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.

Analytical Form of the Fluorescence Correlation Spectroscopy Autocorrelation Function in Chemically Reactive Systems.

Fluorescence correlation spectroscopy (FCS) applied to chemically reactive systems provides information about chemical reaction equilibrium constants and diffusion coefficients of reactants. These physical quantities are determined from the FCS-measured autocorrelation function, G(t), as a function of time, t. In most of the studied cases, the analytical form of G(t) is well-known for reactions that are much faster than the diffusion time of reactants across the focal volume probed by FCS or when they are much slower than the diffusion time. Here, we develop an analytical form of G(t) for reactions occurring at an intermediate time scale comparable to the diffusion time. G(t) depends on the reaction rates in such reactions. We focus on reversibly binding a fluorescently labeled small molecule to a macromolecule in a diluted solution in thermodynamic equilibrium. Our approach allows the analysis of FCS data over a wide range of diffusion coefficients, reaction rate constants, and brightness levels of fluorescent labels. Our G(t) is valid even when the fluorescent label changes its brightness upon binding. The easy-to-implement analytical form of the autocorrelation function greatly helps experimentalists study chemical reactions, determining the equilibrium constants of reactions and the reaction rates.

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.

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 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.

Comment on "Fluorimetric sensing of ATP in water by an imidazolium hydrazone based sensor" by S. Farshbaf and P. Anzenbacher Jr., Chem. Commun., 2019, 55, 1770.

In the paper, "Fluorimetric sensing of ATP in water by an imidazolium hydrazone based sensor," Farshbaf and Anzenbacher presented the application of bisantrene as a fluorescent ATP sensor in organic-inorganic mixtures of solvents. Encouraged by the results presented in the parent study, we aimed to apply this strategy for physiologically relevant water-based buffers and - preferably - intracellular application. Here we present the results of our investigations and point to the limitations of bisantrene applications in vivo as the ATP sensor.

Heteroaggregation of virions and microplastics reduces the number of active bacteriophages in aqueous environments.

The objective of this study is to explore the effects of microplastics on the viability of the bacteriophages in an aqueous environment. Bacteriophages (phages), that is, viruses of bacteria, are essential in homeostasis. It is estimated that phages cause up to 40% of the death of all bacteria daily. Any factor affecting phage activity is vital for the whole food chain and the ecology of numerous niches. We hypothesize that the number of active phages decreases due to the virions' adsorption on microplastic particles or by the released leachables from additives used in the production of plastic, for example, stabilizers, plasticizers, colorants, and reinforcements. We exposed three diverse phages, namely, T4 (tailed), MS2 (icosahedral), and M13 (filamentous), to 1 mg/mL suspension of 12 industrial-grade plastics [acrylonitrile butadiene styrene, high-impact polystyrene, poly-ε-caproamide, polycarbonate, polyethylene, polyethylene terephthalate, poly(methyl methacrylate), polypropylene, polystyrene, polytetrafluoroethylene, polyurethane, and polyvinyl chloride] shredded to obtain microparticles of radius ranging from 2 to 50 µm. The effect of leachables was measured upon exposure of phages not to particles themselves but to the buffer preincubated with microplastics. A double-overlay plaque counting method was used to assess phage titers. We employed a classical linear regression model to verify which physicochemical parameters (65 variables were tested) govern the decrease of phage titers. The key finding is that adsorption mechanisms result in up to complete scavenging of virions, whereas leachables deactivate up to 50% of phages. This study reveals microplastic pollution's plausible and unforeseen ecotoxicological effect causing phage deactivation. Moreover, phage transmission through adsorption can alter the balance of the food chain in the new environment. The effect depends mainly on the zeta potentials of the polymers and the phage type.

Cellular Uptake of Bevacizumab in Cervical and Breast Cancer Cells Revealed by Single-Molecule Spectroscopy.

Bevacizumab is a biological drug that is now extensively studied in clinics against various types of cancer. Although bevacizumab's action is preferably extracellular, there are reports suggesting its internalization into cancer cells, consequently decreasing its therapeutic potential. Here we are solving this issue by applying fluorescence correlation spectroscopy in living cells. We tracked single molecules of fluorescent bevacizumab in MDA-MB-231 and HeLa cells and proved that mobility measurements bring significant added value to standard imaging techniques. We confirmed the presence of the drug in intracellular vesicles. Additionally, we explicitly excluded the presence of a free cytosolic fraction of bevacizumab in both studied cell types. Extracellular and intracellular concentrations of the drug were measured, giving a partition coefficient on the order of 10-5, comparable with the spontaneous uptake of biologically inert nanoparticles. Our work presents how techniques and models developed for physics can answer biological questions.

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.

Effective screening of Coulomb repulsions in water accelerates reactions of like-charged compounds by orders of magnitude.

The reaction kinetics between like-charged compounds in water is extremely slow due to Coulomb repulsions. Here, we demonstrate that by screening these interactions and, in consequence, increasing the local concentration of reactants, we boost the reactions by many orders of magnitude. The reaction between negatively charged Coenzyme A molecules accelerates ~5 million-fold using cationic micelles. That is ~104 faster kinetics than in 0.5 M NaCl, although the salt is ~106 more concentrated. Rate enhancements are not limited to micelles, as evidenced by significant catalytic effects (104-105-fold) of other highly charged species such as oligomers and polymers. We generalize the observed phenomenon by analogously speeding up a non-covalent complex formation-DNA hybridization. A theoretical analysis shows that the acceleration is correlated to the catalysts' surface charge density in both experimental systems and enables predicting and controlling reaction rates of like-charged compounds with counter-charged species.

Entanglement of polymer chains in hypertonic medium enhances the delivery of DNA and other biomacromolecules into cells.

HYPOTHESIS: Most experimental procedures applied in modern biology involve cargo delivering into cells. One of the ways to cargo introduction is osmotic-mediated intracellular vesicle swelling. However, its widespread use was hindered due to cargo size (<10 nm) and cell-type-related restrictions. We addressed the issue of the composition of colloidal loading solution to enhance the efficiency of cellular delivery. EXPERIMENTS: We examined the effectiveness of colloidal loading solutions of varied compositions, including various types and sizes of polymers building osmotic pressure. We used confocal imaging coupled with fluorescence correlation spectroscopy to evaluate the introduction of polymers, proteins, nanoparticles, and DNA plasmids (cargos of sizes 1-175 nm) to cells representing eight cell lines: cancer, normal, epithelial, and mesenchymal ones. FINDINGS: We found that cellular delivery effectiveness strongly correlates with the size and concentration of osmotic pressure building polymers and not with the high value of the osmotic pressure itself. We show that polymer solutions at the entangled regime of concentrations enhance the delivery of large biomacromolecules even of size 200 nm (DNA plasmids) into cells, including MDA-MB-231 cells - so far resistant to the osmotic procedure. We show that the colloid loading medium based on entangled polymer chains is a versatile cargo delivery tool for molecular biology.

Transient dynamics in the outflow of energy from a system in a nonequilibrium stationary state.

We investigate the thermal relaxation of an ideal gas from a nonequilibrium stationary state. The gas is enclosed between two walls, which initially have different temperatures. After making one of the walls adiabatic, the system returns to equilibrium. We notice two distinct modes of heat transport and associated timescales: one connected with a traveling heat front and the other with internal energy diffusion. At the heat front, which moves at the speed of sound, pressure, temperature, and density change abruptly, leaving lower values behind. This is unlike a shock wave, a sound wave, or a thermal wave. The front moves multiple times between the walls and is the dominant heat transport mode until surpassed by diffusion. We found that it can constitute an order 1 factor in shaping the dynamics of the outflow of internal energy. We found that cooling such a system is quicker than heating, and that hotter bodies cool down quicker than colder ones. The latter is known as the Mpemba effect.

Ion Complexation Explains Orders of Magnitude Changes in the Equilibrium Constant of Biochemical Reactions in Buffers Crowded by Nonionic Compounds.

The equilibrium constant (K) of biochemical complex formation in aqueous buffers with high concentration (>20 wt %) of nonionic compounds can vary by orders of magnitude in comparison with the K in a pure buffer. The precise molecular mechanisms of these profound changes are not known. Herein, we show up to a 1000-fold decrease of the K value of DNA hybridization (at nM concentration) in standard molecular crowder systems such as PEG, dextrans, Ficoll, and glycerol. The effect responsible for the decrease of K is the complexation of positively charged ions from a buffer by nonionic polymers/small molecules. We determined the average equilibrium constant for the complexation of ions per monomer (∼0.49 M-1). We retrieve K's original value for a pure buffer if we properly increase the ionic strength of the buffer crowded by the polymers, compensating for the loss of complexed ions.

Internal energy in compressible Poiseuille flow.

We analyze a compressible Poiseuille flow of ideal gas in a plane channel. We provide the form of internal energy U for a nonequilibrium stationary state that includes viscous dissipation and pressure work. We demonstrate that U depends strongly on the ratio Δp/p_{0}, where Δp is the pressure difference between inlet and outlet and p_{0} is the outlet's pressure. In addition, U depends on two other variables: the channel aspect ratio and the parameter equivalent to Reynolds number. The stored internal energy, ΔU=U-U_{0}, is small compared to the internal energy U_{0} of the equilibrium state for a moderate range of values of Δp/p_{0}. However, ΔU can become large for big Δp or close to vacuum conditions at the outlet (p_{0}≈0Pa).

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.

Continuous nonequilibrium transition driven by heat flow.

We discovered an out-of-equilibrium transition in the ideal gas between two walls, divided by an inner, adiabatic, movable wall. The system is driven out-of-equilibrium by supplying energy directly into the volume of the gas. At critical heat flux we have found a continuous transition to the state with a low-density, hot gas on one side of the movable wall and a dense, cold gas on the other side. Molecular dynamic simulations of the soft-sphere fluid confirm the existence of the transition in the interacting system. We introduce a stationary state Helmholtz-like function whose minimum determines the stable positions of the internal wall. This transition can be used as a paradigm of transitions in stationary states and the Helmholtz-like function as a paradigm of the thermodynamic description of these states.

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.

Cellular delivery of dinucleotides by conjugation with small molecules: targeting translation initiation for anticancer applications.

Targeting cap-dependent translation initiation is one of the experimental approaches that could lead to the development of novel anti-cancer therapies. Synthetic dinucleoside 5',5'-triphosphates cap analogs are potent antagonists of eukaryotic translation initiation factor 4E (eIF4E) in vitro and could counteract elevated levels of eIF4E in cancer cells; however, transformation of these compounds into therapeutic agents remains challenging - they do not easily penetrate into cells and are susceptible to enzymatic cleavage. Here, we tested the potential of several small molecule ligands - folic acid, biotin, glucose, and cholesterol - to deliver both hydrolyzable and cleavage-resistant cap analogs into cells. A broad structure-activity relationship (SAR) study using model fluorescent probes and cap-ligand conjugates showed that cholesterol greatly facilitates uptake of cap analogs without disturbing the interactions with eIF4E. The most potent cholesterol conjugate identified showed apoptosis-mediated cytotoxicity towards cancer cells.