Rotational and translational diffusion of biomolecules in complex liquids and HeLa cells.

Diffusive motion accompanies many physical and biological processes. The Stokes-Sutherland-Einstein relation for the translational diffusion coefficient, DT, agrees with experiments done in simple fluids but fails for complex fluids. Moreover, the interdependence between DT and rotational diffusion coefficient, DR, also deviates in complex fluids from the classical relation of DT/DR = 4r2/3 known in simple fluids. Makuch et al. Soft Matter, 2020, 16, 114-124 presented a generalization of the classical translational and rotational diffusion theory for complex fluids. In this work, we empirically verify this model based on simultaneous translational and rotational diffusion measurements. We use fluorescently stained cowpea chlorotic mottle virus (CCMV) particles as monodisperse probes and aqueous polyethylene glycol (PEG) solutions as a model complex fluid. The theory and experimental data obtained from fluorescence correlation spectroscopy (FCS) measurements agreed. Finally, we used the same model and analyzed the diffusion of Yo-Pro-1 stained large ribosomal subunits (LSU) in the cytoplasm and nucleus of living HeLa cells.

Steady-state thermodynamics of a system with heat and mass flow coupling.

Equilibrium thermodynamics describes the energy exchange of a body with its environment. Here, we describe the global energy exchange of an ideal gas in the Coutte flow in a thermodynamic-like manner. We derive a fundamental relation between internal energy as a function of parameters of state. We analyze a non-equilibrium transition in the system and postulate the extremum principle, which determines stable steady states in the system. The steady-state thermodynamic framework resembles equilibrium thermodynamics.

Fundamental Relation for the Ideal Gas in the Gravitational Field and Heat Flow.

We formulate the first law of global thermodynamics for stationary states of the ideal gas in the gravitational field subjected to heat flow. We map the non-uniform system (described by profiles of the density and temperature) onto the uniform one and show that the total internal energy U(S*,V,N,L,M*) is the function of the following parameters of state: the non-equilibrium entropy S*, volume V, number of particles, N, height of the column L along the gravitational force, and renormalized mass of a particle M*. Each parameter corresponds to a different way of energy exchange with the environment. The parameter M* changes internal energy due to the shift of the centre of mass induced by the heat flux. We give analytical expressions for the non-equilibrium entropy S* and effective mass M*. When the heat flow goes to zero, S* approaches equilibrium entropy. Additionally, when the gravitational field vanishes, our fundamental relation reduces to the fundamental relation at equilibrium.

Parameters of State in the Global Thermodynamics of Binary Ideal Gas Mixtures in a Stationary Heat Flow.

In this paper, we formulate the first law of global thermodynamics for stationary states of the binary ideal gas mixture subjected to heat flow. We map the non-uniform system onto the uniform one and show that the internal energy U(S*,V,N1,N2,f1*,f2*) is the function of the following parameters of state: a non-equilibrium entropy S*, volume V, number of particles of the first component, N1, number of particles of the second component N2 and the renormalized degrees of freedom. The parameters f1*,f2*, N1,N2 satisfy the relation (N1/(N1+N2))f1*/f1+(N2/(N1+N2))f2*/f2=1 (f1 and f2 are the degrees of freedom for each component respectively). Thus, only 5 parameters of state describe the non-equilibrium state of the binary mixture in the heat flow. We calculate the non-equilibrium entropy S* and new thermodynamic parameters of state f1*,f2* explicitly. The latter are responsible for heat generation due to the concentration gradients. The theory reduces to equilibrium thermodynamics, when the heat flux goes to zero. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.

Fundamental Relation for Gas of Interacting Particles in a Heat Flow.

There is a long-standing question of whether it is possible to extend the formalism of equilibrium thermodynamics to the case of nonequilibrium systems in steady-states. We have made such an extension for an ideal gas in a heat flow. Here, we investigated whether such a description exists for the system with interactions: the van der Waals gas in a heat flow. We introduced a steady-state fundamental relation and the parameters of state, each associated with a single way of changing energy. The first law of nonequilibrium thermodynamics follows from these parameters. The internal energy U for the nonequilibrium states has the same form as in equilibrium thermodynamics. For the van der Waals gas, U(S*,V,N,a*,b*) is a function of only five parameters of state (irrespective of the number of parameters characterizing the boundary conditions): the effective entropy S*, volume V, number of particles N, and rescaled van der Waals parameters a*, b*. The state parameters, a*, b*, together with S*, determine the net heat exchange with the environment. The net heat differential does not have an integrating factor. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.

Thermodynamics of stationary states of the ideal gas in a heat flow.

There is a long-standing question as to whether and to what extent it is possible to describe nonequilibrium systems in stationary states in terms of global thermodynamic functions. The positive answers have been obtained only for isothermal systems or systems with small temperature differences. We formulate thermodynamics of the stationary states of the ideal gas subjected to heat flow in the form of the zeroth, first, and second law. Surprisingly, the formal structure of steady state thermodynamics is the same as in equilibrium thermodynamics. We rigorously show that U satisfies the following equation dU = T*dS* - pdV for a constant number of particles, irrespective of the shape of the container, boundary conditions, the size of the system, or the mode of heat transfer into the system. We calculate S* and T* explicitly. The theory selects stable nonequilibrium steady states in a multistable system of ideal gas subjected to volumetric heating. It reduces to equilibrium thermodynamics when heat flux goes to zero.

Quantitative analysis of biochemical processes in living cells at a single-molecule level: a case of olaparib-PARP1 (DNA repair protein) interactions.

Quantitative description of biochemical processes inside living cells and at single-molecule levels remains a challenge at the forefront of modern instrumentation and spectroscopy. This paper demonstrates such single-cell, single-molecule analyses performed to study the mechanism of action of olaparib - an up-to-date, FDA-approved drug for germline-BRCA mutated metastatic breast cancer. We characterized complexes formed with PARPi-FL - fluorescent analog of olaparib in vitro and in cancer cells using the advanced fluorescent-based method: Fluorescence Correlation Spectroscopy (FCS) combined with a length-scale dependent cytoplasmic/nucleoplasmic viscosity model. We determined in vitro olaparib-PARP1 equilibrium constant (6.06 × 108 mol L-1). In the cell nucleus, we distinguished three states of olaparib: freely diffusing drug (24%), olaparib-PARP1 complex (50%), and olaparib-PARP1-RNA complex (26%). We show olaparib accumulation in 3D spheroids, where intracellular concentration is twofold higher than in 2D cells. Moreover, olaparib concentration was tenfold higher (506 nmol L-1vs. 57 nmol L-1) in cervical cancer (BRCA1 high abundance) than in breast cancer cells (BRCA1 low abundance) but with a lower toxic effect. Thus we confirmed that the amount of BRCA1 protein in the cells is a better predictor of the therapeutic effect of olaparib than its penetration into cancer tissue. Our single-molecule and single-cell approach give a new perspective of drug action in living cells. FCS provides a detailed in vivo insight, valuable in drug development and targeting.

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.

Ions in an AC Electric Field: Strong Long-Range Repulsion between Oppositely Charged Surfaces.

Two oppositely charged surfaces separated by a dielectric medium attract each other. In contrast we observe a strong repulsion between two plates of a capacitor that is filled with an aqueous electrolyte upon application of an alternating potential difference between the plates. This long-range force increases with the ratio of diffusion coefficients of the ions in the medium and reaches a steady state after a few minutes, which is much larger than the millisecond timescale of diffusion across the narrow gap. The repulsive force, an order of magnitude stronger than the electrostatic attraction observed in the same setup in air, results from the increase in osmotic pressure as a consequence of the field-induced excess of cations and anions due to lateral transport from adjacent reservoirs.

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).

Single-molecule brightness analysis for the determination of anticancer drug interactions with DNA.

Anthracyclines are one of the most studied anticancer drugs approved for medical treatment. The equilibrium constant (K) of the reaction between these drugs with DNA in both in vitro and in vivo experiments lacks consensus. The K values vary from 104 up to 108 M-1, which suggest a 1000-fold error in determining the effective concentration needed to form the drug-DNA complex. Until 2014, only one study by García [J. Phys. Chem. B, 2014, 118, 1288-1295] showed that the binding of anthracycline representative doxorubicin occurs in two reactions. We support this result by brightness analysis at a single molecular level for the four most common anthracyclines: doxorubicin, daunorubicin, epirubicin, and idarubicin.

Joint effect of surfactants and cephalexin on the formation of Escherichia coli filament.

Both antibiotics and surfactants commonly exist in natural environment and have generated great concerns due to their biological influence on the ecosystem. A major concern lies in the capacity of antibiotics to induce bacterial filaments formation, which has potential health risks. However, their joint effect is not clear so far. Here, we studied the joint effect of cephalexin (Cex), a typical antibiotic, and differently charged surfactants on the formation of E. coli filaments. Three kinds of surfactants characterized by different charges were used: cationic surfactant (CTAB), anionic surfactant (SDS) and nonionic surfactant (Tween). Data showed that Cex alone caused the formation of E. coli filaments, elongating their maximum profile from ca. 2 µm (a single E. coli cell) to tens of micrometers (an E. coli filament). A joint use of surfactants with Cex could produce even longer E. coli filaments, elongating the maximum length of the bacteria to larger than 100 µm. The capacity order of different surfactants under their optimum concentrations to produce elongated E. coli filaments was Tween > SDS > CTAB. The E. coli filaments were characterized with a normal DNA distribution and a good cell membrane integrity. We measured the stiffness of bacterial cell wall by atomic force microscopy and correlated the elongation capacity of the E. coli filaments to the stiffness of cell wall. Zeta potential measurement indicated that inserting into or being bound to the cell surface in a large quantity was tested not to be the major way that surfactants interacted with bacteria.

Storage of Energy in Constrained Non-Equilibrium Systems.

We study a quantity T defined as the energy U, stored in non-equilibrium steady states (NESS) over its value in equilibrium U 0 , Δ U = U - U 0 divided by the heat flow J U going out of the system. A recent study suggests that T is minimized in steady states (Phys.Rev.E.99, 042118 (2019)). We evaluate this hypothesis using an ideal gas system with three methods of energy delivery: from a uniformly distributed energy source, from an external heat flow through the surface, and from an external matter flow. By introducing internal constraints into the system, we determine T with and without constraints and find that T is the smallest for unconstrained NESS. We find that the form of the internal energy in the studied NESS follows U = U 0 ∗ f ( J U ) . In this context, we discuss natural variables for NESS, define the embedded energy (an analog of Helmholtz free energy for NESS), and provide its interpretation.

Kinetics and equilibrium constants of oligonucleotides at low concentrations. Hybridization and melting study.

Although DNA hybridization/melting is one of the most important biochemical reactions, the non-trivial kinetics of the process is not yet fully understood. In this work, we use Förster resonance energy transfer (FRET) to investigate the influence of temperature, ionic strength, and oligonucleotide length on the kinetic and equilibrium constants of DNA oligonucleotide binding and dissociation. We show that at low reagent concentrations and ionic strength, the time needed to establish equilibrium between single and double strand forms may be of the order of days, even for simple oligonucleotides of a length of 20 base pairs or less. We also identify and discuss the possible artifacts related to fluorescence-based experiments conducted in extremely dilute solutions. The results should prove useful for the judicious design of technologies based on DNA-matching, including sensors, DNA multiplication, sequencing, and gene manipulation.

Fluorescence correlation spectroscopy for multiple-site equilibrium binding: a case of doxorubicin-DNA interaction.

Quantitative description of the interaction between doxorubicin (DOX), a broadly used anticancer drug, and DNA is the key to understand the action mechanism and side effects of its clinical use. However, the reported equilibrium constants of DOX-DNA interaction obtained using a range of different analytical methods vary even by several orders of magnitude. Herein, we propose a novel application of a single-molecule technique - fluorescence correlation spectroscopy (FCS) - to probe the interaction between DOX and two types of DNA (pUC19 and calf thymus DNA), taking advantage of intrinsic self-fluorescence of DOX. We provide an analytical formula for autocorrelation analysis to determine the equilibrium constant of DOX-DNA complex-formation, where binding of multiple DOX molecules to a DNA chain is included in the reaction-diffusion model. Our FCS-based method not only quantitatively revealed the values of equilibrium constant, but also implied that the stability of DOX-DNA complex is related to the types of base pair rather than the length or structure of the DNA. This work opens a promising pathway toward quantitative determination of molecular interactions in complex systems such as living cells or organisms at single-molecule level.

Propagation of Oscillating Chemical Signals through Reaction Networks.

Akin to electronic systems that can tune to and process signals of select frequencies, systems/networks of chemical reactions also "propagate" time-varying concentration inputs in a frequency-dependent manner. Whereas signals of low frequencies are transmitted, higher frequency inputs are dampened and converted into steady-concentration outputs. Such behavior is observed in both idealized reaction chains as well as realistic signaling cascades, in the latter case explaining the experimentally observed responses of such cascades to input calcium oscillations. These and other results are supported by numerical simulations within the freely available Kinetix web application we developed to study chemical systems of arbitrary architectures, reaction kinetics, and boundary conditions.

Bacteriophage-Based Bioconjugates as a Flow Cytometry Probe for Fast Bacteria Detection.

Robust detection of bacteria can significantly reduce risks of nosocomial infections, which are a serious problem even in developed countries (4.1 million cases each year in Europe). Here we demonstrate utilization of novel multifunctional bioconjugates as specific probes for bacteria detection. Bifunctional magnetic-fluorescent microparticles are coupled with bacteriophages. The T4 bacteriophage, due to its natural affinity to bacterial receptors, namely, OmpC and LPS, enables specific and efficient detection of Escherichia coli bacteria. Prepared probes are cheap, accessible (even in nonbiological laboratories), as well as versatile and easily tunable for different bacteria species. The magnetic properties of the bioconjugates facilitate the separation of captured target bacteria from other components of complex samples and other bacteria strains. Fluorescence enables simple analysis. We chose flow cytometry as the detection method as it is fast and widely used for biotests. The capture efficiency of the prepared bioconjugates is close to 100% in the range of bacteria concentrations from tens to around 105 CFU/mL. The limit of detection is restricted by flow cytometry capabilities and in our case was around 104 CFU/mL.

Evaporation of liquid droplets of nano- and micro-meter size as a function of molecular mass and intermolecular interactions: experiments and molecular dynamics simulations.

Transport of heat to the surface of a liquid is a limiting step in the evaporation of liquids into an inert gas. Molecular dynamics (MD) simulations of a two component Lennard-Jones (LJ) fluid revealed two modes of energy transport from a vapour to an interface of an evaporating droplet of liquid. Heat is transported according to the equation of temperature diffusion, far from the droplet of radius R. The heat flux, in this region, is proportional to temperature gradient and heat conductivity in the vapour. However at some distance from the interface, Aλ, (where λ is the mean free path in the gas), the temperature has a discontinuity and heat is transported ballistically i.e. by direct individual collisions of gas molecules with the interface. This ballistic transport reduces the heat flux (and consequently the mass flux) by the factor R/(R + Aλ) in comparison to the flux obtained from temperature diffusion. Thus it slows down the evaporation of droplets of sizes R ∼ Aλ and smaller (practically for sizes from 103 nm down to 1 nm). We analyzed parameter A as a function of interactions between molecules and their masses. The rescaled parameter, A(kBTb/ε11)1/2, is a linear function of the ratio of the molecular mass of the liquid molecules to the molecular mass of the gas molecules, m1/m2 (for a series of chemically similar compounds). Here ε11 is the interaction parameter between molecules in the liquid (proportional to the enthalpy of evaporation) and Tb is the temperature of the gas in the bulk. We tested the predictions of MD simulations in experiments performed on droplets of ethylene glycol, diethylene glycol, triethylene glycol and tetraethylene glycol. They were suspended in an electrodynamic trap and evaporated into dry nitrogen gas. A changes from ∼1 (for ethylene glycol) to approximately 10 (for tetraethylene glycol) and has the same dependence on molecular parameters as obtained for the LJ fluid in MD simulations. The value of x = A(kBTb/ε11)1/2 is of the order of 1 (for water x = 1.8, glycerol x = 1, ethylene glycol x = 0.4, tetraethylene glycol x = 2.1 evaporating into dry nitrogen at room temperature and for Lennard-Jones fluids x = 2 for m1/m2 = 1 and low temperature).