Living Cell as a Self-Synchronized Chemical Reactor.

Thermal fluctuations power all processes inside living cells. Therefore, these processes are inherently random. However, myriad multistep chemical reactions act in concerto inside a cell, finally leading to this chemical reactor's self-replication. We speculate that an underlying mechanism in nature must exist that allows all of these reactions to synchronize at multiple time and length scales, overcoming in this way the random nature of any single process in a cell. This Perspective discusses what type of research is needed to understand this undiscovered synchronization law.

Influence of molecular rebinding on the reaction rate of complex formation.

We simulated Brownian diffusion and reaction-diffusion processes to study the influence of molecular rebinding on the reaction rates of bimolecular reactions. We found that the number of rebinding events, Nreb, is proportional to the target's size and inversely proportional to the diffusion coefficient D and simulation time-step Δt. We found the proportionality constant close to π-1/2. We confirmed that Nreb is defined as a ratio of the activation-limited rate constant ka to the diffusion-limited rate constant, kD. We provide the formula describing the reactivity coefficient κ, modelling the transient-native complex transition for the activation-controlled reaction rates. We show that κ is proportional to (D/Δt)1/2. Finally, we apply our rebinding-including reaction rate model to the real reactions of photoacid dissociation and protein association. Based on literature data for both types of reactions, we found the Δt time-scale. We show that for the photodissociation of a proton, the Δt is equal to 171 ± 18 fs and the average number of rebinding events is approximately equal to 40. For proteins, Δt is of the order of 100 ps with around 20 rebinding events. In both cases the timescale is similar to the timescale of fluctuation of the solvent molecules surrounding the reactants; vibrations and bending in the case of photoacid dissociation and diffusional motion for proteins.

Two Intercalation Mechanisms of Oxazole Yellow Dimer (YOYO-1) into DNA.

The oxazole yellow dye, YOYO-1 (a symmetric homodimer), is a commonly used molecule for staining DNA. We applied the brightness analysis to study the intercalation of YOYO-1 into the DNA. We distinguished two binding modes of the dye to dsDNA: mono-intercalation and bis-intercalation. Bis-intercalation consists of two consecutive mono-intercalation steps, characterised by two distinct equilibrium constants (with the average number of base pair per binding site equals 3.5): K1=3.36±0.43×107M-1 and K2=1.90±0.61×105M-1, respectively. Mono-intercalation dominates at high concentrations of YOYO-1. Bis-intercalation occurs at low concentrations.

Macroscopic Viscosity of Polymer Solutions from the Nanoscale Analysis.

The effective viscosity in polymer solutions probed by diffusion of nanoparticles depends on their size. It is a well-defined function of the probe size, the radius of gyration, mesh size (correlation length), activation energy, and its parameters. As the nanoparticle's size exceeds the radius of gyration of polymer coils, the effective viscosity approaches its macroscopic limiting value. Here, we apply the equation for effective viscosity in the macroscopic limit to the following polymer solutions: hydroxypropyl cellulose (HPC) in water, polymethylmethacrylate (PMMA) in toluene, and polyacrylonitrile (PAN) in dimethyl sulfoxide (DMSO). We compare them with previous data for PEG/PEO in water and PDMS in ethyl acetate. We determine polymer parameters from the measurements of the macroscopic viscosity in a wide range of average polymer molecular weights (24-300 kg/mol), temperatures (283-303 K), and concentrations (0.005-1.000 g/cm3). In addition, the polydispersity of polymers is taken into account in the appropriate molecular weight averaging functions. We provide the model applicable for the study of nanoscale probe diffusion in polymer solutions and macroscopic characterization of different polymer materials via rheological measurements.

Quantifying Nanoscale Viscosity and Structures of Living Cells Nucleus from Mobility Measurements.

Understanding the mobility of nano-objects in the eukaryotic cell nucleus, at multiple length-scales, is essential for dissecting nuclear structure-function relationships both in space and in time. Here, we demonstrate, using single-molecule fluorescent correlation spectroscopies, that motion of inert probes (proteins, polymers, or nanoparticles) with diameters ranging from 2.6 to 150 nm is mostly unobstructed in a nucleus. Supported by the analysis of electron tomography images, these results advocate the ∼150 nm-wide interchromosomal channels filled with the aqueous diluted protein solution. The nucleus is percolated by these channels to allow various cargos to migrate freely at the nanoscale. We determined the volume of interchromosomal channels in the HeLa cell nucleus to 237 ± 61 fL, which constitutes 34% of the cell nucleus volume. The volume fraction of mobile proteins in channels equals 16% ± 4%, and the concentration is 1 mM.

Transport of nanoprobes in multicellular spheroids.

The efficient delivery of drugs to cells depends on their diffusion through the extracellular matrix (ECM) of tissues. Here we present a study on the diffusion of nanoprobes of radius from 1 nm to over 100 nm in the ECM of spheroids of three cell types (HeLa, MCF-7 and fibroblasts). We quantified the nanoparticle transport in the spheroids' proliferating zone. We determined the size-dependent viscosity of the ECM. We revealed that nanoobjects up to 10 nm in radius exhibited unobstructed diffusion in the ECM, regardless of the spheroid type. The presented length-scale dependent viscosity profiles for spheroids pave the way for advanced modelling of drug administration through tissues.

Nanoscale Viscosity of Cytoplasm Is Conserved in Human Cell Lines.

Metabolic reactions in living cells are limited by diffusion of reagents in the cytoplasm. Any attempt to quantify the kinetics of biochemical reactions in the cytosol should be preceded by careful measurements of the physical properties of the cellular interior. The cytoplasm is a complex, crowded fluid characterized by effective viscosity dependent on its structure at a nanoscopic length scale. In this work, we present and validate the model describing the cytoplasmic nanoviscosity, based on measurements in seven human cell lines, for nanoprobes ranging in diameters from 1 to 150 nm. Irrespective of cell line origin (epithelial-mesenchymal, cancerous-noncancerous, male-female, young-adult), we obtained a similar dependence of the viscosity on the size of the nanoprobes, with characteristic length-scales of 20 ± 11 nm (hydrodynamic radii of major crowders in the cytoplasm) and 4.6 ± 0.7 nm (radii of intercrowder gaps). Moreover, we revealed that the cytoplasm behaves as a liquid for length scales smaller than 100 nm and as a physical gel for larger length scales.

Photoluminescent, Ferromagnetic, and Hydrophobic Sponges for Oil-Water Separation.

To find a facile way to produce a hydrophobic sponge that can effectively absorb oils is urgent to resolve the environmental pollution and ecological disaster caused by oil spillage. Here, alkylated carbon dots (C dots) were prepared from pyrolysis of a mixture of dodecylamine and citric acid followed by purification through silica gel column chromatography. Polyurethane sponge was modified by alkylated C dots by a simple dip-coating method, which endows the photoluminescent and hydrophobic sponge with good absorption capacities for various oils and nonpolar organic solvents with high recyclability. The water contact angle of the modified sponge can reach 138.8°. Interestingly, the sponge enables visual absorption under UV irradiation in the dark, which has not been achieved by other carbon-based adsorbents. The sponge was further made ferromagnetic by introducing alkylated Fe3O4 nanoparticles into its structure, which allowed controllable oil-water separation.

Self-Stabilized Giant Aggregates in Water from Room-Temperature Ionic Liquids with an Asymmetric Polar-Apolar-Polar Architecture.

We report the assembly of four imidazolium bromides, each of which bears a naphthyl on one side of the imidazolium cation and a branched alkyl chain on the other. This design creates a new type of amphiphilic ionic liquid with an apolar-polar-apolar structure and a low melting point (mp, <-20 °C), which has not been achieved by reported counterparts bearing linear alkyl chains. In solvent-free states, microphase segregation occurs where polar and apolar domains arrange bicontinuously as proved by molecular dynamics (MD) simulations. When dispersed in water, self-stabilized giant aggregates formed with ultrahigh colloidal stability (up to years). MD simulations provide clues of discrete bicontinuous phases within the giant aggregates. These newly discovered self-assemblies provide a heterogeneous reservoir that can accommodate guest molecules including the highly apolar fullerene C60, paving the way for a wide range of potential applications.

Analysis of Brightness of a Single Fluorophore for Quantitative Characterization of Biochemical Reactions.

Intrinsic molecular brightness (MB) is a number of emitted photons per second per molecule. When a substrate labeled by a fluorophore and a second unlabeled substrate form a complex in solution, the MB of the fluorophore changes. Here we use this change to determine the equilibrium constant (K) for the formation of the complex at pM concentrations. To illustrate this method, we used a reaction of DNA hybridization, where only one of the strands was fluorescently labeled. We determined K at the substrate concentrations from 80 pM to 30 nM. We validated this method against Förster resonance energy transfer (FRET). This method is much simpler than FRET as it requires only one fluorophore in the complex with a very small (a f̃ew percent) change in MB.

Diffusion and flow in complex liquids.

Thermal motion of particles and molecules in liquids underlies many chemical and biological processes. Liquids, especially in biology, are complex due to structure at multiple relevant length scales. While diffusion in homogeneous simple liquids is well understood through the Stokes-Einstein relation, this equation fails completely in describing diffusion in complex media. Modeling, understanding, engineering and controlling processes at the nanoscale, most importantly inside living cells, requires a theoretical framework for the description of viscous response to allow predictions of diffusion rates in complex fluids. Here we use a general framework with the viscosity η(k) described by a function of wave vector in reciprocal space. We introduce a formulation that allows one to relate the rotational and translational diffusion coefficients and determine the viscosity η(k) directly from experiments. We apply our theory to provide a database for rotational diffusion coefficients of proteins/protein complexes in the bacterium E. coli. We also provide a database for the diffusion coefficient of proteins sliding along major grooves of DNA in E. coli. These parameters allow predictions of rate constants for association of proteins. In addition to constituting a theoretical framework for description of diffusion of probes and viscosity in complex fluids, the formulation that we propose should decrease substantially the cost of numerical simulations of transport in complex media by replacing the simulation of individual crowding particles with a continuous medium characterized by a wave-length dependent viscosity η(k).

Determination of oligomerization state of Drp1 protein in living cells at nanomolar concentrations.

Biochemistry in living cells is an emerging field of science. Current quantitative bioassays are performed ex vivo, thus equilibrium constants and reaction rates of reactions occurring in human cells are still unknown. To address this issue, we present a non-invasive method to quantitatively characterize interactions (equilibrium constants, KD) directly within the cytosol of living cells. We reveal that cytosolic hydrodynamic drag depends exponentially on a probe's size, and provide a model for its determination for different protein sizes (1-70 nm). We analysed oligomerization of dynamin-related protein 1 (Drp1, wild type and mutants: K668E, G363D, C505A) in HeLa cells. We detected the coexistence of wt-Drp1 dimers and tetramers in cytosol, and determined that KD for tetramers was 0.7 ± 0.5 µM. Drp1 kinetics was modelled by independent simulations, giving computational results which matched experimental data. This robust method can be applied to in vivo determination of KD for other protein-protein complexes, or drug-target interactions.

Insight into the fission mechanism by quantitative characterization of Drp1 protein distribution in the living cell.

One of the main players in the process of mitochondrial fragmentation is dynamin-related protein 1 (Drp1), which assembles into a helical ring-like structure on the mitochondria and facilitates fission. The fission mechanism is still poorly understood and detailed information concerning oligomeric form of Drp1, its cellular distribution and the size of the fission complex is missing. To estimate oligomeric forms of Drp1 in the cytoplasm and on the mitochondria, we performed a quantitative analysis of Drp1 diffusion and distribution in gene-edited HeLa cell lines. This paper provides an insight into the fission mechanism based on the quantitative description of Drp1 cellular distribution. We found that approximately half of the endogenous GFP-Drp1 pool remained in the cytoplasm, predominantly in a tetrameric form, at a concentration of 28 ± 9 nM. The Drp1 mitochondrial pool included many different oligomeric states with equilibrium distributions that could be described by isodesmic supramolecular polymerization with a Kd of 31 ± 10 nM. We estimated the average number of Drp1 molecules forming the functional fission complex to be approximately 100, representing not more than 14% of all Drp1 oligomers. We showed that the upregulated fission induced by niclosamide is accompanied by an increase in the number of large Drp1 oligomers.

Apparent Anomalous Diffusion in the Cytoplasm of Human Cells: The Effect of Probes' Polydispersity.

This work, based on in vivo and in vitro measurements, as well as in silico simulations, provides a consistent analysis of diffusion of polydisperse nanoparticles in the cytoplasm of living cells. Using the example of fluorescence correlation spectroscopy (FCS), we show the effect of polydispersity of probes on the experimental results. Although individual probes undergo normal diffusion, in the ensemble of probes, an effective broadening of the distribution of diffusion times occurs-similar to anomalous diffusion. We introduced fluorescently labeled dextrans into the cytoplasm of HeLa cells and found that cytoplasmic hydrodynamic drag, exponentially dependent on probe size, extraordinarily broadens the distribution of diffusion times across the focal volume. As a result, the in vivo FCS data were effectively fitted with the anomalous subdiffusion model while for a monodisperse probe the normal diffusion model was most suitable. Diffusion time obtained from the anomalous diffusion model corresponds to a probe whose size is determined by the weight-average molecular weight of the polymer. The apparent anomaly exponent decreases with increasing polydispersity of the probes. Our results and methodology can be applied in intracellular studies of the mobility of nanoparticles, polymers, or oligomerizing proteins.

Motion of Molecular Probes and Viscosity Scaling in Polyelectrolyte Solutions at Physiological Ionic Strength.

We investigate transport properties of model polyelectrolyte systems at physiological ionic strength (0.154 M). Covering a broad range of flow length scales-from diffusion of molecular probes to macroscopic viscous flow-we establish a single, continuous function describing the scale dependent viscosity of high-salt polyelectrolyte solutions. The data are consistent with the model developed previously for electrically neutral polymers in a good solvent. The presented approach merges the power-law scaling concepts of de Gennes with the idea of exponential length scale dependence of effective viscosity in complex liquids. The result is a simple and applicable description of transport properties of high-salt polyelectrolyte solutions at all length scales, valid for motion of single molecules as well as macroscopic flow of the complex liquid.

How can macromolecular crowding inhibit biological reactions? The enhanced formation of DNA nanoparticles.

In contrast to the already known effect that macromolecular crowding usually promotes biological reactions, solutions of PEG 6k at high concentrations stop the cleavage of DNA by HindIII enzyme, due to the formation of DNA nanoparticles. We characterized the DNA nanoparticles and probed the prerequisites for their formation using multiple techniques such as fluorescence correlation spectroscopy, dynamic light scattering, fluorescence analytical ultracentrifugation etc. In >25% PEG 6k solution, macromolecular crowding promotes the formation of DNA nanoparticles with dimensions of several hundreds of nanometers. The formation of DNA nanoparticles is a fast and reversible process. Both plasmid DNA (2686 bp) and double-stranded/single-stranded DNA fragment (66 bp/nt) can form nanoparticles. We attribute the enhanced nanoparticle formation to the depletion effect of macromolecular crowding. This study presents our idea to enhance the formation of DNA nanoparticles by macromolecular crowding, providing the first step towards a final solution to efficient gene therapy.

Motion of nanoprobes in complex liquids within the framework of the length-scale dependent viscosity model.

This paper deals with the recent phenomenological model of the motion of nanoscopic objects (colloidal particles, proteins, nanoparticles, molecules) in complex liquids. We analysed motion in polymer, micellar, colloidal and protein solutions and the cytoplasm of living cells using the length-scale dependent viscosity model. Viscosity monotonically approaches macroscopic viscosity as the size of the object increases and thus gives a single, coherent picture of motion at the nano and macro scale. The model includes interparticle interactions (solvent-solute), temperature and the internal structure of a complex liquid. The depletion layer ubiquitously occurring in complex liquids is also incorporated into the model. We also discuss the biological aspects of crowding in terms of the length-scale dependent viscosity model.

Tracking structural transitions of bovine serum albumin in surfactant solutions by fluorescence correlation spectroscopy and fluorescence lifetime analysis.

The structural dynamics of proteins is crucial to their biological functions. A precise and convenient method to determine the structural changes of a protein is still urgently needed. Herein, we employ fluorescence correlation spectroscopy (FCS) to track the structural transition of bovine serum albumin (BSA) in low concentrated cationic (cetyltrimethylammonium chloride, CTAC), anionic (sodium dodecyl sulfate, SDS), and nonionic (pentaethylene glycol monododecyl ether, C12E5 and octaethylene glycol monododecyl ether, C12E8) surfactant solutions. BSA is labelled with the fluorescence dye called ATTO-488 (ATTO-BSA) to obtain steady fluorescence signals for measurements. We find that the diffusion coefficient of BSA decreases abruptly with the surfactant concentration in ionic surfactant solutions at concentrations below the critical micelle concentration (CMC), while it is constant in nonionic surfactant solutions. According to the Stokes-Sutherland-Einstein equation, the hydrodynamic radius of BSA in ionic surfactant solutions amounts to ∼6.5 nm, which is 1.7 times larger than in pure water or in nonionic surfactant solutions (3.9 nm). The interaction between BSA and ionic surfactant monomers is believed to cause the structural transition of BSA. We confirm this proposal by observing a sudden shift of the fluorescence lifetime of ATTO-BSA, from 2.3 ns to ∼3.0 ns, in ionic surfactant solutions at the concentration below CMC. No change in the fluorescence lifetime is detected in nonionic surfactant solutions. Moreover, by using FCS we are also able to identify whether the structural change of protein results from its self-aggregation or unfolding.

Length-scale dependent transport properties of colloidal and protein solutions for prediction of crystal nucleation rates.

We propose a scaling equation describing transport properties (diffusion and viscosity) in the solutions of colloidal particles. We apply the equation to 23 different systems including colloids and proteins differing in size (range of diameters: 4 nm to 1 µm), and volume fractions (10(-3)-0.56). In solutions under study colloids/proteins interact via steric, hydrodynamic, van der Waals and/or electrostatic interactions. We implement contribution of those interactions into the scaling law. Finally we use our scaling law together with the literature values of the barrier for nucleation to predict crystal nucleation rates of hard-sphere like colloids. The resulting crystal nucleation rates agree with existing experimental data.

Quantitative influence of macromolecular crowding on gene regulation kinetics.

We introduce macromolecular crowding quantitatively into the model for kinetics of gene regulation in Escherichia coli. We analyse and compute the specific-site searching time for 180 known transcription factors (TFs) regulating 1300 operons. The time is between 160 s (e.g. for SoxS Mw = 12.91 kDa) and 1550 s (e.g. for PepA6 of Mw = 329.28 kDa). Diffusion coefficients for one-dimensional sliding are between for large proteins up to for small monomers or dimers. Three-dimensional diffusion coefficients in the cytoplasm are 2 orders of magnitude larger than 1D sliding coefficients, nevertheless the sliding enhances the binding rates of TF to specific sites by 1-2 orders of magnitude. The latter effect is due to ubiquitous non-specific binding. We compare the model to experimental data for LacI repressor and find that non-specific binding of the protein to DNA is activation- and not diffusion-limited. We show that the target location rate by LacI repressor is optimized with respect to microscopic rate constant for association to non-specific sites on DNA. We analyse the effect of oligomerization of TFs and DNA looping effects on searching kinetics. We show that optimal searching strategy depends on TF abundance.