Reaction-diffusion systems in intracellular molecular transport and control

Macromolecular crowding effects on protein dynamics

Macromolecular crowding experiments bridge the gap between in-vivo and in-vitro studies by mimicking some of the cellular complexities like high viscosity and limited space, while still manageable for experiments and analysis. Macromolecular crowding impacts all biological processes and is a focus of contemporary research. Recent reviews have highlighted the effect of crowding on various protein properties. One of the essential characteristics of protein is its dynamic nature; however, how protein dynamics get modulated in the crowded milieu has been largely ignored. This article discusses how protein translational, rotational, conformational, and solvation dynamics change under crowded conditions, summarizing key observations in the literature. We emphasize our research on microsecond conformational and water dynamics in crowded milieus and their impact on enzymatic activity and stability. Lastly, we provided our outlook on how this field might move forward in the future.

Model to rationalize and predict the formation of organic patterns originating from an enzyme-assisted self-assembly Liesegang-like process of peptides in a host hydrogel

Recently, we have investigated the enzyme-assisted self-assembly of precursor peptides diffusing in an enzyme-containing host gel, leading to various self-assembly profiles within the gel. At high enzyme concentrations, the reaction-diffusion self-assembly processes result in the formation of a continuous non-monotonous peptide self-assembly profile. At low enzyme concentrations, they result in the formation of individual self-assembled peptide microglobules and at intermediate enzyme concentrations both kinds of self-assembled structures coexist. Herein, we develop a Liesegang-type model that considers four major points: (i) the diffusion of the precursor peptides within the host gel, (ii) the diffusion of the enzymes in the gel, (iii) the enzymatic transformation of the precursor peptides into the self-assembling ones and (iv) the nucleation of these building blocks as the starting point of the self-assembly process. This process is treated stochastically. Our model predicts most of the experimentally observed features and in particular (i) the transition from a continuous to a microglobular pattern of self-assembled peptides through five types of patterns by decreasing the enzyme concentration in the host hydrogel. (ii) It also predicts that when the precursor peptide concentration decreases, the enzyme concentration at which the continuous/microglobules transition appears increases. (iii) Finally, it predicts that for peptides whose critical self-assembly concentration in solution decreases, the peptide concentration at which the continuous-to-microglobular transition decreases too. All these predictions are observed experimentally.

Hydroxide-Source-Dependent Polymorphism and Phase Stability of Cobalt(II) Hydroxides in Diffusion-Driven Systems

Hydroxides of cobalt(II) exist predominantly in two polymorphic forms, namely, the blue-green α-form [α-Co(OH)2] and reddish β-form [β-Co(OH)2]. These hydroxides have a layered structure with interlayer galleries of around 7 and 4 Å, respectively, for α- and β-Co(OH)2. In most of the previous studies, both the polymorphs were synthesized separately, and a few of them showed that the α-form gets converted to a thermodynamically more stable β-form via physical processes. In the present work, we have optimized the conditions for the simultaneous synthesis of both polymorphs under identical conditions in the same reactor using the 1D reaction-diffusion framework by employing different outer electrolytes. We found that the polymorph chemistry of Co(OH)2 depends on the source and concentration of OH- rather than other reaction conditions or later physical transformation. The products are characterized to confirm their morphology, structure, and chemical environment. We observed that the use of NaOH and NH4OH as the OH- precursor leads to α-Co(OH)2 only; however, with NaOH, a continuous precipitate is formed, and with NH4OH, periodic precipitation is formed. On the other hand, with hydrazine (HYZ) as the OH- source, Liesegang bands of α-Co(OH)2 and β-Co(OH)2 as granules are formed throughout the diffusion reactor. Another intriguing observation on the HYZ system is that at its high concentration, the bands of α-Co(OH)2 get converted to β-Co(OH)2. We articulate the reasons and mechanism of those observations.

Physicochemical Perspective of Biological Heterogeneity

The vast majority of chemical processes that govern our lives occur within living cells. At the core of every life process, such as gene expression or metabolism, are chemical reactions that follow the fundamental laws of chemical kinetics and thermodynamics. Understanding these reactions and the factors that govern them is particularly important for the life sciences. The physicochemical environment inside cells, which can vary between cells and organisms, significantly impacts various biochemical reactions and increases the extent of population heterogeneity. This paper discusses using physical chemistry approaches for biological studies, including methods for studying reactions inside cells and monitoring their conditions. The potential for development in this field and possible new research areas are highlighted. By applying physical chemistry methodology to biochemistry in vivo, we may gain new insights into biology, potentially leading to new ways of controlling biochemical reactions.

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

Optimizing Binding among Bimolecular Tethered Complexes

Tethered motion is ubiquitous in nature, offering controlled movement and spatial constraints to otherwise chaotic systems. The enhanced functionality and practical utility of tethers has been exploited in biotechnology, catalyzing the design of novel biosensors and molecular assembly techniques. While notable technological advances incorporating tethered motifs have been made, a theoretical gap persists within the paradigm, hindering a comprehensive understanding of tethered-based technologies. In this work, we focus on the characterization of the binding kinetics of two tethered molecules functionalized to a hard surface. Using a mean-field approximation, the binding time of such bimolecular system is determined analytically. Furthermore, estimates of the grafting site separation and polymer lengths which expedite binding are provided. These estimates, along with the analytical theories and frameworks established here, have the potential to improve efficacy in self-assembly methods in DNA nanotechnology and can be extended to more biologically specific endeavors including targeted drug-delivery and molecular sensing.

Periodic Precipitation in a Confined Liquid Layer

Pattern formation is a ubiquitous phenomenon in animate and inanimate systems generated by mass transport and reaction of chemical species. The Liesegang phenomenon is a self-organized periodic precipitation pattern always studied in porous media such as hydrogels and aerogels for over a century. The primary consideration of applying the porous media is to prevent the disintegration of the precipitation structures due to the sedimentation of the precipitate and induced fluid flow. Here, we show that the periodic precipitation patterns can be engineered using a Hele-Shaw cell in a confined liquid phase, restricting hydrodynamic instability. The patterns generated in several precipitation reaction systems exhibit spatiotemporal properties consistent with patterns obtained in solid hydrogels. Furthermore, analysis considering the Rayleigh-Darcy number emphasizes the crucial role of fluidity in generating periodic precipitation structures in a thin liquid film. This exploration promises breakthroughs at the intersection of fundamental understanding and practical applications.

Size Sensitivity of Metabolite Diffusion in Macromolecular Crowds

Metabolites play crucial roles in cellular processes, yet their diffusion in the densely packed interiors of cells remains poorly understood, compounded by conflicting reports in existing studies. Here, we employ pulsed-gradient stimulated-echo NMR and Brownian/Stokesian dynamics simulations to elucidate the behavior of nano- and subnanometer-sized tracers in crowded environments. Using Ficoll as a crowder, we observe a linear decrease in tracer diffusivity with increasing occupied volume fraction, persisting─somewhat surprisingly─up to volume fractions of 30-40%. While simulations suggest a linear correlation between diffusivity slowdown and particle size, experimental findings hint at a more intricate relationship, possibly influenced by Ficoll's porosity. Simulations and numerical calculations of tracer diffusivity in the E. coli cytoplasm show a nonlinear yet monotonic diffusion slowdown with particle size. We discuss our results in the context of nanoviscosity and discrepancies with existing studies.

Beyond microtubules: The cellular environment at the endoplasmic reticulum attracts proteins to the nucleus, enabling nuclear transport

All proteins are translated in the cytoplasm, yet many, including transcription factors, play vital roles in the nucleus. While previous research has concentrated on molecular motors for the transport of these proteins to the nucleus, recent observations reveal perinuclear accumulation even in the absence of an energy source, hinting at alternative mechanisms. Here, we propose that structural properties of the cellular environment, specifically the endoplasmic reticulum (ER), can promote molecular transport to the perinucleus without requiring additional energy expenditure. Specifically, physical interaction between proteins and the ER impedes their diffusion and leads to their accumulation near the nucleus. This result explains why larger proteins, more frequently interacting with the ER membrane, tend to accumulate at the perinucleus. Interestingly, such diffusion in a heterogeneous environment follows Chapman's law rather than the popular Fick's law. Our findings suggest a novel protein transport mechanism arising solely from characteristics of the intracellular environment.

Determinants of viscoelasticity and flow activation energy in biomolecular condensates

The form and function of biomolecular condensates are intimately linked to their material properties. Here, we integrate microrheology with molecular simulations to dissect the physical determinants of condensate fluid phase dynamics. By quantifying the timescales and energetics of network relaxation in a series of heterotypic viscoelastic condensates, we uncover distinctive roles of sticker motifs, binding energy, and chain length in dictating condensate dynamical properties. We find that the mechanical relaxation times of condensate-spanning networks are determined by both intermolecular interactions and chain length. We demonstrate, however, that the energy barrier for network reconfiguration, termed flow activation energy, is independent of chain length and only varies with the strengths of intermolecular interactions. Biomolecular diffusion in the dense phase depends on a complex interplay between viscoelasticity and flow activation energy. Our results illuminate distinctive roles of chain length and sequence-specific multivalent interactions underlying the complex material and transport properties of biomolecular condensates.

A Novel Fractional Brownian Dynamics Method for Simulating the Dynamics of Confined Bottle-Brush Polymers in Viscoelastic Solution

In crowded fluids, polymer segments can exhibit anomalous subdiffusion due to the viscoelasticity of the surrounding environment. Previous single-particle tracking experiments revealed that such anomalous diffusion in complex fluids (e.g., in bacterial cytoplasm) can be described by fractional Brownian motion (fBm). To investigate how the viscoelastic media affects the diffusive behaviors of polymer segments without resolving single crowders, we developed a novel fractional Brownian dynamics method to simulate the dynamics of polymers under confinement. In this work, instead of using Gaussian random numbers ("white Gaussian noise") to model the Brownian force as in the standard Brownian dynamics simulations, we introduce fractional Gaussian noise (fGn) in our homemade fractional Brownian dynamics simulation code to investigate the anomalous diffusion of polymer segments by using a simple "bottle-brush"-type polymer model. The experimental results of the velocity autocorrelation function and the exponent that characterizes the subdiffusion of the confined polymer segments can be reproduced by this simple polymer model in combination with fractional Gaussian noise (fGn), which mimics the viscoelastic media.

Pumping Small Molecules Selectively through an Energy-Assisted Assembling Process at Nonequilibrium States

In living organisms, precise control over the spatial and temporal distribution of molecules, including pheromones, is crucial. This level of control is equally important for the development of artificial active materials. In this study, we successfully controlled the distribution of small molecules in the system at nonequilibrium states by actively transporting them, even against the apparent concentration gradient, with high selectivity. As a demonstration, in the aqueous solution of acid orange (AO7) and TMC10COOH, we found that AO7 molecules can coassemble with transient anhydride (TMC10CO)2O to form larger assemblies in the presence of chemical fuel 1-ethyl-3-(3-(dimethylamino)propyl) carbodiimide hydrochloride (EDC). This led to a decrease in local free AO7 concentration and caused AO7 molecules from other locations in the solution to move toward the assemblies. Consequently, AO7 accumulates at the location where EDC was injected. By continuously injecting EDC, we could maintain a stable high value of the apparent AO7 concentration at the injection point. We also observed that this process which operated at nonequilibrium states exhibited high selectivity.

Cell-Like Synthetic Supramolecular Soft Materials Realized in Multicomponent, Non-/Out-of-Equilibrium Dynamic Systems

Living cells are complex, nonequilibrium supramolecular systems capable of independently and/or cooperatively integrating multiple bio-supramolecules to execute intricate physiological functions that cannot be accomplished by individual biomolecules. These biological design strategies offer valuable insights for the development of synthetic supramolecular systems with spatially controlled hierarchical structures, which, importantly, exhibit cell-like responses and functions. The next grand challenge in supramolecular chemistry is to control the organization of multiple types of supramolecules in a single system, thus integrating the functions of these supramolecules in an orthogonal and/or cooperative manner. In this perspective, the recent progress in constructing multicomponent supramolecular soft materials through the hybridization of supramolecules, such as self-assembled nanofibers/gels and coacervates, with other functional molecules, including polymer gels and enzymes is highlighted. Moreover, results show that these materials exhibit bioinspired responses to stimuli, such as bidirectional rheological responses of supramolecular double-network hydrogels, temporal stimulus pattern-dependent responses of synthetic coacervates, and 3D hydrogel patterning in response to reaction-diffusion processes are presented. Autonomous active soft materials with cell-like responses and spatially controlled structures hold promise for diverse applications, including soft robotics with directional motion, point-of-care disease diagnosis, and tissue regeneration.

Magnetic tweezers in cell mechanics

The chapter provides an overview of the applications of magnetic tweezers in living cells. It discusses the advantages and disadvantages of magnetic tweezers technology with a focus on individual magnetic tweezers configurations, such as electromagnetic tweezers. Solutions to the disadvantages identified are also outlined. The specific role of magnetic tweezers in the field of mechanobiology, such as mechanosensitivity, mechano-allostery and mechanotransduction are also emphasized. The specific usage of magnetic tweezers in mechanically probing cells via specific cell surface receptors, such as mechanosensitive channels is discussed and why mechanical probing has revealed the opening and closing of the channels. Finally, the future direction of magnetic tweezers is presented.

Chemical Reaction Models in Synthetic Promoter Design in Bacteria

We discuss the formalism of chemical reaction networks (CRNs) as a computer-aided design interface for using formal methods in engineering living technologies. We set out by reviewing formal methods within a broader view of synthetic biology. Based on published results, we illustrate, step by step, how mathematical and computational techniques on CRNs can be used to study the structural and dynamic properties of the designed systems. As a case study, we use an E. coli two-component system that relays the external inorganic phosphate concentration signal to genetic components. We show how CRN models can scan and explore phenotypic regimes of synthetic promoters with varying detection thresholds, thereby providing a means for fine-tuning the promoter strength to match the specification.

Increased intracellular diffusivity of macromolecules within a mammalian cell by low-intensity pulsed ultrasound

Whilst a number of studies have demonstrated that low-intensity pulsed ultrasound (LIPUS) is a promising therapeutic ultrasound technique that can be used for delivering mild mechanical stimuli to target tissue non-invasively, the underlying biophysical mechanisms still remain unclear. Most mechanism studies have focused explicitly on the effects of LIPUS on the cell membrane and mechanosensitive receptors. In the present study, we propose an additional mechanism by which LIPUS propagation through living cells may directly impact intracellular dynamics, particularly the diffusion transport of biomolecules. To support our hypothesis, human epithelial-like cells (SaOS-2 and HeLa) seeded on a confocal dish placed on a microscope stage were exposed to LIPUS with various exposure conditions (ultrasound frequencies of 0.5, 1 and 3 MHz, peak acoustic pressure of 200 and 400 kPa, a pulse repetition frequency of 1 kHz and a 20 % duty cycle), and the diffusivities of various sizes of biomolecules in the cytoplasm area were measured using fluorescence recovery after photobleaching (FRAP). Furthermore, giant unilamellar vesicles (GUVs) filled with macromolecules were used to examine the physical causal relationship between LIPUS and molecular diffusion changes. Nucleocytoplasmic transport coefficients were also measured by modified FRAP that bleaches the whole cell nuclear region. Extracellular signal-regulated kinases (ERK) activity (the phosphorylation dynamics) was monitored using fluorescence resonance energy transfer (FRET) microscopy. All the measurements were taken during, before and after the LIPUS exposure. Our experimental results clearly showed that the diffusion coefficients of macromolecules within the cell increased with acoustic pressure by 12.1 to 33.5 % during the sonication, and the increments were proportional to their molecular sizes regardless of the ultrasound frequency used. This observation in living cells was consistent with the GUVs exposed to the LIPUS, which indicated that the diffusivity increase was a passive physical response to the acoustic energy of LIPUS. Under the 1 MHz LIPUS exposure with 400 kPa, the passive nucleocytoplasmic transport of enhanced green fluorescent protein (EGFP) was accelerated by 21.4 %. With the same LIPUS exposure condition, both the diffusivity and phosphorylation of ERK induced by EGF treatment were significantly elevated simultaneously, which implied that LIPUS could also modify the kinase kinetics in the signal transduction process. Taken together, this study is the first attempt to uncover the physical link between LIPUS and the dynamics of intracellular macromolecules and related biological processes that LIPUS can possibly increase the diffusivity of intracellular macromolecules, leading to the changes in the basic cellular processes: passive nucleocytoplasmic transport and ERK. Our findings can provide a novel perspective that the mechanotransduction process that the intracellular region, in addition to the cell membrane, can convert the acoustic stimuli of LIPUS to biochemical signals.

Single-Molecule Displacement Mapping Indicates Unhindered Intracellular Diffusion of Small (≲1 kDa) Solutes

While fundamentally important, the intracellular diffusion of small (≲1 kDa) solutes has been difficult to elucidate due to challenges in both labeling and measurement. Here we quantify and spatially map the translational diffusion patterns of small solutes in mammalian cells by integrating several recent advances. In particular, by executing tandem stroboscopic illumination pulses down to 400 μs separation, we extend single-molecule displacement/diffusivity mapping (SMdM), a super-resolution diffusion quantification tool, to small solutes with high diffusion coefficients D of >300 μm2/s. We thus show that for multiple water-soluble dyes and dye-tagged nucleotides, intracellular diffusion is dominated by vast regions of high diffusivity ∼60-70% of that in vitro, up to ∼250 μm2/s in the fastest cases. Meanwhile, we also visualize sub-micrometer foci of substantial slowdowns in diffusion, thus underscoring the importance of spatially resolving the local diffusion behavior. Together, these results suggest that the intracellular diffusion of small solutes is only modestly scaled down by the slightly higher viscosity of the cytosol over water but otherwise not further hindered by macromolecular crowding. We thus lift a paradoxically low speed limit for intracellular diffusion suggested by previous experiments.

Size-Dependent Suppression of Molecular Diffusivity in Expandable Hydrogels: A Single-Molecule Study

By repurposing the recently popularized expansion microscopy to control the meshwork size of hydrogels, we examine the size-dependent suppression of molecular diffusivity in the resultant tuned hydrogel nanomatrices over a wide range of polymer fractions of ∼0.14-7 wt %. With our recently developed single-molecule displacement/diffusivity mapping (SMdM) microscopy methods, we thus show that with a fixed meshwork size, larger molecules exhibit more impeded diffusion and that, for the same molecule, diffusion is progressively more suppressed as the meshwork size is reduced; this effect is more prominent for the larger molecules. Moreover, we show that the meshwork-induced obstruction of diffusion is uncoupled from the suppression of diffusion due to increased solution viscosities. Thus, the two mechanisms, respectively, being diffuser-size-dependent and independent, may separately scale down molecular diffusivity to produce the final diffusion slowdown in complex systems like the cell.

Cells function as a ternary logic gate to decide migration direction under integrated chemical and fluidic cues

Cells sense various environmental cues and subsequently process intracellular signals to decide their migration direction in many physiological and pathological processes. Although several signaling molecules and networks have been identified in these directed migrations, it still remains ambiguous to predict the migration direction under multiple and integrated cues, specifically chemical and fluidic cues. Here, we investigated the cellular signal processing machinery by reverse-engineering directed cell migration under integrated chemical and fluidic cues. We imposed controlled chemical and fluidic cues to cells using a microfluidic platform and analyzed the extracellular coupling of the cues with respect to the cellular detection limit. Then, the cell's migratory behavior was reverse-engineered to build a cellular signal processing system as a logic gate, which is based on a "selection" gate. This framework is further discussed with a minimal intracellular signaling network of a shared pathway model. The proposed framework of the ternary logic gate suggests a systematic view to understand how cells decode multiple cues and make decisions about the migration direction.

Single-molecule displacement mapping indicates unhindered intracellular diffusion of small (<~1 kDa) solutes

While fundamentally important, the intracellular diffusion of small (<~1 kDa) solutes has been difficult to elucidate due to challenges in both labeling and measurement. Here we quantify and spatially map the translational diffusion patterns of small solutes in mammalian cells by integrating several recent advances. In particular, by executing tandem stroboscopic illumination pulses down to 400-μs separation, we extend single-molecule displacement/diffusivity mapping (SM d M), a super-resolution diffusion quantification tool, to small solutes with high diffusion coefficients D of >300 μm ² /s. We thus show that for multiple water-soluble dyes and dye-tagged nucleotides, intracellular diffusion is dominated by vast regions of high diffusivity ~60-70% of that in vitro , up to ~250 μm ² /s in the fastest cases. Meanwhile, we also visualize sub-micrometer foci of substantial slowdowns in diffusion, thus underscoring the importance of spatially resolving the local diffusion behavior. Together, these results suggest that the intracellular diffusion of small solutes is only modestly scaled down by the slightly higher viscosity of the cytosol over water, but otherwise not further hindered by macromolecular crowding. We thus lift a paradoxically low speed limit for intracellular diffusion suggested by previous experiments.

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Chemically Driven Multimodal Locomotion of Active, Flexible Sheets

The inhibitor-promoter feedback loop is a vital component in regulatory pathways that controls functionality in living systems. In this loop, the production of chemical A at one site promotes the production of chemical B at another site, but B inhibits the production of A. In solution, differences in the volumes of the reactants and products of this reaction can generate buoyancy-driven fluid flows, which will deform neighboring soft material. To probe the intrinsic interrelationship among chemistry, hydrodynamics, and fluid-structure interactions, we model a bio-inspired system where a flexible sheet immersed in solution encompasses two spatially separated catalytic patches, which drive the A-B inhibitor-promotor reaction. The convective rolls of fluid generated above the patches can circulate inward or outward depending on the chemical environment. Within the regime displaying chemical oscillations, the dynamic fluid-structure interactions morph the shape of the sheet to periodically "fly", "crawl", or "swim" along the bottom of the confining chamber, revealing an intimate coupling between form and function in this system. The oscillations in the sheet's motion in turn affect the chemical oscillations in the solution. In the regime with non-oscillatory chemistry, the induced flow still morphs the shape of the sheet, but now, the fluid simply translates the sheet along the length of the chamber. The findings reveal the potential for enzymatic reactions in the body to generate hydrodynamic behavior that modifies the shape of neighboring soft tissue, which in turn modifies both the fluid dynamics and the enzymatic reaction. The findings indicate that this non-linear dynamic behavior can be playing a critical role in the functioning of regulatory pathways in living systems.

Controlling the Periodicity of a Reaction-Diffusion Wave in Artificial Cells by a Two-Way Energy Supplier

Reaction-diffusion (RD) waves, which are dynamic self-organization structures generated by nanosize molecules, are a fundamental mechanism from patterning in nano- and micromaterials to spatiotemporal regulations in living cells, such as cell division and motility. Although the periods of RD waves are the critical element for these functions, the development of a system to control their period is challenging because RD waves result from nonlinear physical dynamics under far-from-equilibrium conditions. Here, we developed an artificial cell system with tunable period of an RD-driven wave (Min protein wave), which determines a cell division site plane in living bacterial cells. The developed system is based on our finding that Min waves are generated by energy consumption of either ATP or dATP, and the period of the wave is different between these two energy suppliers. We showed that the Min-wave period was modulated linearly by the mixing ratio of ATP and dATP and that it was also possible to estimate the mixing ratio of ATP and dATP from the period. Our findings illuminated a previously unidentified principle to control the dissipative dynamics of biomolecules and, simultaneously, built an important framework to construct molecular robots with spatiotemporal units.

ANALYTICAL SINGULAR VALUE DECOMPOSITION FOR A CLASS OF STOICHIOMETRY MATRICES

We present the analytical singular value decomposition of the stoichiometry matrix for a spatially discrete reaction-diffusion system. The motivation for this work is to develop a matrix decomposition that can reveal hidden spatial flux patterns of chemical reactions. We consider a 1D domain with two subregions sharing a single common boundary. Each of the subregions is further partitioned into a finite number of compartments. Chemical reactions can occur within a compartment, whereas diffusion is represented as movement between adjacent compartments. Inspired by biology, we study both (1) the case where the reactions on each side of the boundary are different and only certain species diffuse across the boundary and (2) the case where reactions and diffusion are spatially homogeneous. We write the stoichiometry matrix for these two classes of systems using a Kronecker product formulation. For the first scenario, we apply linear perturbation theory to derive an approximate singular value decomposition in the limit as diffusion becomes much faster than reactions. For the second scenario, we derive an exact analytical singular value decomposition for all relative diffusion and reaction time scales. By writing the stoichiometry matrix using Kronecker products, we show that the singular vectors and values can also be written concisely using Kronecker products. Ultimately, we find that the singular value decomposition of the reaction-diffusion stoichiometry matrix depends on the singular value decompositions of smaller matrices. These smaller matrices represent modified versions of the reaction-only stoichiometry matrices and the analytically known diffusion-only stoichiometry matrix. Lastly, we present the singular value decomposition of the model for the Calvin cycle in cyanobacteria and demonstrate the accuracy of our formulation. The MATLAB code, available at www.github.com/MathBioCU/ReacDiffStoicSVD, provides routines for efficiently calculating the SVD for a given reaction network on a 1D spatial domain.

How macromolecules softness affects diffusion under crowding

Diffusion in a macromolecularly crowded environment is essential for many intracellular processes, from metabolism and catalysis to gene transcription and translation. So far, theoretical and experimental work has focused on anomalous subdiffusion, and the effects of interactions, shapes, and composition, while the compactness or softness of macromolecules has received less attention. Herein, we use Brownian dynamics simulations to study how the softness of crowders affects macromolecular diffusion. We find that in most cases, soft crowders slow down the diffusion less effectively than hard crowders like Ficoll. For instance, at a 30% occupied volume fraction, the diffusion in Ficoll70 is about 20% slower than in soft crowders of the same size. However, our simulations indicate that elongated macromolecules, such as double-stranded DNA pieces, can diffuse comparably or even faster in hard crowders. We relate these effects to the volume excluded by soft and hard crowders to different tracers. Our results show that the softness and shape of macromolecules are crucial factors determining diffusion under crowding, relevant to diverse intracellular environments.

Nuclear RNA binding regulates TDP-43 nuclear localization and passive nuclear export

Nuclear clearance of the RNA-binding protein TDP-43 is a hallmark of neurodegeneration and an important therapeutic target. Our current understanding of TDP-43 nucleocytoplasmic transport does not fully explain its predominantly nuclear localization or mislocalization in disease. Here, we show that TDP-43 exits nuclei by passive diffusion, independent of facilitated mRNA export. RNA polymerase II blockade and RNase treatment induce TDP-43 nuclear efflux, suggesting that nuclear RNAs sequester TDP-43 in nuclei and limit its availability for passive export. Induction of TDP-43 nuclear efflux by short, GU-rich oligomers (presumably by outcompeting TDP-43 binding to endogenous nuclear RNAs), and nuclear retention conferred by splicing inhibition, demonstrate that nuclear TDP-43 localization depends on binding to GU-rich nuclear RNAs. Indeed, RNA-binding domain mutations markedly reduce TDP-43 nuclear localization and abolish transcription blockade-induced nuclear efflux. Thus, the nuclear abundance of GU-RNAs, dictated by the balance of transcription, pre-mRNA processing, and RNA export, regulates TDP-43 nuclear localization.

Shear strain and inflammation-induced fixed charge density loss in the knee joint cartilage following ACL injury and reconstruction: A computational study

Excessive tissue deformation near cartilage lesions and acute inflammation within the knee joint after anterior cruciate ligament (ACL) rupture and reconstruction surgery accelerate the loss of fixed charge density (FCD) and subsequent cartilage tissue degeneration. Here, we show how biomechanical and biochemical degradation pathways can predict FCD loss using a patient-specific finite element model of an ACL reconstructed knee joint exhibiting a chondral lesion. Biomechanical degradation was based on the excessive maximum shear strains that may result in cell apoptosis, while biochemical degradation was driven by the diffusion of pro-inflammatory cytokines. We found that the biomechanical model was able to predict substantial localized FCD loss near the lesion and on the medial areas of the lateral tibial cartilage. In turn, the biochemical model predicted FCD loss all around the lesion and at intact areas; the highest FCD loss was at the cartilage-synovial fluid-interface and decreased toward the deeper zones. Interestingly, simulating a downturn of an acute inflammatory response by reducing the cytokine concentration exponentially over time in synovial fluid led to a partial recovery of FCD content in the cartilage. Our novel numerical approach suggests that in vivo FCD loss can be estimated in injured cartilage following ACL injury and reconstruction. Our novel modeling platform can benefit the prediction of PTOA progression and the development of treatment interventions such as disease-modifying drug testing and rehabilitation strategies.

Progressive Local Accumulation of Self-Assembled Nanoreactors in a Hydrogel Matrix through Repetitive Injections of ATP

Cellular functions are regulated with high spatial control through the local activation of chemical processes in a complex inhomogeneous matrix. The development of synthetic macroscopic systems with a similar capacity allows fundamental studies aimed at understanding the relationship between local molecular events and the emergence of functional properties at the macroscopic level. Here, we show that a kinetically stable inhomogeneous hydrogel matrix is spontaneously formed upon the local injection of ATP. Locally, ATP templates the self-assembly of amphiphiles into large nanoreactors with a much lower diffusion rate compared to unassembled amphiphiles. The local depletion of unassembled amphiphiles near the injection point installs a concentration gradient along which unassembled amphiphiles diffuse from the surroundings to the center. This allows for a progressive local accumulation of self-assembled nanoreactors in the matrix upon repetitive cycles of ATP injection separated by time intervals during which diffusion of unassembled amphiphiles takes place. Contrary to the homogeneous matrix containing the same components, in the inhomogeneous matrix the local upregulation of a chemical reaction occurs. Depending on the way the same amount of injected ATP is administered to the hydrogel matrix different macroscopic distributions of nanoreactors are obtained, which affect the location in the matrix where the chemical reaction is upregulated.

Phototriggered Spatially Controlled Out-of-Equilibrium Patterns of Peptide Nanofibers in a Self-Sorting Double Network Hydrogel

Out-of-equilibrium patterns arising from diffusion processes are ubiquitous in nature, although they have not been fully exploited for the design of artificial materials. Here, we describe the formation of phototriggered out-of-equilibrium patterns using photoresponsive peptide-based nanofibers in a self-sorting double network hydrogel. Light irradiation using a photomask followed by thermal incubation induced the spatially controlled condensation of peptide nanofibers. According to confocal images and spectroscopic analyses, metastable nanofibers photodecomposed in the irradiated areas, where thermodynamically stable nanofibers reconstituted and condensed with a supply of monomers from the nonirradiated areas. These supramolecular events were regulated by light and diffusion to facilitate the creation of unique out-of-equilibrium patterns, including two lines from a one-line photomask and a line pattern of a protein immobilized in the hydrogel.

Signal processing capacity of the cellular sensory machinery regulates the accuracy of chemotaxis under complex cues

Chemotaxis is ubiquitous in many biological processes, but it still remains elusive how cells sense and decipher multiple chemical cues. In this study, we postulate a hypothesis that the chemotactic performance of cells under complex cues is regulated by the signal processing capacity of the cellular sensory machinery. The underlying rationale is that cells in vivo should be able to sense and process multiple chemical cues, whose magnitude and compositions are entangled, to determine their migration direction. We experimentally show that the combination of transforming growth factor-β and epidermal growth factor suppresses the chemotactic performance of cancer cells using independent receptors to sense the two cues. Based on this observation, we develop a biophysical framework suggesting that the antagonism is caused by the saturation of the signal processing capacity but not by the mutual repression. Our framework suggests the significance of the signal processing capacity in the cellular sensory machinery.

Kinetic and structural roles for the surface in guiding SAS-6 self-assembly to direct centriole architecture

Discovering mechanisms governing organelle assembly is a fundamental pursuit in biology. The centriole is an evolutionarily conserved organelle with a signature 9-fold symmetrical chiral arrangement of microtubules imparted onto the cilium it templates. The first structure in nascent centrioles is a cartwheel, which comprises stacked 9-fold symmetrical SAS-6 ring polymers emerging orthogonal to a surface surrounding each resident centriole. The mechanisms through which SAS-6 polymerization ensures centriole organelle architecture remain elusive. We deploy photothermally-actuated off-resonance tapping high-speed atomic force microscopy to decipher surface SAS-6 self-assembly mechanisms. We show that the surface shifts the reaction equilibrium by ~10⁴ compared to solution. Moreover, coarse-grained molecular dynamics and atomic force microscopy reveal that the surface converts the inherent helical propensity of SAS-6 polymers into 9-fold rings with residual asymmetry, which may guide ring stacking and impart chiral features to centrioles and cilia. Overall, our work reveals fundamental design principles governing centriole assembly.

The centriole exhibits an evolutionarily conserved 9-fold radial symmetry that stems from a cartwheel containing vertically stacked ring polymers that harbor 9 homodimers of the protein SAS-6. Here the authors show how dual properties inherent to surface-guided SAS-6 self-assembly possess spatial information that dictates correct scaffolding of centriole architecture.

Exploring the influence of cytosolic and membrane FAK activation on YAP/TAZ nuclear translocation

Membrane binding and unbinding dynamics play a crucial role in the biological activity of several nonintegral membrane proteins, which have to be recruited to the membrane to perform their functions. By localizing to the membrane, these proteins are able to induce downstream signal amplification in their respective signaling pathways. Here, we present a 3D computational approach using reaction-diffusion equations to investigate the relation between membrane localization of focal adhesion kinase (FAK), Ras homolog family member A (RhoA), and signal amplification of the YAP/TAZ signaling pathway. Our results show that the theoretical scenarios in which FAK is membrane bound yield robust and amplified YAP/TAZ nuclear translocation signals. Moreover, we predict that the amount of YAP/TAZ nuclear translocation increases with cell spreading, confirming the experimental findings in the literature. In summary, our in silico predictions show that when the cell membrane interaction area with the underlying substrate increases, for example, through cell spreading, this leads to more encounters between membrane-bound signaling partners and downstream signal amplification. Because membrane activation is a motif common to many signaling pathways, this study has important implications for understanding the design principles of signaling networks.

Photo-Responsive Self-Assembly of Plasmonic Magnetic Janus Nanoparticles

Stimuli-responsive self-assembly of nanoparticles is a versatile approach for the bottom-up fabrication of adaptive and functional nanomaterials. For this purpose, anisotropic building blocks are of particular importance due to the unique shapes and structures that can be obtained upon self-assembly. Here, we demonstrate the photo-responsive self-assembly of plasmonic magnetic "dumbbell" Janus nanoparticles (Au-Fe₃O₄) via the host-guest interaction of the supramolecular host cyclodextrin and the molecular photoswitch arylazopyrazole. We developed efficient ligand exchange procedures that enable the introduction of functional ligands, respectively, to the surface of the gold or magnetite core of the dumbbell. Our results indicate that distinct nanoparticle superstructures arise in aqueous solutions if nanoparticle aggregation is crosslinker-induced or self-induced and that the reversible formation and fragmentation of the superstructures can be modulated with light.

Effects of spatial heterogeneity on bacterial genetic circuits

Intracellular spatial heterogeneity is frequently observed in bacteria, where the chromosome occupies part of the cell's volume and a circuit's DNA often localizes within the cell. How this heterogeneity affects core processes and genetic circuits is still poorly understood. In fact, commonly used ordinary differential equation (ODE) models of genetic circuits assume a well-mixed ensemble of molecules and, as such, do not capture spatial aspects. Reaction-diffusion partial differential equation (PDE) models have been only occasionally used since they are difficult to integrate and do not provide mechanistic understanding of the effects of spatial heterogeneity. In this paper, we derive a reduced ODE model that captures spatial effects, yet has the same dimension as commonly used well-mixed models. In particular, the only difference with respect to a well-mixed ODE model is that the association rate constant of binding reactions is multiplied by a coefficient, which we refer to as the binding correction factor (BCF). The BCF depends on the size of interacting molecules and on their location when fixed in space and it is equal to unity in a well-mixed ODE model. The BCF can be used to investigate how spatial heterogeneity affects the behavior of core processes and genetic circuits. Specifically, our reduced model indicates that transcription and its regulation are more effective for genes located at the cell poles than for genes located on the chromosome. The extent of these effects depends on the value of the BCF, which we found to be close to unity. For translation, the value of the BCF is always greater than unity, it increases with mRNA size, and, with biologically relevant parameters, is substantially larger than unity. Our model has broad validity, has the same dimension as a well-mixed model, yet it incorporates spatial heterogeneity. This simple-to-use model can be used to both analyze and design genetic circuits while accounting for spatial intracellular effects.

Macromolecular Crowding: How Shape and Interactions Affect Diffusion

A significant fraction of the cell volume is occupied by various proteins, polysaccharides, nucleic acids, etc., which considerably reduces the mobility of macromolecules. Theoretical and experimental work so far have mainly focused on the dependence of the mobility on the occupied volume, while the effect of a macromolecular shape received less attention. Herein, using fluorescence correlation spectroscopy (FCS) and Brownian dynamics (BD) simulations, we report on a dramatic slowdown of tracer diffusion by cylindrically shaped double-stranded (ds) DNAs (16 nm in length). We find, for instance, that the translational diffusion coefficient of a streptavidin tracer is reduced by about 60% for a volume fraction of dsDNA as low as just 5%. For comparison, for a spherical crowder (Ficoll70) the slowdown is only 10% at the same volume fraction and 60% reduction occurs at a volume fraction as high as 35%. BD simulations reveal that this reduction can be attributed to a larger volume excluded to a tracer by dsDNA particles, as compared with spherical Ficoll70 at the same volume fraction, and to the differences in the tracer-crowder attractive interactions. In addition, we find using BD simulations that rotational diffusion of dsDNA is less affected by the crowder shape than its translational motion. Our results show that diffusion in crowded systems is determined not merely by the occupied volume fraction, but that the shape and interactions can determine diffusion, which is relevant to the diverse intracellular environments inside living cells.

Microfluidic Fabrication of Click Chemistry-Mediated Hyaluronic Acid Microgels: A Bottom-Up Material Guide to Tailor a Microgel's Physicochemical and Mechanical Properties

The demand for tailored, micrometer-scaled biomaterials in cell biology and (cell-free) biotechnology has led to the development of tunable microgel systems based on natural polymers, such as hyaluronic acid (HA). To precisely tailor their physicochemical and mechanical properties and thus to address the need for well-defined microgel systems, in this study, a bottom-up material guide is presented that highlights the synergy between highly selective bio-orthogonal click chemistry strategies and the versatility of a droplet microfluidics (MF)-assisted microgel design. By employing MF, microgels based on modified HA-derivates and homobifunctional poly(ethylene glycol) (PEG)-crosslinkers are prepared via three different types of click reaction: Diels-Alder [4 + 2] cycloaddition, strain-promoted azide-alkyne cycloaddition (SPAAC), and UV-initiated thiol-ene reaction. First, chemical modification strategies of HA are screened in-depth. Beyond the microfluidic processing of HA-derivates yielding monodisperse microgels, in an analytical study, we show that their physicochemical and mechanical properties-e.g., permeability, (thermo)stability, and elasticity-can be systematically adapted with respect to the type of click reaction and PEG-crosslinker concentration. In addition, we highlight the versatility of our HA-microgel design by preparing non-spherical microgels and introduce, for the first time, a selective, hetero-trifunctional HA-based microgel system with multiple binding sites. As a result, a holistic material guide is provided to tailor fundamental properties of HA-microgels for their potential application in cell biology and (cell-free) biotechnology.

Force generation by a propagating wave of supramolecular nanofibers

Dynamic spatiotemporal patterns that arise from out-of-equilibrium biochemical reactions generate forces in living cells. Despite considerable recent efforts, rational design of spatiotemporal patterns in artificial molecular systems remains at an early stage of development. Here, we describe force generation by a propagating wave of supramolecular nanofibers. Inspired by actin dynamics, a reaction network is designed to control the formation and degradation of nanofibers by two chemically orthogonal stimuli. Real-time fluorescent imaging successfully visualizes the propagating wave based on spatiotemporally coupled generation and collapse of nanofibers. Numerical simulation indicates that the concentration gradient of degradation stimulus and the smaller diffusion coefficient of the nanofiber are critical for wave emergence. Moreover, the force (0.005 pN) generated by chemophoresis and/or depletion force of this propagating wave can move nanobeads along the wave direction.

Mechanobiological model for simulation of injured cartilage degradation via pro-inflammatory cytokines and mechanical stimulus

Post-traumatic osteoarthritis (PTOA) is associated with cartilage degradation, ultimately leading to disability and decrease of quality of life. Two key mechanisms have been suggested to occur in PTOA: tissue inflammation and abnormal biomechanical loading. Both mechanisms have been suggested to result in loss of cartilage proteoglycans, the source of tissue fixed charge density (FCD). In order to predict the simultaneous effect of these degrading mechanisms on FCD content, a computational model has been developed. We simulated spatial and temporal changes of FCD content in injured cartilage using a novel finite element model that incorporates (1) diffusion of the pro-inflammatory cytokine interleukin-1 into tissue, and (2) the effect of excessive levels of shear strain near chondral defects during physiologically relevant loading. Cytokine-induced biochemical cartilage explant degradation occurs near the sides, top, and lesion, consistent with the literature. In turn, biomechanically-driven FCD loss is predicted near the lesion, in accordance with experimental findings: regions near lesions showed significantly more FCD depletion compared to regions away from lesions (p<0.01). Combined biochemical and biomechanical degradation is found near the free surfaces and especially near the lesion, and the corresponding bulk FCD loss agrees with experiments. We suggest that the presence of lesions plays a role in cytokine diffusion-driven degradation, and also predisposes cartilage for further biomechanical degradation. Models considering both these cartilage degradation pathways concomitantly are promising in silico tools for predicting disease progression, recognizing lesions at high risk, simulating treatments, and ultimately optimizing treatments to postpone the development of PTOA.

Chasing Synthetic Life: A Tale of Forms, Chemical Fossils, and Biomorphs

This Essay focuses briefly on early studies elaborated by natural and chemical philosophers, and the once-called synthetic biologists, who postulated the transition from inanimate to animate matter and even foresaw the possibility of creating artificial life on the basis of physical and chemical principles only. Such ideas and speculations, ranging from soundness to weirdness, paved however the way to current developments in areas like abiotic pattern formation, cell compartmentalization, biomineralization, or the origin of life itself. In particular, the generation of biomorphs and their relationship to microfossils represents an active research domain and seems to be the logical way to bring the historical work up to the future, as some scientists are trying to make artificial cells. The last sections of this essay will also highlight modern science aimed at understanding what life is and, whether or not, it can be redefined in chemical terms.

Intra-mitochondrial reaction for cancer cell imaging and anti-cancer therapy by aggregation-induced emission

Controlled intracellular chemical reactions to regulate cellular functions remain a challenge in biology mimetic systems. Herein, we developed an intra-mitochondrial bio-orthogonal reaction to induce aggregation induced emission. In situ carbonyl ligation inside mitochondria drives the molecules to form nano-aggregates with green fluorescence, which leads to depolarization of the mitochondrial membrane, generation of ROS, and subsequently mitochondrial dysfunction. This intra-mitochondrial carbonyl ligation shows great potential for anticancer treatment in various cancer cell lines.

Controlled intracellular chemical reactions to regulate cellular function remain a challenge in biology mimetic systems.

Regulation of spatiotemporal patterning in artificial cells by a defined protein expression system

Spatiotemporal patterning is a fundamental mechanism for developmental differentiation and homeostasis in living cells. Because spatiotemporal patterns are based on higher-order collective motions of elements synthesized from genes, their behavior dynamically changes according to the element amounts. Thus, to understand life and use this process for material application, creation of artificial cells with time development of spatiotemporal patterning by changes of element levels is necessary. However, realizing coupling between spatiotemporal patterning and synthesis of elements in artificial cells has been particularly challenging. In this study, we established a system that can synthesize a patterning mechanism of the bacterial cell division plane (the so-called Min system) in artificial cells by modifying a defined protein expression system and demonstrated that artificial cells can show time development of spatiotemporal patterning similar to living cells. This system also allows generation and disappearance of spatiotemporal patterning, is controllable by a small molecule in artificial cells, and has the ability for application in cargo transporters. The system developed here provides a new material and a technique for understanding life, development of drug delivery tools, and creation of molecular robots.

Catalytic transport of molecular cargo using diffusive binding along a polymer track

Transport at the molecular scale is a prerequisite for the development of future molecular factories. Here, we have designed oligoanionic molecular sliders on polycationic tracks that exploit Brownian motion and diffusive binding to transport cargo without using a chemical fuel. The presence of the polymer tracks increases the rate of bimolecular reactions between modified sliders by over two orders of magnitude. Molecular dynamics simulations showed that the sliders not only diffuse, but also jump and hop surprisingly efficiently along polymer tracks. Inspired by acetyl-coenzyme A transporting and delivering acetyl groups in many essential biochemical processes, we developed a new and unconventional type of catalytic transport involving sliders (including coenzyme A) picking up, transporting and selectively delivering molecular cargo. Furthermore, we show that the concept of diffusive binding can also be utilized for the spatially controlled transport of chemical groups across gels. This work represents a new concept for designing functional nanosystems based on random Brownian motion.

Repurposing of auranofin: Thioredoxin reductase remains a primary target of the drug

Auranofin is a gold (I)-containing compound used for the treatment of rheumatic arthritis. Auranofin has anticancer activity in animal models and is approved for clinical trials for lung and ovarian carcinomas. Both the cytosolic and mitochondrial forms of the selenoprotein thioredoxin reductase (TrxR) are well documented targets of auranofin. Auranofin was recently reported to also inhibit proteasome activity at the level of the proteasome-associated deubiquitinases (DUBs) UCHL5 and USP14. We here set out to re-examine the molecular mechanism underlying auranofin cytotoxicity towards cultured cancer cells. The effects of auranofin on the proteasome were examined in cells and in vitro, effects on DUB activity were assessed using different substrates. The cellular response to auranofin was compared to that of the 20S proteasome inhibitor bortezomib and the 19S DUB inhibitor b-AP15 using proteomics. Auranofin was found to inhibit mitochondrial activity and to an induce oxidative stress response at IC₅₀ doses. At 2-3-fold higher doses, auranofin inhibits proteasome processing in cells. At such supra-pharmacological concentrations USP14 activity was inhibited. Analysis of protein expression profiles in drug-exposed tumor cells showed that auranofin induces a response distinct from that of the 20S proteasome inhibitor bortezomib and the DUB inhibitor b-AP15, both of which induced similar responses. Our results support the notion that the primary mechanism of action of auranofin is TrxR inhibition and suggest that proteasome DUB inhibition is an off-target effect. Whether proteasome inhibition will contribute to the antineoplastic effect of auranofin in treated patients is unclear but remains a possibility.