Viscoelastic phenotyping of red blood cells.

Red blood cells (RBCs) are the simplest cell types with complex dynamical and viscoelastic phenomenology. While the mechanical rigidity and the flickering noise of RBCs have been extensively investigated, an accurate determination of the constitutive equations of the relaxational kinetics is lacking. Here we measure the force relaxation of RBCs under different types of tensional and compressive extension-jump protocols by attaching an optically trapped bead to the RBC membrane. Relaxational kinetics follows linear response from 60 pN (tensional) to -20 pN (compressive) applied forces, exhibiting a triple exponential function with three well-separated timescales over four decades (0.01-100 s). While the fast timescale (τF∼0.02(1)s) corresponds to the relaxation of the membrane, the intermediate and slow timescales (τI=4(1)s; τS=70(8)s) likely arise from the cortex dynamics and the cytosol viscosity. Relaxation is highly heterogeneous across the RBC population, yet the three relaxation times are correlated, showing dynamical scaling. Finally, we find that glucose depletion and laser illumination of RBCs lead to faster triple exponential kinetics and RBC rigidification. Viscoelastic phenotyping is a promising dynamical biomarker applicable to other cell types and active systems.

Information-to-work conversion in single-molecule experiments: From discrete to continuous feedback.

We theoretically investigate the extractable work in single molecule unfolding-folding experiments with applied feedback. Using a simple two-state model, we obtain a description of the full work distribution from discrete to continuous feedback. The effect of the feedback is captured by a detailed fluctuation theorem, accounting for the information aquired. We find analytical expressions for the average work extraction as well as an experimentally measurable bound thereof, which becomes tight in the continuous feedback limit. We further determine the parameters for maximal power or rate of work extraction. Although our two-state model only depends on a single effective transition rate, we find qualitative agreement with Monte Carlo simulations of DNA hairpin unfolding-folding dynamics.

Experimental Test of Sinai's Model in DNA Unzipping.

The experimental measurement of correlation functions and critical exponents in disordered systems is key to testing renormalization group (RG) predictions. We mechanically unzip single DNA hairpins with optical tweezers, an experimental realization of the diffusive motion of a particle in a one-dimensional random force field, known as the Sinai model. We measure the unzipping forces F_{w} as a function of the trap position w in equilibrium and calculate the force-force correlator Δ_{m}(w), its amplitude, and correlation length, finding agreement with theoretical predictions. We study the universal scaling properties since the effective trap stiffness m^{2} decreases upon unzipping. Fluctuations of the position of the base pair at the unzipping junction u scales as u∼m^{-ζ}, with a roughness exponent ζ=1.34±0.06, in agreement with the analytical prediction ζ=4/3. Our study provides a single-molecule test of the functional RG approach for disordered elastic systems in equilibrium.

Generalized continuous Maxwell demons.

We introduce a family of generalized continuous Maxwell demons (GCMDs) operating on idealized single-bit equilibrium devices that combine the single-measurement Szilard and the repeated measurements of the continuous Maxwell demon protocols. We derive the cycle distributions for extracted work, information content, and time and compute the power and information-to-work efficiency fluctuations for the different models. We show that the efficiency at maximum power is maximal for an opportunistic protocol of continuous type in the dynamical regime dominated by rare events. We also extend the analysis to finite-time work extracting protocols by mapping them to a three-state GCMD. We show that dynamical finite-time correlations in this model increase the information-to-work conversion efficiency, underlining the role of temporal correlations in optimizing information-to-energy conversion. The effect of finite-time work extraction and demon memory resetting is also analyzed. We conclude that GCMD models are thermodynamically more efficient than the single-measurement Szilard and preferred for describing biological processes in an information-redundant world.

N-States Continuous Maxwell Demon.

Maxwell's demon is a famous thought experiment and a paradigm of the thermodynamics of information. It is related to Szilard's engine, a two-state information-to-work conversion device in which the demon performs single measurements and extracts work depending on the state measurement outcome. A variant of these models, the continuous Maxwell demon (CMD), was recently introduced by Ribezzi-Crivellari and Ritort where work was extracted after multiple repeated measurements every time that τ is in a two-state system. The CMD was able to extract unbounded amounts of work at the cost of an unbounded amount of information storage. In this work, we built a generalization of the CMD to the N-state case. We obtained generalized analytical expressions for the average work extracted and the information content. We show that the second law inequality for information-to-work conversion is fulfilled. We illustrate the results for N-states with uniform transition rates and for the N = 3 case.

Temperature-dependent elastic properties of DNA.

Knowledge of the elastic properties, e.g., the persistence length or interphosphate distance, of single-stranded (ss) and double-stranded (ds) DNA under different experimental conditions is critical to characterizing molecular reactions studied with single-molecule techniques. While previous experiments have addressed the dependence of the elastic parameters upon varying ionic strength and contour length, temperature-dependent effects are less studied. Here, we examine the temperature-dependent elasticity of ssDNA and dsDNA in the range 5°C-50°C using a temperature-jump optical trap. We find a temperature softening for dsDNA and a temperature stiffening for ssDNA. Our results highlight the need for a general theory explaining the phenomenology observed.

Folding Free Energy Determination of an RNA Three-Way Junction Using Fluctuation Theorems.

Nonequilibrium work relations and fluctuation theorems permit us to extract equilibrium information from nonequilibrium measurements. They find application in single-molecule pulling experiments where molecular free energies can be determined from irreversible work measurements by using unidirectional (e.g., Jarzynski's equality) and bidirectional (e.g., Crooks fluctuation theorem and Bennet's acceptance ratio (BAR)) methods. However, irreversibility and the finite number of pulls limit their applicability: the higher the dissipation, the larger the number of pulls necessary to estimate ΔG within a few kBT. Here, we revisit pulling experiments on an RNA three-way junction (3WJ) that exhibits significant dissipation and work-distribution long tails upon mechanical unfolding. While bidirectional methods are more predictive, unidirectional methods are strongly biased. We also consider a cyclic protocol that combines the forward and reverse work values to increase the statistics of the measurements. For a fixed total experimental time, faster pulling rates permit us to efficiently sample rare events and reduce the bias, compensating for the increased dissipation. This analysis provides a more stringent test of the fluctuation theorem in the large irreversibility regime.

Nucleic Acid Thermodynamics Derived from Mechanical Unzipping Experiments.

Force-spectroscopy techniques have led to significant progress in studying the physicochemical properties of biomolecules that are not accessible in bulk assays. The application of piconewton forces with laser optical tweezers to single nucleic acids has permitted the characterization of molecular thermodynamics and kinetics with unprecedented accuracy. Some examples are the hybridization reaction between complementary strands in DNA and the folding of secondary, tertiary, and other heterogeneous structures, such as intermediate and misfolded states in RNA. Here we review the results obtained in our lab on deriving the nearest-neighbor free energy parameters in DNA and RNA duplexes from mechanical unzipping experiments. Remarkable nonequilibrium effects are also observed, such as the large irreversibility of RNA unzipping and the formation of non-specific secondary structures in single-stranded DNA. These features originate from forming stem-loop structures along the single strands of the nucleic acid. The recently introduced barrier energy landscape model quantifies kinetic trapping effects due to stem-loops being applicable to both RNA and DNA. The barrier energy landscape model contains the essential features to explain the many behaviors observed in heterogeneous nucleic-acid folding.

Measurement of the specific and non-specific binding energies of Mg2+ to RNA.

Determining the non-specific and specific electrostatic contributions of magnesium binding to RNA is a challenging problem. We introduce a single-molecule method based on measuring the folding energy of a native RNA in magnesium and at its equivalent sodium concentration. The latter is defined so that the folding energy in sodium equals the non-specific electrostatic contribution in magnesium. The sodium equivalent can be estimated according to the empirical 100/1 rule (1 M NaCl is equivalent to 10 mM MgCl2), which is a good approximation for most RNAs. The method is applied to an RNA three-way junction (3WJ) that contains specific Mg2+ binding sites and misfolds into a double hairpin structure without binding sites. We mechanically pull the RNA with optical tweezers and use fluctuation theorems to determine the folding energies of the native and misfolded structures in magnesium (10 mM MgCl2) and at the equivalent sodium condition (1 M NaCl). While the free energies of the misfolded structure are equal in magnesium and sodium, they are not for the native structure, the difference being due to the specific binding energy of magnesium to the 3WJ, which equals ΔG≃ 10 kcal/mol. Besides stabilizing the 3WJ, Mg2+ also kinetically rescues it from the misfolded structure over timescales of tens of seconds in a force-dependent manner. The method should generally be applicable to determine the specific binding energies of divalent cations to other tertiary RNAs.

Molten globule-like transition state of protein barnase measured with calorimetric force spectroscopy.

SignificanceUnderstanding the molecular forces driving the unfolded polypeptide chain to self-assemble into a functional native structure remains an open question. However, identifying the states visited during protein folding (e.g., the transition state between the unfolded and native states) is tricky due to their transient nature. Here, we introduce calorimetric force spectroscopy in a temperature jump optical trap to determine the enthalpy, entropy, and heat capacity of the transition state of protein barnase. We find that the transition state has the properties of a dry molten globule, that is, high free energy and low configurational entropy, being structurally similar to the native state. This experimental single-molecule study characterizes the thermodynamic properties of the transition state in funneled energy landscapes.

Force-Dependent Folding Kinetics of Single Molecules with Multiple Intermediates and Pathways.

Most single-molecule studies derive the kinetic rates of native, intermediate, and unfolded states from equilibrium hopping experiments. Here, we apply the Kramers kinetic diffusive model to derive the force-dependent kinetic rates of intermediate states from nonequilibrium pulling experiments. From the kinetic rates, we also extract the force-dependent kinetic barriers and the equilibrium folding energies. We apply our method to DNA hairpins with multiple folding pathways and intermediates. The experimental results agree with theoretical predictions. Furthermore, the proposed nonequilibrium single-molecule approach permits us to characterize kinetic and thermodynamic properties of native, unfolded, and intermediate states that cannot be derived from equilibrium hopping experiments.

Stem-loop formation drives RNA folding in mechanical unzipping experiments.

Accurate knowledge of RNA hybridization is essential for understanding RNA structure and function. Here we mechanically unzip and rezip a 2-kbp RNA hairpin and derive the 10 nearest-neighbor base pair (NNBP) RNA free energies in sodium and magnesium with 0.1 kcal/mol precision using optical tweezers. Notably, force-distance curves (FDCs) exhibit strong irreversible effects with hysteresis and several intermediates, precluding the extraction of the NNBP energies with currently available methods. The combination of a suitable RNA synthesis with a tailored pulling protocol allowed us to obtain the fully reversible FDCs necessary to derive the NNBP energies. We demonstrate the equivalence of sodium and magnesium free-energy salt corrections at the level of individual NNBP. To characterize the irreversibility of the unzipping-rezipping process, we introduce a barrier energy landscape of the stem-loop structures forming along the complementary strands, which compete against the formation of the native hairpin. This landscape correlates with the hysteresis observed along the FDCs. RNA sequence analysis shows that base stacking and base pairing stabilize the stem-loops that kinetically trap the long-lived intermediates observed in the FDC. Stem-loops formation appears as a general mechanism to explain a wide range of behaviors observed in RNA folding.

Force Dependence of Proteins' Transition State Position and the Bell-Evans Model.

Single-molecule force spectroscopy has opened a new field of research in molecular biophysics and biochemistry. Pulling experiments on individual proteins permit us to monitor conformational transitions with high temporal resolution and measure their free energy landscape. The force-extension curves of single proteins often present large hysteresis, with unfolding forces that are higher than refolding ones. Therefore, the high energy of the transition state (TS) in these molecules precludes kinetic rates measurements in equilibrium hopping experiments. In irreversible pulling experiments, force-dependent kinetic rates measurements show a systematic discrepancy between the sum of the folding and unfolding TS distances derived by the kinetic Bell-Evans model and the full molecular extension predicted by elastic models. Here, we show that this discrepancy originates from the force-induced movement of TS. Specifically, we investigate the highly kinetically stable protein barnase, using pulling experiments and the Bell-Evans model to characterize the position of its kinetic barrier. Experimental results show that while the TS stays at a roughly constant distance relative to the native state, it shifts with force relative to the unfolded state. Interestingly, a conversion of the protein extension into amino acid units shows that the TS position follows the Leffler-Hammond postulate: the higher the force, the lower the number of unzipped amino acids relative to the native state. The results are compared with the quasi-reversible unfolding-folding of a short DNA hairpin.

Mechanical characterization of base analogue modified nucleic acids by force spectroscopy.

We use mechanical unfolding of single DNA hairpins with modified bases to accurately assess intra- and intermolecular forces in nucleic acids. As expected, the modification stabilizes the hybridized hairpin, but we also observe intriguing stacking interactions in the unfolded hairpin. Our study highlights the benefit of using base-modified nucleic acids in force-spectroscopy.

Sugar-Pucker Force-Induced Transition in Single-Stranded DNA.

The accurate knowledge of the elastic properties of single-stranded DNA (ssDNA) is key to characterize the thermodynamics of molecular reactions that are studied by force spectroscopy methods where DNA is mechanically unfolded. Examples range from DNA hybridization, DNA ligand binding, DNA unwinding by helicases, etc. To date, ssDNA elasticity has been studied with different methods in molecules of varying sequence and contour length. A dispersion of results has been reported and the value of the persistence length has been found to be larger for shorter ssDNA molecules. We carried out pulling experiments with optical tweezers to characterize the elastic response of ssDNA over three orders of magnitude in length (60-14 k bases). By fitting the force-extension curves (FECs) to the Worm-Like Chain model we confirmed the above trend:the persistence length nearly doubles for the shortest molecule (60 b) with respect to the longest one (14 kb). We demonstrate that the observed trend is due to the different force regimes fitted for long and short molecules, which translates into two distinct elastic regimes at low and high forces. We interpret this behavior in terms of a force-induced sugar pucker conformational transition (C3'-endo to C2'-endo) upon pulling ssDNA.

Direct detection of molecular intermediates from first-passage times.

All natural phenomena are governed by energy landscapes. However, the direct measurement of this fundamental quantity remains challenging, particularly in complex systems involving intermediate states. Here, we uncover key details of the energy landscapes that underpin a range of experimental systems through quantitative analysis of first-passage time distributions. By combined study of colloidal dynamics in confinement, transport through a biological pore, and the folding kinetics of DNA hairpins, we demonstrate conclusively how a short-time, power-law regime of the first-passage time distribution reflects the number of intermediate states associated with each of these processes, despite their differing length scales, time scales, and interactions. We thereby establish a powerful method for investigating the underlying mechanisms of complex molecular processes.

Dynamics of individual molecular shuttles under mechanical force.

Molecular shuttles are the basis of some of the most advanced synthetic molecular machines. In these devices a macrocycle threaded onto a linear component shuttles between different portions of the thread in response to external stimuli. Here, we use optical tweezers to measure the mechanics and dynamics of individual molecular shuttles in aqueous conditions. Using DNA as a handle and as a single molecule reporter, we measure thousands of individual shuttling events and determine the force-dependent kinetic rates of the macrocycle motion and the main parameters governing the energy landscape of the system. Our findings could open avenues for the real-time characterization of synthetic devices at the single molecule level, and provide crucial information for designing molecular machinery able to operate under physiological conditions.

Lymph microvascularization as a prognostic indicator in neuroblastoma.

Neuroblastoma is the most common extra-cranial solid pediatric cancer and causes approximately 15% of all childhood deaths from cancer. Although lymphatic vasculature is a prerequisite for the maintenance of tissue fluid balance and immunity in the body, little is known about the relationship between lymphatic vascularization and prognosis in neuroblastoma. We used our previously-published custom-designed tool to close open-outline vessels and measure the density, size and shape of all lymphatic vessels and microvascular segments in 332 primary neuroblastoma contained in tissue microarrays. The results were correlated with clinical and biological features of known prognostic value and with risk of progression to establish histological lymphatic vascular patterns associated with unfavorable histology. A high proportion of irregular intermediate lymphatic capillaries and irregular small collector vessels were present in tumors from patients with metastatic stage, undifferentiating neuroblasts and/or classified in the high risk. In addition, a higher lymphatic microvascularization density was found to be predictive of overall survival. Our findings show the crucial role of lymphatic vascularization in metastatic development and maintenance of tumor tissue homeostasis. These patterns may therefore help to indicate more accurate pre-treatment risk stratification and could provide candidate targets for novel therapies.

Probing cellular mechanics with acoustic force spectroscopy.

A large number of studies demonstrate that cell mechanics and pathology are intimately linked. In particular, deformability of red blood cells (RBCs) is key to their function and is dramatically altered in the time course of diseases such as anemia and malaria. Due to the physiological importance of cell mechanics, many methods for cell mechanical probing have been developed. While single-cell methods provide very valuable information, they are often technically challenging and lack the high data throughput needed to distinguish differences in heterogeneous populations, while fluid-flow high-throughput methods miss the accuracy to detect subtle differences. Here we present a new method for multiplexed single-cell mechanical probing using acoustic force spectroscopy (AFS). We demonstrate that mechanical differences induced by chemical treatments of known effect can be measured and quantified. Furthermore, we explore the effect of extracellular vesicles (EVs) uptake on RBC mechanics and demonstrate that EVs uptake increases RBC deformability. Our findings demonstrate the ability of AFS to manipulate cells with high stability and precision and pave the way to further new insights into cellular mechanics and mechanobiology in health and disease, as well as potential biomedical applications.