Tomasz Kalwarczyk

Comparative analysis of viscosity of complex liquids and cytoplasm of mammalian cells at the nanoscale.

We present a scaling formula for size-dependent viscosity coefficients for proteins, polymers, and fluorescent dyes diffusing in complex liquids. The formula was used to analyze the mobilities of probes of different sizes in HeLa and Swiss 3T3 mammalian cells. This analysis unveils in the cytoplasm two length scales: (i) the correlation length ξ (approximately 5 nm in HeLa and 7 nm in Swiss 3T3 cells) and (ii) the limiting length scale that marks the crossover between nano- and macroscale viscosity (approximately 86 nm in HeLa and 30 nm in Swiss 3T3 cells). During motion, probes smaller than ξ experienced matrix viscosity: η(matrix) ≈ 2.0 mPa·s for HeLa and 0.88 mPa·s for Swiss 3T3 cells. Probes much larger than the limiting length scale experienced macroscopic viscosity, η(macro) ≈ 4.4 × 10(-2) and 2.4 × 10(-2) Pa·s for HeLa and Swiss 3T3 cells, respectively. Our results are persistent for the lengths scales from 0.14 nm to a few hundred nanometers.

Biologistics--diffusion coefficients for complete proteome of Escherichia coli.

Motivation: Biologistics provides data for quantitative analysis of transport (diffusion) processes and their spatio-temporal correlations in cells. Mobility of proteins is one of the few parameters necessary to describe reaction rates for gene regulation. Although understanding of diffusion-limited biochemical reactions in vivo requires mobility data for the largest possible number of proteins in their native forms, currently, there is no database that would contain the complete information about the diffusion coefficients (DCs) of proteins in a given cell type. Results: We demonstrate a method for the determination of in vivo DCs for any molecule—regardless of its molecular weight, size and structure—in any type of cell. We exemplify the method with the database of in vivo DC for all proteins (4302 records) from the proteome of K12 strain of Escherichia coli, together with examples of DC of amino acids, sugars, RNA and DNA. The database follows from the scale-dependent viscosity reference curve (sdVRC). Construction of sdVRC for prokaryotic or eukaryotic cell requires ~20 in vivo measurements using techniques such as fluorescence correlation spectroscopy (FCS), fluorescence recovery after photobleaching (FRAP), nuclear magnetic resonance (NMR) or particle tracking. The shape of the sdVRC would be different for each organism, but the mathematical form of the curve remains the same. The presented method has a high predictive power, as the measurements of DCs of several inert, properly chosen probes in a single cell type allows to determine the DCs of thousands of proteins. Additionally, obtained mobility data allow quantitative study of biochemical interactions in vivo. Contact: rholyst@ichf.edu.pl Supplementary information: Supplementary data are available at Bioinformatics Online.

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.

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.

Crossover regime for the diffusion of nanoparticles in polyethylene glycol solutions: influence of the depletion layer

The viscosity in soft matter systems is a scale dependent quantity. In polymer solutions the viscosity of nanoprobes of size R approaches the macroscopic viscosity when R exceeds the radius of gyration of the polymer, Rg. The nano to macroviscosity crossover occurs for R ∼ Rg. Here we analyze diffusion in a polymer (polyethylene glycol) solution of nanoparticles in the crossover regime. We report a scale dependent diffusion coefficient in this regime due to non-uniform viscosity in the depletion layer around particles. The phenomenological scaling of the slow diffusion coefficient as a function of probe size is compared to the same scaling for macroscopic viscosity as a function of polymer size.

Reverse Vesicles from a Salt-Free Catanionic Surfactant System: A Confocal Fluorescence Microscopy Study

We give a detailed confocal fluorescence microscopy study on reverse vesicles from a salt-free catanionic surfactant system. When tetradecyltrimethylammonium laurate (TTAL) and lauric acid (LA) are mixed in cyclohexane at the presence of a small amount of water, stable reverse vesicular phases form spontaneously. The reverse vesicular phases can be easily labeled with dyes of varying molecular size and hydrophobicity while the dyes are nearly insoluble in cyclohexane without reverse vesicles. This indicates the reverse vesicular phases can be good candidates to host guest molecules. With the help of a fluorescence microscope combined a confocal method, the features of these interesting reverse supramolecular self-assemblies were revealed for the first time. Because of the absence of electrostatic repulsions and hydration forces between adjacent vesicles, the reverse vesicles have a strong propensity to aggregate with each other and form three-dimensional clusters. The size distributions of both individual reverse vesicles and clusters are polydisperse. Huge multilamellar reverse vesicles with closely stacked thick walls (giant reverse onions) were observed. Besides the spherical reverse vesicles and onions, other supramolecular structures such as tubes have also been detected and structural evolutions between different structures were noticed. These interesting supramolecular self-assemblies form in a nonpolar organic solvent may serve as ideal micro- or nanoreaction centers for biological reactions and synthesis of inorganic nanomaterials.

Formation and structure of PEI/DNA complexes: quantitative analysis

Controlled formation of gene delivery complexes (DNA and a vector, usually a cationic polymer) is one of the key challenges in developing efficient gene delivery systems. The researchers focused their procedures on the ratio of vector to DNA, neglecting the influence of concentration on the complex formation process. In this study we show, by studying the association of polyethylenimine (PEI) and 66-base pair (bp) DNA fragments, that the concentration of the gene delivery system greatly influences the formation of PEI/DNA complexes even at a fixed PEI/DNA ratio. We find that the charge and the size of PEI/DNA complexes are increasing functions of their concentration even in a highly dilute regime of concentrations. The number of PEI/DNA molecules in a complex was calculated from the measured charge and electrophoretic mobility. We established a model, on the basis of Smoluchowski theory, to explain the relation between the concentration and the size of PEI/DNA complexes. We analyzed the structure of the complexes and found out that a large proportion of space in the PEI/DNA complexes is occupied by the solvent. This study indicates that the influence of concentration should be seriously considered in gene delivery studies, since large PEI/DNA complexes can be prepared by scaling up their concentration simultaneously without increasing the dosage of PEI.

The effect of macromolecular crowding on mobility of biomolecules, association kinetics, and gene expression in living cells

We discuss a quantitative influence of macromolecular crowding on biological processes: motion, bimolecular reactions, and gene expression in prokaryotic and eukaryotic cells. We present scaling laws relating diffusion coefficient of an object moving in a cytoplasm of cells to a size of this object and degree of crowding. Such description leads to the notion of the length scale dependent viscosity characteristic for all living cells. We present an application of the length-scale dependent viscosity model to the description of motion in the cytoplasm of both eukaryotic and prokaryotic living cells. We compare the model with all recent data on diffusion of nanoscopic objects in HeLa, and E. coli cells. Additionally a description of the mobility of molecules in cell nucleus is presented. Finally we discuss the influence of crowding on the bimolecular association rates and gene expression in living cells.

Manipulation of multiple-responsive fluorescent supramolecular materials based on the inclusion complexation of cyclodextrins with Tyloxapol

A fluorescent supramolecular hydrogel was prepared by α-cyclodextrin (α-CD) and Tyloxapol, which can be considered as an oligomer of the nonionic surfactant polyoxyethylene tert-octylphenyl ether (Triton X-100, TX-100) with a polymerization degree below 7. For comparison, both Tyloxapol and TX-100 were selected to form hydrogels with α-CD to get more information about the interaction between different types of surfactants and cyclodextrin. These hydrogels have been thoroughly characterized using various techniques including phase behavior observation, transmission electron microscopy (TEM), field emission scanning electron microscopy (FE-SEM), fluorescence spectra, fluorescence microscopy observations, Fourier transform infrared (FT-IR) spectroscopy, 1H NMR, 2D 1H-1H ROESY NMR, small-angle X-ray scattering (SAXS), X-ray diffraction (XRD) and rheological measurements. The hydrogels of α-CD/Tyloxapol are responsive to external stimuli including temperature, pH and guest molecules, and present gelation-induced quenching fluorescence emission properties. The reason for this phenomenon may be that Tyloxapol molecules come into the cavity of α-CD and form the inclusion complexes. Due to the high electron density of the narrow cavity of α-CD, it induces the shift of the electron on the benzene ring which can weaken the π–π interaction and lead to the fluorescence quenching. Moreover, the hydrogel formed by α-CD/Tyloxapol is highly responsive to the formaldehyde (HCHO). The addition of a small amount of HCHO can induce a gel-to-sol transition. Interestingly, once the gel transforms into solution, it becomes fluorescent. This makes the α-CD/Tyloxapol hydrogel a promising candidate for HCHO detection and removal in home furnishings to reduce indoor environmental pollutants.

Influence of nano-viscosity and depletion interactions on cleavage of DNA by enzymes in glycerol and poly(ethylene glycol) solutions: qualitative analysis

Biochemical reactions in living systems take place in an environment crowded by various macromolecules and ligands. Therefore experimental data obtained in buffer do not reflect in vivo conditions. We have used glycerol, poly(ethylene glycol) (PEG) 6000 and PEG 8 M solutions to investigate the influence of the crowded environment on cleavage of plasmid DNA by restriction enzyme HindIII. PEG 6000 solution can effectively slow down the cleavage process. However, neither PEG 8 M solution of the same viscosity as PEG 6000 solution nor glycerol solution of the same concentration as PEG 6000 solution slows the cleavage of DNA appreciably. The viscosity experienced by the biomolecules (here called nano-viscosity) and aggregation induced by the depletion interactions between DNA molecules in polymer solution (PEG 6000) are two factors responsible for slow cleavage of DNA. We have ruled out the change of pH and denaturation of HindIII as possible sources for the effect.