. The filtration protocol described in this work offers a better description of the fungal diversity of aerosols and should be used in fungal aerosol studies., (Copyright © 2019 American Society for Microbiology.)

We numerically investigate the adsorption of a variety of Janus particles (dumbbells, elongated dumbbells and spherocylinders) at a fluid-fluid interface by using a numerical method that takes into account the interfacial deformations. We first determine the equilibrium configuration of a single adsorbed particle, and we find that the overall shape of the induced deformation field has a strong hexapolar mode while non-Janus particles of the same shape do not induce any interfacial deformation. We then calculate the capillary interactions between two Janus spherocylinders adsorbed at an interface. The hexapolar deformation field induces capillary attractions for laterally aligned Janus spherocylinders and repulsions for laterally anti-aligned ones. We also experimentally synthesize micrometer-sized charged Janus dumbbells and let them adsorb at a water-decane interface. After several hours we observe the formation of aggregates of dumbbells predominantly induced by interactions that appear to be capillary in nature. Our Janus dumbbells attach laterally and are all aligned, as predicted by our numerical calculations.

Striking morphological similarities found between superstructures of a wide variety of seemingly unrelated crystalline membrane systems hint at the existence of a common formation mechanism. Resembling systems such as multiwalled carbon nanotubes, bacterial protein shells, or peptide nanotubes, the self-assembly of SDS/β-cyclodextrin complexes leads to monodisperse multilamellar microtubes. We uncover the mechanism of this hierarchical self-assembly process by time-resolved small- and ultrasmall-angle x-ray scattering. In particular, we show that symmetric crystalline bilayers bend into hollow cylinders as a consequence of membrane line tension and an anisotropic elastic modulus. Starting from single-walled microtubes, successive nucleation of new cylinders inside preexisting ones drives an inward growth. As both the driving forces that underlie the self-assembly behavior and the resulting morphologies are common to systems of ordered membranes, we believe that this formation mechanism has a similarly general applicability.

The spontaneous encapsulation of genomic and non-genomic polyanions by coat proteins of simple icosahedral viruses is driven, in the first instance, by electrostatic interactions with polycationic RNA binding domains on these proteins. The efficiency with which the polyanions can be encapsulated in vitro, and presumably also in vivo, must in addition be governed by the loss of translational and mixing entropy associated with co-assembly, at least if this co-assembly constitutes a reversible process. These forms of entropy counteract the impact of attractive interactions between the constituents and hence they counteract complexation. By invoking mass action-type arguments and a simple model describing electrostatic interactions, we show how these forms of entropy might settle the competition between negatively charged polymers of different molecular weights for co-assembly with the coat proteins. In direct competition, mass action turns out to strongly work against the encapsulation of RNAs that are significantly shorter, which is typically the case for non-viral (host) RNAs. We also find that coat proteins favor forming virus particles over nonspecific binding to other proteins in the cytosol even if these are present in vast excess. Our results rationalize a number of recent in vitro co-assembly experiments showing that short polyanions are less effective at attracting virus coat proteins to form virus-like particles than long ones do, even if both are present at equal weight concentrations in the assembly mixture.

In an era of globalized trade relations where food and pharmaceutical products cross borders effortlessly, consumers face counterfeit and deteriorated products at elevated rates. This paper presents multifunctional, biodegradable hydrogel microparticles that can provide information on the authenticity and the potential deterioration of the tagged food or pharmaceutical formulations. These microparticles integrate spatially patterned authenticity code with two sensors-the first one detects possible presence of pathogenic microbes through monitoring pH while the second one identifies products stored above optimal temperatures via optical monitoring of the microparticle degradation. Particles are synthesized from a biocompatible polymer and a photoinitiator, dextran modified with 2-hydroxyethylmethacrylate and riboflavin, respectively, using a continuous, high throughput method stop-flow lithography. The proposed synthesis approach also enables crosslinking with visible light bringing about additional flexibility to flow lithography. Model liquid and solid food and pharmaceutical products are successfully labeled with microparticles and the functionality of the sensors in aqueous solutions is demonstrated., (© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Concentration gradients play a critical role in embryogenesis, bacterial locomotion, as well as the motility of active particles. Particles develop concentration profiles around them by dissolution, adsorption, or the reactivity of surface species. These gradients change the surface energy of the particles, driving both their self-propulsion and governing their interactions. Here, we uncover a regime in which solute gradients mediate interactions between slowly dissolving droplets without causing autophoresis. This decoupling allows us to directly measure the steady-state, repulsive force, which scales with interparticle distance as F∼1/r^{2}. Our results show that the dissolution process is diffusion rather than reaction rate limited, and the theoretical model captures the dependence of the interactions on droplet size and solute concentration, using a single fit parameter, l=16±3nm, which corresponds to the length scale of a swollen micelle. Our results shed light on the out-of-equilibrium behavior of particles with surface reactivity.

Fuel-driven assembly operates under the continuous influx of energy and results in superstructures that exist out of equilibrium. Such dissipative processes provide a route toward structures and transient behavior unreachable by conventional equilibrium self-assembly. Although perfected in biological systems like microtubules, this class of assembly is only sparsely used in synthetic or colloidal analogues. Here, we present a novel colloidal system that shows transient clustering driven by a chemical fuel. Addition of fuel causes an increase in hydrophobicity of the building blocks by actively removing surface charges, thereby driving their aggregation. Depletion of fuel causes reappearance of the charged moieties and leads to disassembly of the formed clusters. This reassures that the system returns to its initial, equilibrium state. By taking advantage of the cyclic nature of our system, we show that clustering can be induced several times by simple injection of new fuel. The fuel-mediated assembly of colloidal building blocks presented here opens new avenues to the complex landscape of nonequilibrium colloidal structures, guided by biological design principles.

Individual regulatory proteins are typically charged with the simultaneous regulation of a battery of different genes. As a result, when one of these proteins is limiting, competitive effects have a significant impact on the transcriptional response of the regulated genes. Here we present a general framework for the analysis of any generic regulatory architecture that accounts for the competitive effects of the regulatory environment by isolating these effects into an effective concentration parameter. These predictions are formulated using the grand-canonical ensemble of statistical mechanics and the fold-change in gene expression is predicted as a function of the number of transcription factors, the strength of interactions between the transcription factors and their DNA binding sites, and the effective concentration of the transcription factor. The effective concentration is set by the transcription factor interactions with competing binding sites within the cell and is determined self-consistently. Using this approach, we analyze regulatory architectures in the grand-canonical ensemble ranging from simple repression and simple activation to scenarios that include repression mediated by DNA looping of distal regulatory sites. It is demonstrated that all the canonical expressions previously derived in the case of an isolated, non-competing gene, can be generalised by a simple substitution to their grand canonical counterpart, which allows for simple intuitive incorporation of the influence of multiple competing transcription factor binding sites. As an example of the strength of this approach, we build on these results to present an analytical description of transcriptional regulation of the lac operon.

Association and dissociation of particles are elementary steps in many natural and technological relevant processes. For many such processes, the presence of multiple binding sites is essential. For instance, protein complexes and regular structures such as virus shells are formed from elementary building blocks with multiple binding sites. Here we address a fundamental question concerning the role of multivalency of binding sites in the association kinetics of such complexes. Using single replica transition interface sampling simulations, we investigate the influence of the multivalency on the binding kinetics and the association mechanism of patchy particles that form polyhedral clusters. When the individual bond strength is fixed, the kinetics naturally is very dependent on the multivalency, with dissociation rate constants exponentially decreasing with the number of bonds. In contrast, we find that when the total bond energy per particle is kept constant, association and dissociation rate constants turn out rather independent of multivalency, although of course still very dependent on the total energy. The association and dissociation mechanisms, however, depend on the presence and nature of the intermediate states. For instance, pathways that visit intermediate states are less prevalent for particles with five binding sites compared to the case of particles with only three bonds. The presence of intermediate states can lead to kinetic trapping and malformed aggregates. We discuss implications for natural forming complexes such as virus shells and for the design of artificial colloidal patchy particles.

We report the first example of reversible encapsulation of micron-sized particles by oppositely charged submicron smaller colloids. The reversibility of this encapsulation process is regulated by pH-responsive poly(acrylic acid) (PAA) present in solution. The competitive adsorption between the small colloids and the poly(acrylic acid) on the surface of the large colloids plays a key role in the encapsulation behavior of the system. pH offers an experimental knob to tune the electrostatic interactions between the two oppositely charged particle species via regulation of the charge density of the poly(acrylic acid). This results in an increased surface coverage of the large colloids by the smaller colloids when decreasing pH. Furthermore, the poly(acrylic acid) also acts as a steric barrier limiting the strength of the attractive forces between the oppositely charged particle species, thereby enabling detachment of the smaller colloids. Finally, based on the pH tunability of the encapsulation behavior and the ability of the small colloids to detach, reversible encapsulation is achieved by cycling pH in the presence of the PAA polyelectrolytes. The role of polyelectrolytes revealed in this work provides a new and facile strategy to control heteroaggregation behavior between oppositely charged colloids, paving the way to prepare sophisticated hierarchical assemblies.

In this article, we report the synthesis and physical characterization of colloidal polystyrene particles that carry water-soluble supramolecular N , N ', N ″,-trialkyl-benzene-1,3,5-tricarboxamides (BTAs) on their surface. These molecules are known to assemble into one-dimensional supramolecular polymers via noncovalent interactions. By tethering the BTAs to charge-stabilized particles, the clustering behavior of the resulting colloids was dictated by a balance between interparticle electrostatic repulsion and the BTA-mediated attractions. Through careful tuning of the dispersing medium's ionic strength, a regime was found in which particle aggregation could be reversibly induced upon heating the dispersion. These findings clearly indicate that hydrophobic interactions, which become stronger upon heating, play an important role during the clustering process. Besides the thermoreversible nature of the generated hydrophobic interparticle attractions, we found the clustering to be selective, that is, the BTA-functionalized colloids do not interact with nonfunctionalized hydrophobic polystyrene particles. This selectivity in the association process can be rationalized by the preferred stacking of the surface-tethered BTAs. These selective intermolecular/particle bonds are likely stabilized by the formation of hydrogen bonds, as previously observed for analogous molecular BTA assemblies. The resulting driving force responsible for particle clustering is therefore dual in nature and depends on both hydrophobic attractions and hydrogen bonding., Competing Interests: The authors declare no competing financial interest.

In this paper, we demonstrate the stabilization of polystyrene microspheres by encapsulating them with dumbbell-shaped colloids with a sticky and a nonsticky lobe. Upon adding a depletant, an effective short ranged attraction is induced between the microspheres and the smaller, smooth lobes of the dumbbells, making those specifically sticky, whereas the interaction with the larger lobes of the dumbbells is considerably less attractive due to their rough surface, which reduces the overlap volume and leaves them nonsticky. The encapsulation of the microspheres by these rough-smooth patchy dumbbells is investigated using a combination of experiments and computer simulations, both resulting in partial coverage of the template particles. For larger microspheres, the depletion attraction is stronger, resulting in a larger fraction of dumbbells that are attached with both lobes to the surface of microspheres. We thus find a template curvature dependent orientation of the dumbbells. In the Monte Carlo simulations, the introduction of such a small, curvature dependent attraction between the rough lobes of the dumbbells resulted in an increased coverage. However, kinetic constraints imposed by the dumbbell geometry seem to prevent optimal packing of the dumbbells on the template particles under all investigated conditions in experiments and simulations. Despite the incomplete coverage, the encapsulation by dumbbell particles does prevent aggregation of the microspheres, thus acting as a colloid-sized steric stabilizer.

Chemically anisotropic dumbbell-shaped colloids are prepared starting from cross-linked polymer seed particles coated with a chlorinated outer layer. These chlorinated seeds are swollen with monomer. Subsequently, a liquid protrusion is formed on the surface of the seed particle by phase separation between the monomer and the swollen polymer network. Solidification of these liquid lobes by polymerization leads to the desired dumbbell-shaped colloids. The chlorine groups remain confined on the seed lobe of the particles, ensuring chemical anisotropy of the resulting particles. Exploiting the asymmetric distribution of the chemically reactive surface chlorine groups allows for site-specific surface modifications. Here we show that the geometry of the resulting chemically anisotropic dumbbells can be systematically tuned by a number of experimental parameters including the volume of styrene by which the seeds are swollen, the cross-link density of the chlorinated seeds and chemical composition/thickness of the chlorinated coating deposited on the seed particles. Being able to control the particle geometry, and therefore the Janus balance of these chemically anisotropic particles, provides a promising starting point for the synthesis of sophisticated building blocks for future (self-assembly) studies., (Copyright © 2016 Elsevier Inc. All rights reserved.)

Virus coat proteins spontaneously self-assemble into empty shells in aqueous solution under the appropriate physicochemical conditions, driven by an interaction free energy per bond on the order of 2-5 times the thermal energy kBT. For this seemingly modest interaction strength, each protein building block nonetheless gains a very large binding free energy, between 10 and 20 kBT. Because of this, there is debate about whether the assembly process is reversible or irreversible. Here we discuss capsid polymorphism observed in in vitro experiments from the perspective of nucleation theory and of the thermodynamics of mass action. We specifically consider the potential contribution of a curvature free energy term to the effective interaction potential between the proteins. From these models, we propose experiments that may conclusively reveal whether virus capsid assembly into a mixture of polymorphs is a reversible or an irreversible process.

Particles with directional interactions are promising building blocks for new functional materials and may serve as models for biological structures. Mutually attractive nanoparticles that are deformable owing to flexible surface groups, for example, may spontaneously order themselves into strings, sheets and large vesicles. Furthermore, anisotropic colloids with attractive patches can self-assemble into open lattices and the colloidal equivalents of molecules and micelles. However, model systems that combine mutual attraction, anisotropy and deformability have not yet been realized. Here we synthesize colloidal particles that combine these three characteristics and obtain self-assembled microcapsules. We propose that mutual attraction and deformability induce directional interactions via colloidal bond hybridization. Our particles contain both mutually attractive and repulsive surface groups that are flexible. Analogously to the simplest chemical bond--in which two isotropic orbitals hybridize into the molecular orbital of H2--these flexible groups redistribute on binding. Via colloidal bond hybridization, isotropic spheres self-assemble into planar monolayers, whereas anisotropic snowman-shaped particles self-assemble into hollow monolayer microcapsules. A modest change in the building blocks thus results in much greater complexity of the self-assembled structures. In other words, these relatively simple building blocks self-assemble into markedly more complex structures than do similar particles that are isotropic or non-deformable.

The depletion interaction as induced between colloids by the addition of a polymer depletant is one of the few ways in which short-ranged attractions between particles can be controlled. Due to these tunable interactions, colloid-polymer mixtures have contributed to a better understanding of the role of attractions both in equilibrium phenomena such as phase transitions and liquid surfaces as well as in systems out of equilibrium such as gelation and the glass transition. It is known that, by simple geometric effects, surface roughness decreases the strength of the depletion interaction. In this study, we demonstrate both by Monte Carlo simulations and experiments that it is possible to generate enough difference in attraction strength to induce phase separation in smooth particles but not in rough particles. Roughness was induced by coating smooth particles with smaller spherical colloids. We indicate how effective potentials can be obtained through simulations and how the interplay between gravity and the depletion interaction with a flat container wall can be used to obtain a simple measure of the interaction strengths as a function of roughness.

Predicting the self-assembly kinetics of particles with anisotropic interactions, such as colloidal patchy particles or proteins with multiple binding sites, is important for the design of novel high-tech materials, as well as for understanding biological systems, e.g., viruses or regulatory networks. Often stochastic in nature, such self-assembly processes are fundamentally governed by rotational and translational diffusion. Whereas the rotational diffusion constant of particles is usually considered to be coupled to the translational diffusion via the Stokes-Einstein relation, in the past decade it has become clear that they can be independently altered by molecular crowding agents or via external fields. Because virus capsids naturally assemble in crowded environments such as the cell cytoplasm but also in aqueous solution in vitro, it is important to investigate how varying the rotational diffusion with respect to transitional diffusion alters the kinetic pathways of self-assembly. Kinetic trapping in malformed or intermediate structures often impedes a direct simulation approach of a kinetic network by dramatically slowing down the relaxation to the designed ground state. However, using recently developed path-sampling techniques, we can sample and analyze the entire self-assembly kinetic network of simple patchy particle systems. For assembly of a designed cluster of patchy particles we find that changing the rotational diffusion does not change the equilibrium constants, but significantly affects the dynamical pathways, and enhances (suppresses) the overall relaxation process and the yield of the target structure, by avoiding (encountering) frustrated states. Besides insight, this finding provides a design principle for improved control of nanoparticle self-assembly.

The self-assembly of anisotropic patchy particles with a triangular shape was studied by experiments and computer simulations. The colloidal particles were synthesized in a two-step seeded emulsion polymerization process, and consist of a central smooth lobe connected to two rough lobes at an angle of ∼90°, resembling the shape of a "Mickey Mouse" head. Due to the difference in overlap volume, adding an appropriate depletant induces an attractive interaction between the smooth lobes of the colloids only, while the two rough lobes act as steric constraints. The essentially planar geometry of the Mickey Mouse particles is a first geometric deviation of dumbbell shaped patchy particles. This new geometry enables the formation of one-dimensional tube-like structures rather than spherical, essentially zero-dimensional micelles. At sufficiently strong attractions, we indeed find tube-like structures with the sticky lobes at the core and the non-sticky lobes pointing out as steric constraints that limit the growth to one direction, providing the tubes with a well-defined diameter but variable length both in experiments and simulations. In the simulations, we found that the internal structure of the tubular fragments could either be straight or twisted into so-called Bernal spirals.

Manipulation of the self-assembly of magnetic colloidal particles by an externally applied magnetic field paves a way toward developing novel stimuli responsive photonic structures. Using microradian X-ray scattering technique we have investigated the different crystal structures exhibited by self-assembly of core-shell magnetite/silica nanoparticles. An external magnetic field was employed to tune the colloidal crystallization. We find that the equilibrium structure in absence of the field is random hexagonal close-packed (RHCP) one. External field drives the self-assembly toward a body-centered tetragonal (BCT) structure. Our findings are in good agreement with simulation results on the assembly of these particles., (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

In colloids with competing short-range attractions and long-range repulsions, microcrystalline gels are experimentally formed under conditions where computer simulations point to a lamellar phase as the ground state. Here, upon applying a low-frequency alternating electric field, we bring the system from an initial gel state to a columnar-like state. While molecular dynamics simulations on monodisperse colloids reveal that a columnar structure spontaneously evolves towards a lamellar phase, the columnar-like state in experiments relaxes back to the initial disordered gel state once the electric field is switched off. Similarly, a columnar phase in molecular dynamics simulations decomposes into finite-size crystalline clusters as the relative polydispersity of the colloids is around 1.0%. We conclude that the experimentally observed melting of the columnar structure is driven by polydispersity. Moreover, further simulations reveal that the critical polydispersity required to destabilize a long-range ordered structure increases with the attraction range, pointing to the possibility of observing periodic structures in experiments if the attraction range is sufficiently long compared to the polydispersity of the colloids.

The proteins associated with gene regulation are often shared between multiple pathways simultaneously. By way of contrast, models in regulatory biology often assume these pathways act independently. We demonstrate a framework for calculating the change in gene expression for the interacting case by decoupling repressor occupancy across the cell from the gene of interest by way of a chemical potential. The details of the interacting regulatory architecture are encompassed in an effective concentration, and thus, a single scaling function describes a collection of gene expression data from diverse regulatory situations and collapses it onto a single master curve.

In this paper, we present a robust way to tune the surface potential of polystyrene colloids without changing the pH, ionic strength, etc. The colloids are composed of a cross-linked polystyrene core and a cross-linked vinylbenzyl chloride layer. Besides the chlorine groups, the particle surface contains sulfate/sulfonate groups (arising from the polymerization initiators) that provide a negative surface potential. Performing a Menschutkin reaction on the surface chlorine groups with tertiary amines allows us to introduce quaternary, positively charged amines. The overall charge on the particles is then determined by the ratio between the sulfate/sulfonate moieties and the quaternary amines. Using this process, we were able to invert the charge in a continuous manner without losing colloidal stability upon passing the isoelectric point. The straightforward reaction mechanism together with the fact that the reaction could be quenched rapidly resulted in a colloidal system in which the ζ potential can be tuned between -80 and 45 mV. As proof of principle, the positively charged particles were used in heterocoagulation experiments with nanometer- and micrometer-sized negatively charged silica particles to create geometrically well-defined colloidal (nano) clusters.

The phase behavior of colloids that interact via competing interactions - short-range attraction and long-range repulsion - is studied by computer simulation. In particular, for a fixed strength and range of repulsion, the effect of the strength of an attractive interaction (ε) on the phase behavior is investigated at various colloid densities (ρ). A thermodynamically stable equilibrium colloidal cluster phase, consisting of compact crystalline clusters, is found below the fluid-solid coexistence line in the ε-ρ parameter space. The mean cluster size is found to linearly increase with the colloid density. At large ε and low densities, and at small ε and high densities, a non-equilibrium cluster phase, consisting of elongated Bernal spiral-like clusters, is observed. Although gelation can be induced either by increasing ε at constant density or vice versa, the gelation mechanism is different in either route. While in the ρ route gelation occurs via a glass transition of compact clusters, gelation in the ε route is characterized by percolation of elongated clusters. This study both provides the location of equilibrium and non-equilibrium cluster phases with respect to the fluid-solid coexistence, and reveals the dependencies of the gelation mechanism on the preparation route.

We have investigated the effect of particle shape in Pickering emulsions by employing, for the first time, cubic and peanut-shaped particles. The interfacial packing and orientation of anisotropic microparticles are revealed at the single-particle level by direct microscopy observations. The uniform anisotropic hematite microparticles adsorb irreversibly at the oil-water interface in monolayers and form solid-stabilized o/w emulsions via the process of limited coalescence. Emulsions were stable against further coalescence for at least 1 year. We found that cubes assembled at the interface in monolayers with a packing intermediate between hexagonal and cubic and average packing densities of up to 90%. Local domains displayed densities even higher than theoretically achievable for spheres. Cubes exclusively orient parallel with one of their flat sides at the oil-water interface, whereas peanuts preferentially attach parallel with their long side. Those peanut-shaped microparticles assemble in locally ordered, interfacial particle stacks that may interlock. Indications for long-range capillary interactions were not found, and we hypothesize that this is related to the observed stable orientations of cubes and peanuts that marginalize deformations of the interface.

Repeptization (redispersion) from an aggregated state is usually only possible in charge-stabilized colloidal systems if the system is either coagulated in the secondary minimum of the interaction potential or if the system cannot settle completely into the primary minimum. In this work, we analyze the zeta potential, conductivity, and long-term stability of colloidal systems of iron(III) pyrophosphate and surprisingly find that the system seems to defy conventional wisdom as it can be repeptized from its coagulated state regardless of aging time and background ions. Moreover, after having been stored for up to a month in 2 M NaCl, dialysis of iron pyrophosphate will yield a colloidal dispersion that is actually stable for a longer period of time than a fresh system with background electrolyte removed.

The ionic strength of a solution decreases during the precipitation of an insoluble salt, which can cause an initially unstable colloidal system to stabilize during its formation. We show this effect in the precipitation and aging of colloidal iron(III) pyrophosphate, where we observe two distinct stages in the aggregation process. The first stage is the formation of nanoparticles that immediately aggregate into clusters with sizes on the order of 200 nm. In the second stage these clusters slowly grow in size but remain in dispersion for days, even months for dialyzed systems. Eventually these clusters become macroscopically large and sediment out of dispersion. Noting the clear instability of the nanoparticles, it is interesting to find two stages in their aggregation even without the use of additives such as surface active molecules. This is explained by accounting for the rapid decrease of ionic strength during precipitation, rendering the nanoparticles relatively stable when precipitation is complete. Calculating the interaction potentials for this scenario we find good agreement with the experimental observations. These results indicate that coupling of ionic strength to aggregation state can be significant and should be taken into account when considering colloidal stability of insoluble salts., (Copyright © 2012 Elsevier Inc. All rights reserved.)

Colloidal particles with site-specific directional interactions, so called "patchy particles", are promising candidates for bottom-up assembly routes towards complex structures with rationally designed properties. Here we present an experimental realization of patchy colloidal particles based on material independent depletion interaction and surface roughness. Curved, smooth patches on rough colloids are shown to be exclusively attractive due to their different overlap volumes. We discuss in detail the case of colloids with one patch that serves as a model for molecular surfactants both with respect to their geometry and their interactions. These one-patch particles assemble into clusters that resemble surfactant micelles with the smooth and attractive sides of the colloids located at the interior. We term these clusters "colloidal micelles". Direct Monte Carlo simulations starting from a homogeneous state give rise to cluster size distributions that are in good agreement with those found in experiments. Important differences with surfactant micelles originate from the colloidal character of our model system and are investigated by simulations and addressed theoretically. Our new "patchy" model system opens up the possibility for self-assembly studies into finite-sized superstructures as well as crystals with as of yet inaccessible structures.

We put forward a modified Zipper model inspired by the statics and dynamics of the spontaneous reconstitution of rodlike tobacco mosaic virus particles in solutions containing the coat protein and the single-stranded RNA of the virus. An important ingredient of our model is an allosteric switch associated with the binding of the first protein unit to the origin-of-assembly domain of the viral RNA. The subsequent addition and conformational switching of coat proteins to the growing capsid we believe is catalyzed by the presence of the helical arrangement of bound proteins to the RNA. The model explains why the formation of complete viruses is favored over incomplete ones, even though the process is quasi-one-dimensional in character. We numerically solve the relevant kinetic equations and show that time evolution is different for the assembly and disassembly of the virus, the former exhibiting a time lag even if all forward rate constants are equal. We find the late-stage assembly kinetics in the presence of excess protein to be governed by a single-exponential relaxation, which agrees with available experimental data on TMV reconstruction., (Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

We report a computational study on the spontaneous self-assembly of spherical particles into two-dimensional crystals. The experimental observation of such structures stabilized by spherical objects appeared paradoxical so far. We implement patchy interactions with the patches point-symmetrically (icosahedral and cubic) arranged on the surface of the particle. In these conditions, preference for self-assembly into sheet-like structures is observed. We explain our findings in terms of the inherent symmetry of the patches and the competition between binding energy and vibrational entropy. The simulation results explain why hollow spherical shells observed in some Keplerate-type polyoxometalates (POM) appear. Our results also provide an explanation for the experimentally observed layer-by-layer growth of apoferritin--a quasi-spherical protein.

We present the synthesis of polymer colloids with continuously tunable anisotropy dimensions: patchiness, roughness, and branching. Our method makes use of controlled fusion of multiple protrusions on highly cross-linked polymer particles produced by seeded emulsion polymerization. Carefully changing the synthesis conditions, we can tune the number of protrusions, or branching, of the obtained particles from spheres with one to three patches to raspberry-like particles with multiple protrusions. In addition to that, roughness is generated on the seed particles by adsorption of secondary nucleated particles during synthesis. The size of the roughness relative to the smooth patches can be continuously tuned by the initiator, surfactant, and styrene concentrations. Seed colloids chemically different from the protrusions induce patches of different chemical nature. The underlying generality of the synthesis procedure allows for application to a variety of seed particle sizes and materials. We demonstrate the use of differently sized polyNIPAM (poly-N-isopropylacrylamide), as well as polystyrene and magnetite filled polyNIPAM seed particles, the latter giving rise to magnetically anisotropic colloids. The high yield together with the uniform, anisotropic shape make them interesting candidates for use as smart building blocks in self-assembling systems.

The reversible properties of cluster phases have been described by theories that invoke Coulomb interactions as a stabilizing mechanism. What is lacking so far is direct measurement of these charges. This contribution aims at predicting what to expect if electrophoresis measurements were to be performed on these systems. As a result, we get a picture that exhibits several interesting features: (1) The existence of monomers and clusters lead to distinctly different mobilities (zeta potentials) in a single sample. (2) Strong dependence of the mobilities on particle volume fraction. It is our aim that the theory outlined in this paper may serve as a guideline to interpret the expectedly "messy" electrophoretic measurements.

The equilibrium size of two largely different kinds of hollow objects behave qualitatively differently with respect to certain experimental conditions. Yet, we show that they can be described within the same theoretical framework. The objects we consider are 'minivesicles' of ionic and nonionic surfactant mixtures, and shells of Keplerate-type polyoxometalates. The finite-size of the objects in both systems is manifested by electrostatic interactions. We emphasize the importance of constant charge and constant potential boundary conditions. Taking these conditions into account, indeed, leads to the experimentally observed qualitatively different behavior of the equilibrium size of the objects.