Stochastic or Not? Method To Predict and Quantify the Stochastic Effects on the Association Reaction Equilibria in Nanoscopic Systems

Chemical Kinetics in Microdroplets

Micrometer-sized compartments play significant roles in driving heterogeneous transformations within atmospheric and biochemical systems as well as providing vehicles for drug delivery and novel reaction environments for the synthesis of industrial chemicals. Many reports now indicate that reaction kinetics are accelerated under microconfinement, for example, in sprays, thin films, droplets, aerosols, and emulsions. These observations are dramatic, posing a challenge to our understanding of chemical reaction mechanisms with potentially significant practical consequences for predicting the complex chemistry in natural systems. Here we introduce the idea of kinetic confinement, which is intended to provide a conceptual backdrop for understanding when and why microdroplet reaction kinetics differ from their macroscale analogs.

Breakdown of Langmuir Adsorption Isotherm in Small Closed Systems

For more than a century, monolayer adsorptions in which adsorbate molecules and adsorbing sites behave ideally have been successfully described by Langmuir's adsorption isotherm. For example, the amount of adsorbed material, as a function of concentration of the material which is not adsorbed, obeys Langmuir's equation. In this paper, we argue that this relation is valid only for macroscopic systems. However, when particle numbers of adsorbate molecules and/or adsorbing sites are small, Langmuir's model fails to describe the chemical equilibrium of the system. This is because the kinetics of forming, or the probability of observing, occupied sites arises from two-body interactions, and as such, ought to include cross-correlations between particle numbers of the adsorbate and adsorbing sites. The effect of these correlations, as reflected by deviations in predicting composition when correlations are ignored, increases with decreasing particle numbers and becomes substantial when only few adsorbate molecules, or adsorbing sites, are present in the system. In addition, any change that augments the fraction of occupied sites at equilibrium (e.g., smaller volume, lower temperature, or stronger adsorption energy) further increases the discrepancy between observed properties of small systems and those predicted by Langmuir's theory. In contrast, for large systems, these cross-correlations become negligible, and therefore when expressing properties involving two-body processes, it is possible to consider independently the concentration of each component. By applying statistical mechanics concepts, we derive a general expression of the equilibrium constant for adsorption. It is also demonstrated that in ensembles in which total numbers of particles are fixed, the magnitudes of fluctuations in particle numbers alone can predict the average chemical composition of the system. Moreover, an alternative adsorption equation, predicting the average fraction of occupied sites from the value of the equilibrium constant, is proposed. All derived relations were tested against results obtained by Monte Carlo simulations.

Super-Resolution Imaging of Voltages in the Interior of Individual, Vital Mitochondria

We present super-resolution microscopy of isolated functional mitochondria, enabling real-time studies of structure and function (voltages) in response to pharmacological manipulation. Changes in mitochondrial membrane potential as a function of time and position can be imaged in different metabolic states (not possible in whole cells), created by the addition of substrates and inhibitors of the electron transport chain, enabled by the isolation of vital mitochondria. By careful analysis of structure dyes and voltage dyes (lipophilic cations), we demonstrate that most of the fluorescent signal seen from voltage dyes is due to membrane bound dyes, and develop a model for the membrane potential dependence of the fluorescence contrast for the case of super-resolution imaging, and how it relates to membrane potential. This permits direct analysis of mitochondrial structure and function (voltage) of isolated, individual mitochondria as well as submitochondrial structures in the functional, intact state, a major advance in super-resolution studies of living organelles.

Reconstitution of actin-based cellular processes: Why encapsulation changes the rules

While in vitro reconstitution of cellular processes is progressing rapidly, the encapsulation of biomimetic systems to reproduce the cellular environment is a major challenge. Here we review the difficulties, using reconstitution of processes dependent on actin polymerization as an example. Some of the problems are purely technical, due to the need for engineering strategies to encapsulate concentrated solutions in micrometer-sized compartments. However, other significant issues arise from the reduction of experimental volumes, which alters the chemical evolution of these non-equilibrium systems. Important parameters to consider for successful reconstitutions are the amount of each component, their consumption and renewal rates to guarantee their continuous availability.

Modeling control and transduction of electrochemical gradients in acid-stressed bacteria

Transmembrane electrochemical gradients drive solute uptake and constitute a substantial fraction of the cellular energy pool in bacteria. These gradients act not only as "homeostatic contributors," but also play a dynamic and keystone role in several bacterial functions, including sensing, stress response, and metabolism. At the system level, multiple gradients interact with ion transporters and bacterial behavior in a complex, rapid, and emergent manner; consequently, experiments alone cannot untangle their interdependencies. Electrochemical gradient modeling provides a general framework to understand these interactions and their underlying mechanisms. We quantify the generation, maintenance, and interactions of electrical, proton, and potassium potential gradients under lactic acid-stress and lactic acid fermentation. Further, we elucidate a gradient-mediated mechanism for intracellular pH sensing and stress response. We demonstrate that this gradient model can yield insights on the energetic limitations of membrane transport, and can predict bacterial behavior across changing environments.

A Digital Microfluidic Device Integrated with Electrochemical Impedance Spectroscopy for Cell-Based Immunoassay

The dynamic immune response to various diseases and therapies has been considered a promising indicator of disease status and therapeutic effectiveness. For instance, the human peripheral blood mononuclear cell (PBMC), as a major player in the immune system, is an important index to indicate a patient's immune function. Therefore, establishing a simple yet sensitive tool that can frequently assess the immune system during the course of disease and treatment is of great importance. This study introduced an integrated system that includes an electrochemical impedance spectroscope (EIS)-based biosensor in a digital microfluidic (DMF) device, to quantify the PBMC abundance with minimally trained hands. Moreover, we exploited the unique droplet manipulation feature of the DMF platform and conducted a dynamic cell capture assay, which enhanced the detection signal by 2.4-fold. This integrated system was able to detect as few as 104 PBMCs per mL, presenting suitable sensitivity to quantify PBMCs. This integrated system is easy-to-operate and sensitive, and therefore holds great potential as a powerful tool to profile immune-mediated therapeutic responses in a timely manner, which can be further evolved as a point-of-care diagnostic device to conduct near-patient tests from blood samples.

Colocalization of different neurotransmitter transporters on synaptic vesicles is sparse except for VGLUT1 and ZnT3

Vesicular transporters (VTs) define the type of neurotransmitter that synaptic vesicles (SVs) store and release. While certain mammalian neurons release multiple transmitters, it is not clear whether the release occurs from the same or distinct vesicle pools at the synapse. Using quantitative single-vesicle imaging, we show that a vast majority of SVs in the rodent brain contain only one type of VT, indicating specificity for a single neurotransmitter. Interestingly, SVs containing dual transporters are highly diverse (27 types) but small in proportion (2% of all SVs), excluding the largest pool that carries VGLUT1 and ZnT3 (34%). Using VGLUT1-ZnT3 SVs, we demonstrate that the transporter colocalization influences the SV content and synaptic quantal size. Thus, the presence of diverse transporters on the same vesicle is bona fide, and depending on the VT types, this may act to regulate neurotransmitter type, content, and release in space and time.

Kinetics of Cu(II) complexation by ATCUN/NTS and related peptides: a gold mine of novel ideas for copper biology

Cu(II)-peptide complexes are intensely studied as models for biological peptides and proteins and for their direct importance in copper homeostasis and dyshomeostasis in human diseases. In particular, high-affinity ATCUN/NTS (amino-terminal copper and nickel/N-terminal site) motifs present in proteins and peptides are considered as Cu(II) transport agents for copper delivery to cells. The information on the affinities and structures of such complexes derived from steady-state methods appears to be insufficient to resolve the mechanisms of copper trafficking, while kinetic studies have recently shown promise in explaining them. Stopped-flow experiments of Cu(II) complexation to ATCUN/NTS peptides revealed the presence of reaction steps with rates much slower than the diffusion limit due to the formation of novel intermediate species. Herein, the state of the field in Cu(II)-peptide kinetics is reviewed in the context of physiological data, leading to novel ideas in copper biology, together with the discussion of current methodological issues.

The Proton in Biochemistry: Impacts on Bioenergetics, Biophysical Chemistry, and Bioorganic Chemistry

The proton is the smallest atomic particle, and in aqueous solution it is the smallest hydrated ion, having only two waters in its first hydration shell. In this article we survey key aspects of the proton in chemistry and biochemistry, starting with the definitions of pH and pK _a and their application inside biological cells. This includes an exploration of pH in nanoscale spaces, distinguishing between bulk and interfacial phases. We survey the Eigen and Zundel models of the structure of the hydrated proton, and how these can be used to explain: a) the behavior of protons at the water-hydrophobic interface, and b) the extraordinarily high mobility of protons in bulk water via Grotthuss hopping, and inside proteins via proton wires. Lastly, we survey key aspects of the effect of proton concentration and proton transfer on biochemical reactions including ligand binding and enzyme catalysis, as well as pH effects on biochemical thermodynamics, including the Chemiosmotic Theory. We find, for example, that the spontaneity of ATP hydrolysis at pH ≥ 7 is not due to any inherent property of ATP (or ADP or phosphate), but rather to the low concentration of H⁺. Additionally, we show that acidification due to fermentation does not derive from the organic acid waste products, but rather from the proton produced by ATP hydrolysis.

The Bioinorganic Chemistry of Mammalian Metallothioneins

The functions, purposes, and roles of metallothioneins have been the subject of speculations since the discovery of the protein over 60 years ago. This article guides through the history of investigations and resolves multiple contentions by providing new interpretations of the structure-stability-function relationship. It challenges the dogma that the biologically relevant structure of the mammalian proteins is only the one determined by X-ray diffraction and NMR spectroscopy. The terms metallothionein and thionein are ambiguous and insufficient to understand biological function. The proteins need to be seen in their biological context, which limits and defines the chemistry possible. They exist in multiple forms with different degrees of metalation and types of metal ions. The homoleptic thiolate coordination of mammalian metallothioneins is important for their molecular mechanism. It endows the proteins with redox activity and a specific pH dependence of their metal affinities. The proteins, therefore, also exist in different redox states of the sulfur donor ligands. Their coordination dynamics allows a vast conformational landscape for interactions with other proteins and ligands. Many fundamental signal transduction pathways regulate the expression of the dozen of human metallothionein genes. Recent advances in understanding the control of cellular zinc and copper homeostasis are the foundation for suggesting that mammalian metallothioneins provide a highly dynamic, regulated, and uniquely biological metal buffer to control the availability, fluctuations, and signaling transients of the most competitive Zn(II) and Cu(I) ions in cellular space and time.

Probing the Structure and Function of the Cytosolic Domain of the Human Zinc Transporter ZnT8 with Nickel(II) Ions

The human zinc transporter ZnT8 provides the granules of pancreatic β-cells with zinc (II) ions for assembly of insulin hexamers for storage. Until recently, the structure and function of human ZnTs have been modelled on the basis of the 3D structures of bacterial zinc exporters, which form homodimers with each monomer having six transmembrane α-helices harbouring the zinc transport site and a cytosolic domain with an α,β structure and additional zinc-binding sites. However, there are important differences in function as the bacterial proteins export an excess of zinc ions from the bacterial cytoplasm, whereas ZnT8 exports zinc ions into subcellular vesicles when there is no apparent excess of cytosolic zinc ions. Indeed, recent structural investigations of human ZnT8 show differences in metal binding in the cytosolic domain when compared to the bacterial proteins. Two common variants, one with tryptophan (W) and the other with arginine (R) at position 325, have generated considerable interest as the R-variant is associated with a higher risk of developing type 2 diabetes. Since the mutation is at the apex of the cytosolic domain facing towards the cytosol, it is not clear how it can affect zinc transport through the transmembrane domain. We expressed the cytosolic domain of both variants of human ZnT8 and have begun structural and functional studies. We found that (i) the metal binding of the human protein is different from that of the bacterial proteins, (ii) the human protein has a C-terminal extension with three cysteine residues that bind a zinc(II) ion, and (iii) there are small differences in stability between the two variants. In this investigation, we employed nickel(II) ions as a probe for the spectroscopically silent Zn(II) ions and utilised colorimetric and fluorimetric indicators for Ni(II) ions to investigate metal binding. We established Ni(II) coordination to the C-terminal cysteines and found differences in metal affinity and coordination in the two ZnT8 variants. These structural differences are thought to be critical for the functional differences regarding the diabetes risk. Further insight into the assembly of the metal centres in the cytosolic domain was gained from potentiometric investigations of zinc binding to synthetic peptides corresponding to N-terminal and C-terminal sequences of ZnT8 bearing the metal-coordinating ligands. Our work suggests the involvement of the C-terminal cysteines, which are part of the cytosolic domain, in a metal chelation and/or acquisition mechanism and, as now supported by the high-resolution structural work, provides the first example of metal-thiolate coordination chemistry in zinc transporters.

Adsorption under nanoconfinement: a theoretical-computational study revealing significant enhancement beyond the Langmuirian levels

The principal goal of this work is to predict characteristics unique to equilibrated adsorption of a small number of molecules on atomic sites located inside a closed nanoscale space. Compared to the thermodynamic limit of macroscopic systems, significantly enlarged adsorbate coverage under nanoconfinement constitutes a major finding of the modeling. Concomitantly, nanoconfined adsorbates are expected to exhibit extra thermal stability against desorption. These effects on adsorption are explored using canonical partition-functions as well as an original relationship between coverage variations and the Langmuir constant, both in the frameworks of the ideal gas and lattice-gas models. With reported DFT adsorption-energies as input, adsorption isotherms are derived numerically for H2 on Ti-doped graphene-like nanostructures. Remarkable deviations from the classical Langmuir isotherm are predicted for the first time, namely, system-size dependent enhanced H2 adsorbate coverage. The effects are computed also for CO2 inside MOF single-molecule traps, including their relationships to adsorption-energy, specific-heat and to coverage fluctuations. According to preliminary modeling, nanoconfinement effects are anticipated also for adsorption in nanopores undergoing molecular exchange with the external environment, and for impurity segregation in nanoparticle and nanocrystalline solids. The entropic origin of the nanoconfinement effect on equilibrium adsorption (NCEEA) is demonstrated analogously to the nanoconfinement effect on equilibrated chemical reactions studied by us previously. Besides unraveling some basic theoretical issues in physical nanochemistry, this study is expected to be pertinent to nanotechnological applications, such as gas storage and separation in nanoporous materials and other solid adsorbents.

A kinetic description of how interfaces accelerate reactions in micro-compartments

A kinetic expression is derived to explain how interfaces alter bulk chemical equilibria and accelerate reactions in micro-compartments. This description, aided by the development of a stochastic model, quantitatively predicts previous experimental observations of accelerated imine synthesis in micron-sized emulsions. The expression accounts for how reactant concentration and compartment size together lead to accelerated reaction rates under micro-confinement. These rates do not depend solely on concentration, but rather the fraction of total molecules in the compartment that are at the interface. Although there are ∼10⁷ to 10¹³ solute molecules in a typical micro-compartment, a kind of "stochasticity" appears when compartment size and reagent concentration yield nearly equal numbers of bulk and interfacial molecules. Although this is distinct from the stochasticity produced by nano-confinement, these results show how interfaces can govern chemical transformations in larger atmospheric, geologic and biological compartments.