Diffusiophoresis-enhanced Turing patterns

Induction and Manipulation of Biomolecular Condensates Through Spatially Heterogeneous Solution Conditions

The study of biomolecular condensates (BMCs) is of great current interest because of the proposed roles of these types of assemblies in biological function and disease. In living cells, BMCs form in a highly heterogeneous environment and are influenced by concentration gradients of various relevant species. Furthermore, the biological functionality of the BMCs requires precise spatial control of their formation in some cases. In recent years, a number of in vitro experimental approaches have emerged that allow the generation, study, and manipulation of BMCs through the creation of well-defined spatially heterogeneous solution conditions relevant for BMC formation. In this concept article, it is presented in what way such methods can contribute to improved understanding and control of BMCs.

Taming the diffusiophoretic convective instability in colloidal suspensions

A suspension of Brownian colloidal particles stabilised against aggregation is expected to be stable against convection when its density decreases monotonically with height. Surprisingly, a recent experimental investigation has shown that when colloidal particles are dispersed uniformly in a solvent with a stabilising stratification of a molecular solute, the system develops a convective instability under generic conditions [Anzivino et al., J. Phys. Chem. Lett., 2024, 15, 9030]. This instability arises because the solute concentration gradient induces an upward diffusiophoretic motion of the colloidal particles, triggering a diffusiophoretic convective instability (DCI). In this work, we investigate the stability of a colloidal suspension against convection in the presence of a stable density stratification of the sample, under different initial conditions. In particular, we study the condition where both the colloid and the molecular solute are initially localized in the lower half of the sample prior to merging with the upper half made of pure water. This is unlike the previously studied setup where the colloid was initially present also in the upper half, suspended in water. We show that only when the concentration of glycerol exceeds a fairly large threshold value of approximately 0.3 w/w the system develops the convective instability. Hence, this new setup offers the possibility to tame DCI by changing the initial conditions. We model the experimental results by numerically solving the nonlinear double diffusion equations in the presence of a diffusiophoretic coupling to determine the time evolution of the base state of the system. The theoretical analysis allows us to elucidate the physical reason for the existence of the threshold value of the glycerol concentration and to establish that the interactions between the colloidal particles do not play a significant role in the DCI.

Diffusioosmotic Reversal of Colloidal Focusing Direction in a Microfluidic T-Junction

Solute gradients next to an interface drive a diffusioosmotic flow, the origin of which lies in the intermolecular interactions between the solute and the interface. These flows on the surface of colloids introduce an effective slip velocity, driving their diffusiophoretic migration. In confined environments, the interplay between diffusiophoresis and diffusioosmosis governs the motion of colloids. Previous studies have indeed demonstrated the quantitative modulation of phoretic migration by the osmotic flows. Here, we show that diffusioosmotic flows can lead to qualitatively distinct outcomes, reversing the direction of colloidal focusing expected from diffusiophoresis alone. Using microfluidic experiments in a T-junction, numerical simulations, and theoretical modeling, we explain our observations to be due to an interplay between diffusiophoretic migration of colloids toward the walls and their entrainment in a diffusioosmotic vortex. We show this focusing to be persistent for a range of salt types, salt gradients, and flow rates, and establish a criterion for its emergence. Our work sheds light on how boundaries modulate the solute-mediated transport of colloids in confined environments and how the colloidal trajectories can be utilized to infer the surface properties.

Artificial chemotaxis under electrodiffusiophoresis

HYPOTHESIS

Through a large parameter space, electric fields can tune colloidal interactions and forces leading to diverse static and dynamical structures. So far, however, field-driven interactions have been limited to dipole-dipole and hydrodynamic contributions. Nonetheless, in this work, we propose that under the right conditions, electric fields can also induce interactions based on local chemical fields and diffusiophoretic flows.

EXPERIMENTS

Herein, we present a strategy to generate and measure 3D chemical gradients under electric fields. In this approach, faradaic reactions at electrodes induce global pH gradients that drive long-range transport through electrodiffusiophoresis. Simultaneously, the electric field induces local pH gradients by driving the particle's double layer far from equilibrium.

FINDINGS

As a result, while global pH gradients lead to 2D focusing away from electrodes, local pH gradients induce aggregation in the third dimension. Evidence points to a mechanism of interaction based on diffusiophoresis. Interparticle interactions display a strong dependence on surface chemistry, zeta potential and diameter of particles. Furthermore, pH gradients can be readily tuned by adjusting the voltage and frequency of the electric field. For large Péclet numbers, we observed a collective chemotactic-like collapse of particles. Remarkably, such collapse occurs without reactions at a particle's surface. By mixing particles with different sizes, we also demonstrate, through experiments and Brownian dynamics simulations, the emergence of non-reciprocal interactions, where small particles are more drawn towards large ones.

Structure of random Turing-like patterns in discrete-time systems is determined by the initial conditions

Patterns, spatiotemporal ordered structures, are prevalent in diverse systems, arising from the emergence of complexity. Turing proposed a mechanism that involves a short-range activator and a long-range inhibitor to explain the formation of patterns, and patterns that satisfy this mechanism are called Turing patterns. Patterns with similar structures but not caused by the Turing mechanism are referred to as Turing-like patterns. In the absence of external influences, the structure of Turing patterns is generally determined by control parameters. In this study, we revealed that the structure of Turing-like patterns in discrete-time systems is only determined by the ratio of states in the initial conditions. As the ratio changes, the structure of patterns transitions from spots to labyrinth and eventually to inverse spots. We proposed the structure parameter for the quantitative description of the structure of the patterns. And the structure parameter is directly proportional to the ratio in the initial conditions. The mechanism underlying this structure control is attributed to the traversability of multiperiodic states in discrete-time systems, where each local point will go through all states in the periodic orbit. Our findings shed light on the pattern formation for Turing-like patterns in discrete-time systems.

Structural stability and thermodynamics of artistic composition

Inspired by the way that digital artists zoom out of the canvas to assess the visual impact of their works, we introduce a conceptually simple yet effective metric for quantifying the clarity of digital images. This metric contrasts original images with progressively "melted" counterparts, produced by randomly flipping adjacent pixel pairs. It measures the presence of stable structures, assigning the value zero to completely uniform or random images and finite values for those with discernible patterns. This metric respects the color diversity of the original image and withstands image compression and color quantization. Its suitability for diverse image analysis problems is demonstrated through its effective evaluation of textural images, the identification of structural transitions in physical systems like the Potts model, and its consistency with color theory in digital arts. This allows us to demonstrate that color in visual art functions as a state variable, akin to the spin configuration in magnets, driving artistic designs to transition between states with distinct clarity. When combined with the Shannon entropy, which quantifies color diversity, the structural stability metric can serve as a navigation tool for artists to explore pathways on the complex structural information landscape toward the completion of their artwork. As a practical demonstration, we apply our metric to refine and optimize an emote design for a video game. The structural stability metric emerges as a versatile tool for extracting nuanced structural information from digital images, which may enhance decision-making and data analysis across scientific and creative domains.

Diffusiophoretically Mediated Nanopatterning by Solvent Nanodroplets on Polystyrene Surfaces

Dissolution is a ubiquitous process in nature and industry. However, due to technical difficulties, the detailed dissolution process at the nanoscale has seldom been captured experimentally. In this study, we investigated the dissolution dynamics in the confinement of toluene surface nanodroplets on polystyrene (PS) thin films in oversaturated toluene/water mixture solutions. This was achieved by adjusting the immersion durations from several minutes to 9 h. Dissolution takes place upon the deposition of nanodroplets on the PS surfaces, leading to the formation of surface nanostructures. Interestingly, we found that the induced nanostructures underwent complex morphological changes, from complex nanocraters with central bulges and/or multiple rims to simple nanocraters. We speculate that diffusiophoresis plays a key role in the formation of the complex nanocraters, as it facilitates the transportation of dissolved PS molecules inside the nanodroplets. We believe this finding not only enhances our understanding of dissolution dynamics at the nanoscale but also holds promise for applications in dissolution-based nanopatterning.

Micropattern Fabricated by Acropetal Migration Controlled through Sequential Photo and Thermal Polymerization

Bottom-up patterning technology plays a significant role in both nature and synthetic materials, owing to its inherent advantages such as ease of implementation, spontaneity, and noncontact attributes, etc. However, constrained by the uncontrollability of molecular movement, energy interaction, and stress, obtained micropatterns tend to exhibit an inevitable arched outline, resulting in the limitation of applicability. Herein, inspired by auxin's action mode in apical dominance, a versatile strategy is proposed for fabricating precision self-organizing micropatterns with impressive height based on polymerization-induced acropetal migration. The copolymer containing fluorocarbon chains (low surface energy) and tertiary amine (coinitiator) is designed to self-assemble on the surface of the photo-curing system. The selective exposure under a photomask establishes a photocuring boundary and the radicals would be generated on the surface, which is pivotal in generating a vertical concentration difference of monomer. Subsequent heating treatment activates the material continuously transfers from the unexposed area to the exposed area and is accompanied by the obviously vertical upward mass transfer, resulting in the manufacture of a rectilinear profile micropattern. This strategy significantly broadens the applicability of self-organizing patterns, offering the potential to mitigate the complexity and time-consuming limitations associated with top-down methods.

Motorless transport of microtubules along tubulin, RanGTP, and salt gradients

Microtubules are dynamic filaments that assemble spindles for eukaryotic cell division. As the concentration profiles of soluble tubulin and regulatory proteins are non-uniform during spindle assembly, we asked if diffusiophoresis - motion of particles under solute gradients - can act as a motorless transport mechanism for microtubules. We identify the migration of stable microtubules along cytoplasmic and higher concentration gradients of soluble tubulin, MgCl2, Mg-ATP, Mg-GTP, and RanGTP at speeds O(100) nm/s, validating the diffusiophoresis hypothesis. Using two buffers (BRB80 and CSF-XB), microtubule behavior under MgCl2 gradients is compared with negatively charged particles and analyzed with a multi-ion diffusiophoresis and diffusioosmosis model. Microtubule diffusiophoresis under gradients of tubulin and RanGTP is also compared with the charged particles and analyzed with a non-electrolyte diffusiophoresis model. Further, we find that tubulin and RanGTP display concentration dependent cross-diffusion that influences microtubule diffusiophoresis. Finally, using Xenopus laevis egg extract, we show that diffusiophoretic transport occurs in an active cytoplasmic environment.

Salt Gradient-Induced Phoresis of Vesicles and Enhanced Membrane Fusion in a Crowded Milieu

Phoresis of biocolloidal objects in response to chemical gradients is a matter of interest among diverse scientific disciplines owing to their importance in the spatiotemporal orchestration of biochemical processes. Although there are reports of soft matter transport/phoresis in the gradient of ions or salts in the aqueous system, their phoretic behavior in the presence of macromolecular crowder is largely unexplored. Notably, cellular cytoplasm is illustrated as a crowded milieu and thereby understanding biomolecular phoresis in the presence of polymeric macromolecules would endorse phoretic behavior in a biomimetic environment. Here, we report the phoresis-induced enhanced aggregation and fusion of vesicles in gradients of monovalent (NaCl) and divalent salt (MgCl2), in the presence of polymeric crowder, polyethylene glycol of molecular weight 400 (PEG 400). Apart from diffusiophoresis, depletion force plays a crucial factor in crowded environments to control localized vesicle aggregation in a salt gradient. This demonstration will potentially show the pathway to future research related to spatiotemporally correlated liposomal transport and membrane-dependent function (such as content mixing and signaling) in a physiologically relevant crowded environment.

Convective Instability Driven by Diffusiophoresis of Colloids in Binary Liquid Mixtures

In a binary fluid mixture, the concentration gradient of a heavier molecular solute leads to a diffusive flux of solvent and solute to achieve thermodynamic equilibrium. If the solute concentration decreases with height, the system is always in a condition of stable mechanical equilibrium against gravity. We show experimentally that this mechanical equilibrium becomes unstable in case colloidal particles are dispersed uniformly within the mixture and that the resulting colloidal suspension undergoes a transient convective instability with the onset of convection patterns. By means of a numerical analysis, we clarify the microscopic mechanism from which the observed destabilization process originates. The solute concentration gradient drives an upward diffusiophoretic migration of colloids, in turn causing the development of a mechanically unstable layer within the sample, where the density of the suspension increases with height. Convective motions arise to minimize this localized rise in gravitational potential energy.

Reaction-Driven Diffusiophoresis of Liquid Condensates: Potential Mechanisms for Intracellular Organization

The cellular environment, characterized by its intricate composition and spatial organization, hosts a variety of organelles, ranging from membrane-bound ones to membraneless structures that are formed through liquid-liquid phase separation. Cells show precise control over the position of such condensates. We demonstrate that organelle movement in external concentration gradients, diffusiophoresis, is distinct from the one of colloids because fluxes can remain finite inside the liquid-phase droplets and movement of the latter arises from incompressibility. Within cellular domains diffusiophoresis naturally arises from biochemical reactions that are driven by a chemical fuel and produce waste. Simulations and analytical arguments within a minimal model of reaction-driven phase separation reveal that the directed movement stems from two contributions: Fuel and waste are refilled or extracted at the boundary, resulting in concentration gradients, which (i) induce product fluxes via incompressibility and (ii) result in an asymmetric forward reaction in the droplet's surroundings (as well as asymmetric backward reaction inside the droplet), thereby shifting the droplet's position. We show that the former contribution dominates and sets the direction of the movement, toward or away from fuel source and waste sink, depending on the product molecules' affinity toward fuel and waste, respectively. The mechanism thus provides a simple means to organize condensates with different composition. Particle-based simulations and systems with more complex reaction cycles corroborate the robustness and universality of this mechanism.

Unraveling biochemical spatial patterns: Machine learning approaches to the inverse problem of stationary Turing patterns

The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is challenging. To address this, we aim to solve the inverse problem in artificial and experimental Turing patterns. This task is challenging since patterns are often corrupted by noise and slight changes in initial conditions can lead to different patterns. We used both least squares to explore the problem and physics-informed neural networks to build a noise-robust method. We elucidate the functionality of our network in scenarios mimicking biological noise levels and showcase its application using an experimentally obtained chemical pattern. The findings reveal the significant promise of machine learning in steering the creation of synthetic patterns in bioengineering, thereby advancing our grasp of morphological intricacies within biological systems while acknowledging existing limitations.

Unsolved morphogenesis problems and the hidden order

In this work, the morphogenesis mechanisms are considered from the complexity perspective. It is shown that both morphogenesis and the functioning of organs should be unstable in the case of short-range interaction potentials. The repeatability of forms during evolution is a strong argument for its directionality. The formation of organs during evolution can occur only in the presence of a priori information about the structure of such an organ. The focus of the discussion is not merely on constraining potential possibilities but on the concept of directed evolution itself. A morphogenesis model was constructed based on nontrivial quantum effects. These interaction effects between biologically important molecules ensure the accurate synthesis of cells, tissues, and organs.

4D printing for biomedical applications

While three-dimensional (3D) printing excels at fabricating static constructs, it fails to emulate the dynamic behavior of native tissues or the temporal programmability desired for medical devices. Four-dimensional (4D) printing is an advanced additive manufacturing technology capable of fabricating constructs that can undergo pre-programmed changes in shape, property, or functionality when exposed to specific stimuli. In this Perspective, we summarize the advances in materials chemistry, 3D printing strategies, and post-printing methodologies that collectively facilitate the realization of temporal dynamics within 4D-printed soft materials (hydrogels, shape-memory polymers, liquid crystalline elastomers), ceramics, and metals. We also discuss and present insights about the diverse biomedical applications of 4D printing, including tissue engineering and regenerative medicine, drug delivery, in vitro models, and medical devices. Finally, we discuss the current challenges and emphasize the importance of an application-driven design approach to enable the clinical translation and widespread adoption of 4D printing.

Periodic pattern formation during embryonic development

During embryonic development many organs and structures require the formation of series of repeating elements known as periodic patterns. Ranging from the digits of the limb to the feathers of the avian skin, the correct formation of these embryonic patterns is essential for the future form and function of these tissues. However, the mechanisms that produce these patterns are not fully understood due to the existence of several modes of pattern generation which often differ between organs and species. Here, we review the current state of the field and provide a perspective on future approaches to studying this fundamental process of embryonic development.

A work in progress: William Bateson's vibratory theory of repetition of parts

In 1891 Cambridge biologist William Bateson (1861-1926) announced his idea that the symmetrical segmentation in living organisms resulted from energy peaks of some vibratory force acting on tissues during morphogenesis. He also demonstrated topographically how folding a radially symmetric organism could produce another with bilateral symmetry. Bateson attended many lectures at the Cambridge Philosophical Society and viewed mechanical models prepared by eminent physicists that illustrated how vibrations affected materials. In his subsequent research, Bateson utilized analogies and metaphors based upon his observations of nature to build a thought model on the effects of vibrations on living tissue, because he realized that the chemistry and biology of his day lacked technologies to perform actual experiments on the subject. He concluded the production of organic segmentation was both a chemical and mechanical phenomenon. By the time of his death Bateson had incorporated new ideas about embryonic organizer regions to suggest a center from which a rhythmic force emanated and then produced the observed repetitive segmentation as a common feature in living organisms.