Flexoelectric origin of nanomechanic deflection in DNA-microcantilever system

The membrane theory is used to study the recently observed nanomechanical bending of cantilevers, which have processed biomolecular adsorption or biochemical reactions. To be different from entropy-controlling bending mechanism discussed before, we propose that the flexoelectric effect induces cantilever bending. With the introduction of flexoelectric spontaneous curvature, the relation between the bending and biopolymer character is constructed by a simple analytical formula. The cantilever motion induced by adsorption of single-strand DNA and DNA hybridization reaction is quantified analytically and our results show good agreement with experiments.     

Perspective: a stirring role for metabolism in cells

Based on recent findings indicating that metabolism might be governed by a limit on the rate at which cells can dissipate Gibbs energy, in this Perspective, we propose a new mechanism of how metabolic activity could globally regulate biomolecular processes in a cell. Specifically, we postulate that Gibbs energy released in metabolic reactions is used to perform work, allowing enzymes to self‐propel or to break free from supramolecular structures. This catalysis‐induced enzyme movement will result in increased intracellular motion, which in turn can compromise biomolecular functions. Once the increased intracellular motion has a detrimental effect on regulatory mechanisms, this will establish a feedback mechanism on metabolic activity, and result in the observed thermodynamic limit. While this proposed explanation for the identified upper rate limit on cellular Gibbs energy dissipation rate awaits experimental validation, it offers an intriguing perspective of how metabolic activity can globally affect biomolecular functions and will hopefully spark new research.     

Bioassay of prostate-specific antigen (PSA) using microcantilevers

Diagnosis and monitoring of complex diseases such as cancer require quantitative detection of multiple proteins. Recent work has shown that when specific biomolecular binding occurs on one surface of a microcantilever beam, intermolecular nanomechanics bend the cantilever, which can be optically detected. Although this label-free technique readily lends itself to formation of microcantilever arrays, what has remained unclear is the technologically critical issue of whether it is sufficiently specific and sensitive to detect disease-related proteins at clinically relevant conditions and concentrations. As an example, we report here that microcantilevers of different geometries have been used to detect two forms of prostate-specific antigen (PSA) over a wide range of concentrations from 0.2 ng/ml to 60 microg/ml in a background of human serum albumin (HSA) and human plasminogen (HP) at 1 mg/ml, making this a clinically relevant diagnostic technique for prostate cancer. Because cantilever motion originates from the free-energy change induced by specific biomolecular binding, this technique may offer a common platform for high-throughput label-free analysis of protein-protein binding, DNA hybridization, and DNA-protein interactions, as well as drug discovery.     

The Universal Statistical Distributions of the Affinity,Equilibrium Constants,Kinetics and Specificity in Biomolecular Recognition

We uncovered the universal statistical laws for the biomolecular recognition/binding process. We quantified the statistical energy landscapes for binding, from which we can characterize the distributions of the binding free energy (affinity), the equilibrium constants, the kinetics and the specificity by exploring the different ligands binding with a particular receptor. The results of the analytical studies are confirmed by the microscopic flexible docking simulations. The distribution of binding affinity is Gaussian around the mean and becomes exponential near the tail. The equilibrium constants of the binding follow a log-normal distribution around the mean and a power law distribution in the tail. The intrinsic specificity for biomolecular recognition measures the degree of discrimination of native versus non-native binding and the optimization of which becomes the maximization of the ratio of the free energy gap between the native state and the average of non-native states versus the roughness measured by the variance of the free energy landscape around its mean. The intrinsic specificity obeys a Gaussian distribution near the mean and an exponential distribution near the tail. Furthermore, the kinetics of binding follows a log-normal distribution near the mean and a power law distribution at the tail. Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors. The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics.     

Optimal specificity and function for flexible biomolecular recognition

Biomolecular associations often accompanied by large conformational changes, sometimes folding and unfolding. By exploring an exactly solvable model, we constructed the free energy landscape and established a general framework for studying the biomolecular flexible binding process. We derived an optimal criterion for the specificity and function for flexible biomolecular binding where the binding and conformational folding are coupled.     

Microcantilever biosensors

Biosensors are sensors in which biomolecular interactions are used as sensing reactions. Biomolecular interactions, when combined with a microcantilever platform, can produce an extremely powerful biosensing design. The resonance frequency of a microcantilever shifts sensitively due to mass loading from molecular interaction as in the case of any acoustic sensors. In addition, the microcantilevers also undergo bending if the molecular adsorption is confined to a single surface of a microcantilever. This cantilever bending is due to a differential surface stress caused by the forces involved in the adsorption process and is amplified by making the cantilever surfaces chemically different. Lack of specificity, the main disadvantage of the cantilevers, can be overcome by using the extremely selective biochemical reactions such as receptor-ligand, antibody-antigen, or enzyme-substrate reactions. Here we review the microcantilever technology and discuss a number of highly sensitive biochemical sensor applications based on microcantilevers.     

A class of exact solutions for biomacromolecule diffusion-reaction in live cells

A class of novel explicit analytic solutions for a system of n+1 coupled partial differential equations governing biomolecular mass transfer and reaction in living organisms are proposed, evaluated, and analyzed. The solution process uses Laplace and Hankel transforms and results in a recursive convolution of an exponentially scaled Gaussian with modified Bessel functions. The solution is developed for wide range of biomolecular binding kinetics from pure diffusion to multiple binding reactions. The proposed approach provides solutions for both Dirac and Gaussian laser beam (or fluorescence-labeled biomacromolecule) profiles during the course of a Fluorescence Recovery After Photobleaching (FRAP) experiment. We demonstrate that previous models are simplified forms of our theory for special cases. Model analysis indicates that at the early stages of the transport process, biomolecular dynamics is governed by pure diffusion. At large times, the dominant mass transfer process is effective diffusion. Analysis of the sensitivity equations, derived analytically and verified by finite difference differentiation, indicates that experimental biologists should use full space-time profile (instead of the averaged time series) obtained at the early stages of the fluorescence microscopy experiments to extract meaningful physiological information from the protocol. Such a small time frame requires improved bioinstrumentation relative to that in use today. Our mathematical analysis highlights several limitations of the FRAP protocol and provides strategies to improve it. The proposed model can be used to study biomolecular dynamics in molecular biology, targeted drug delivery in normal and cancerous tissues, motor-driven axonal transport in normal and abnormal nervous systems, kinetics of diffusion-controlled reactions between enzyme and substrate, and to validate numerical simulators of biological mass transport processes in vivo.     

4-aminophenylalanine as a biocompatible nucleophilic catalyst for hydrazone ligations at low temperature and neutral pH

Hydrazone formation and similar reactions are highly versatile and specific, but their application to biological systems has been limited by their characteristically slow reaction kinetics at neutral pH. Catalysis of these reactions through imine formation with aromatic amines such as aniline has broadened the applicability of these reactions to biomolecular labeling. High concentrations of the catalyst are necessary, which may be incompatible with the native structure of certain proteins. In this study, we investigated the utility of 4-aminophenylalanine (4a-Phe) as a catalyst for these reactions. We find that 4a-Phe is nearly as effective as aniline in catalyzing hydrazone formation between the reactive amino acid 3-formyltyrosine (3f-Tyr) and hydrazine-containing fluorophores, both free in solution and incorporated into the protein tubulin. The catalyst 4a-Phe maintains ～70% of the catalytic efficacy of aniline and is less detrimental to the native structure of tubulin. Examination of the temperature dependence of imine formation between 3f-Tyr and 4a-Phe shows an increase in imine concentration accompanying a decrease in temperature, confirming the exothermic nature of the equilibrium reaction. Interestingly, decreasing the temperature of the 4a-Phe-catalyzed hydrazone reaction between 3f-Tyr and the fluorophore 7-hydrazinyl-4-methylcoumarin increases the overall rate of the reaction. This result indicates that the temperature dependence of the catalyst-aldehyde equilibrium is greater than the temperature dependence of the rate constant for hydrazone formation from this intermediate, and that the rate of hydrazone formation a direct function of the concentration of the intermediate imine. These results provide a platform for conducting nucleophilic catalysis under conditions that are more compatible with biomolecular targets than previously demonstrated, thereby expanding the utility of hydrazone ligations in biological systems.     

A regenerable flow-through affinity sensor for label-free detection of proteins and DNA

Label-free monitoring of biomolecular reactions in real-time is of great interest since it can provide valuable information about binding kinetics and equilibrium constants. In this report, a sensor based on White Light Reflectance Spectroscopy (WLRS) is presented that is capable of real-time monitoring of biomolecular reactions taking place on top of a polymer covered silicon dioxide reflective surface. The optical set-up consists of a visible–near infrared light source, a bifurcated optical fiber and a spectrometer. The outer part of the optical fiber guides the light vertically onto the surface where the biomolecular reactions occur, whereas the reflected light is driven from the central part of the fiber to the spectrometer. A microfluidic module in combination with a pump supplies the reagents at a constant rate. The biomolecular interactions are monitored as shifts of the wavelength of the interference minimum. The proposed methodology was applied for real-time and label-free monitoring mouse gamma-globulins binding onto immobilized anti-mouse IgG antibody. Mouse gamma-globulins at concentrations down to 150 pM were detected in reaction times of 1-min. Regeneration of immobilized antibody was accomplished up to seven times without loss of its activity. In addition, real-time monitoring of hybridization reaction between complementary oligonucleotides was accomplished. The proposed sensor provides a simple, fast, low cost approach for label-free monitoring of biomolecular interactions and therefore it should by suitable for a wide range of analytical applications.     

Unconstrained enhanced sampling for free energy calculations of biomolecules: a review

Abstract

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations.     

Thermodynamic analysis of biodegradation pathways

Microorganisms provide a wealth of biodegradative potential in the reduction and elimination of xenobiotic compounds in the environment. One useful metric to evaluate potential biodegradation pathways is thermodynamic feasibility. However, experimental data for the thermodynamic properties of xenobiotics is scarce. The present work uses a group contribution method to study the thermodynamic properties of the University of Minnesota Biocatalysis/Biodegradation Database. The Gibbs free energies of formation and reaction are estimated for 914 compounds (81%) and 902 reactions (75%), respectively, in the database. The reactions are classified based on the minimum and maximum Gibbs free energy values, which accounts for uncertainty in the free energy estimates and a feasible concentration range relevant to biodegradation. Using the free energy estimates, the cumulative free energy change of 89 biodegradation pathways (51%) in the database could be estimated. A comparison of the likelihood of the biotransformation rules in the Pathway Prediction System and their thermodynamic feasibility was then carried out. This analysis revealed that when evaluating the feasibility of biodegradation pathways, it is important to consider the thermodynamic topology of the reactions in the context of the complete pathway. Group contribution is shown to be a viable tool for estimating, a priori, the thermodynamic feasibility and the relative likelihood of alternative biodegradation reactions. This work offers a useful tool to a broad range of researchers interested in estimating the feasibility of the reactions in existing or novel biodegradation pathways. Biotechnol. Bioeng. 2009;103: 532–541. © 2009 Wiley Periodicals, Inc.     

Energy Sources,Self-organization,and the Origin of Life

The emergence and early developments of life are considered from the point of view that contingent events that inevitably marked evolution were accompanied by deterministic driving forces governing the selection between different alternatives. Accordingly, potential energy sources are considered for their propensity to induce self-organization within the scope of the chemical approach to the origin of life. Requirements in terms of quality of energy locate thermal or photochemical activation in the atmosphere as highly likely processes for the formation of activated low-molecular weight organic compounds prone to induce biomolecular self-organization through their ability to deliver quanta of energy matching the needs of early biochemical pathways or the reproduction of self-replicating entities. These lines of reasoning suggest the existence of a direct connection between the free energy content of intermediates of early pathways and the quanta of energy delivered by available sources of energy.     

A 31P-NMR study of the mechanism of and salt effect on Mg2(+)-ATP exchange

The study of exchange between free and metal-bound ligands by NMR methods is discussed with reference to differentiation between unimolecular dissociation of the metal-bound complex and biomolecular exchange of metal ion between two ligands. This is applied to exchange of ATP4- between the free and Mg2(+)-bound states and problems of interpretation in the presence of a strong kinetic salt effect are discussed. Contrary to a previous report, exchange is inferred to occur mainly via unimolecular dissociation of MgATP2- over a range of temperatures, concentrations, and pH values, which include those expected in vivo. For the model system Mg2(+)-tripolyphosphate, an activation energy of 52 +/- 5 kJ.mol-1, inferred to be that for dissociation of MgTPPH2-, is found for the exchange process.     

Prebiotic sources of biomolecular handedness

Fischer demonstrated (1890–1919) that functional biomolecules are composed specifically of the D-sugars and the L-amino acids, and that in the laboratory synthetic reactions of such molecules propagate with chiral stereoselectivity. Given a primordial enantiomer, biomolecular homochirality followed without the intervention of the chiral natural force conjectured by Pasteur (1860), except prebiotically. Polarized solar radiation and other classical chiral forces were proposed as agencies generating a prebiotic enantiomeric excess, but the forces then known were found to be evenhanded on a time and space average, exemplifying parity conservation (1927). The weak nuclear force, shown to violate parity (1956), was unified with electromagnetism in the electroweak force (1970). Ab initio estimations including the chiral electroweak force indicate that the L-amino acids and the D-sugars are more stable than the corresponding enantiomers. The small energy difference between these enantiomer pairs, with Darwinian reaction kinetics in a flow reactor, account for the choice of biomolecular handedness made when life began.     

An evaluation of Poisson-Boltzmann electrostatic free energy calculations through comparison with experimental mutagenesis data

For systems involving highly and oppositely charged proteins, electrostatic forces dominate association and contribute to biomolecular complex stability. Using experimental or theoretical alanine-scanning mutagenesis, it is possible to elucidate the contribution of individual ionizable amino acids to protein association. We evaluated our electrostatic free energy calculations by comparing calculated and experimental data for alanine mutants of five protein complexes. We calculated Poisson-Boltzmann electrostatic free energies based on a thermodynamic cycle, which incorporates association in a reference (Coulombic) and solvated (solution) state, as well as solvation effects. We observe that Coulombic and solvation free energy values correlate with experimental data in highly and oppositely charged systems, but not in systems comprised of similarly charged proteins. We also observe that correlation between solution and experimental free energies is dependent on dielectric coefficient selection for the protein interior. Free energy correlations improve as protein dielectric coefficient increases, suggesting that the protein interior experiences moderate dielectric screening, despite being shielded from solvent. We propose that higher dielectric coefficients may be necessary to more accurately predict protein-protein association. Additionally, our data suggest that Coulombic potential calculations alone may be sufficient to predict relative binding of protein mutants.     

Circular permutation prediction reveals a viable backbone disconnection for split proteins: an approach in identifying a new functional split intein

Split-protein systems have emerged as a powerful tool for detecting biomolecular interactions and reporting biological reactions. However, reliable methods for identifying viable split sites are still unavailable. In this study, we demonstrated the feasibility that valid circular permutation (CP) sites in proteins have the potential to act as split sites and that CP prediction can be used to search for internal permissive sites for creating new split proteins. Using a protein ligase, intein, as a model, CP predictor facilitated the creation of circular permutants in which backbone opening imposes the least detrimental effects on intein folding. We screened a series of predicted intein CPs and identified stable and native-fold CPs. When the valid CP sites were introduced as split sites, there was a reduction in folding enthalpy caused by the new backbone opening; however, the coincident loss in entropy was sufficient to be compensated, yielding a favorable free energy for self-association. Since split intein is exploited in protein semi-synthesis, we tested the related protein trans-splicing (PTS) activities of the corresponding split inteins. Notably, a novel functional split intein composed of the N-terminal 36 residues combined with the remaining C-terminal fragment was identified. Its PTS activity was shown to be better than current reported two-piece intein with a short N-terminal segment. Thus, the incorporation of in silico CP prediction facilitated the design of split intein as well as circular permutants.     

Survey of the year 2008: applications of isothermal titration calorimetry

Isothermal titration calorimetry (ITC) is a fast, accurate and label‐free method for measuring the thermodynamics and binding affinities of molecular associations in solution. Because the method will measure any reaction that results in a heat change, it is applicable to many different fields of research from biomolecular science, to drug design and materials engineering, and can be used to measure binding events between essentially any type of biological or chemical ligand. ITC is the only method that can directly measure binding energetics including Gibbs free energy, enthalpy, entropy and heat capacity changes. Not only binding thermodynamics but also catalytic reactions, conformational rearrangements, changes in protonation and molecular dissociations can be readily quantified by performing only a small number of ITC experiments. In this review, we highlight some of the particularly interesting reports from 2008 employing ITC, with a particular focus on protein interactions with other proteins, nucleic acids, lipids and drugs. As is tradition in these reviews we have not attempted a comprehensive analysis of all 500 papers using ITC, but emphasize those reports that particularly captured our interest and that included more thorough discussions we consider exemplify the power of the technique and might serve to inspire other users. Copyright © 2010 John Wiley & Sons, Ltd.     

Geometric and potential driving formation and evolution of biomolecular surfaces

This paper presents new geometrical flow equations for the theoretical modeling of biomolecular surfaces in the context of multiscale implicit solvent models. To account for the local variations near the biomolecular surfaces due to interactions between solvent molecules, and between solvent and solute molecules, we propose potential driven geometric flows, which balance the intrinsic geometric forces that would occur for a surface separating two homogeneous materials with the potential forces induced by the atomic interactions. Stochastic geometric flows are introduced to account for the random fluctuation and dissipation in density and pressure near the solvent–solute interface. Physical properties, such as free energy minimization (area decreasing) and incompressibility (volume preserving), are realized by some of our geometric flow equations. The proposed approach for geometric and potential forces driving the formation and evolution of biological surfaces is illustrated by extensive numerical experiments and compared with established minimal molecular surfaces and molecular surfaces. Local modification of biomolecular surfaces is demonstrated with potential driven geometric flows. High order geometric flows are also considered and tested in the present work for surface generation. Biomolecular surfaces generated by these approaches are typically free of geometric singularities. As the speed of surface generation is crucial to implicit solvent model based molecular dynamics, four numerical algorithms, a semi-implicit scheme, a Crank–Nicolson scheme, and two alternating direction implicit (ADI) schemes, are constructed and tested. Being either stable or conditionally stable but admitting a large critical time step size, these schemes overcome the stability constraint of the earlier forward Euler scheme. Aided with the Thomas algorithm, one of the ADI schemes is found to be very efficient as it balances the speed and accuracy.      

Concepts and protocols for electrostatic free energies

Electrostatic free energies play an essential role in numerous biomolecular processes occurring in solution. Difficulties arise when the long-range Coulomb interaction is computed for idealised infinite simulation models with periodic boundary conditions. To maintain a neutral simulation box and a finite per-box energy, a neutralising charge density or ‘gellium’ is commonly used, leading to a mean box potential that is constrained to be rigorously equal to zero at all times. Thus, in considering quantities such as ion solvation free energy, the potential drop to move from solvent into the usual, gas phase reference state is missing. In fact, for an infinite molecular system, the electrostatic potential itself is not uniquely defined, but takes the form of an infinite series that is only conditionally convergent. This leads to several possible computational conventions that give different values for the potential and field, all mathematically valid. For experimentally measurable quantities, however, unique results are obtained when sufficiently large simulation boxes are utilised. These concepts are detailed, as well as a fundamental, linear response theoretical framework that provides qualitative understanding of the physical processes involved, especially dielectric relaxation of the environment in response to a new solute charge. Illustrative applications to ligand binding and biomolecular electron transfer are described.     

Bioenergetics of the formyl-methanofuran dehydrogenase and heterodisulfide reductase reactions in Methanothermobacter thermautotrophicus.

The synthesis of formyl-methanofuran and the reduction of the heterodisulfide (CoM-S-S-CoB) of coenzyme M (HS-CoM) and coenzyme B (HS-CoB) are two crucial, H2-dependent reactions in the energy metabolism of methanogenic archaea. The bioenergetics of the reactions in vivo were studied in chemostat cultures and in cell suspensions of Methanothermobacter thermautotrophicus metabolizing at defined dissolved hydrogen partial pressures ( pH2). Formyl-methanofuran synthesis is an endergonic reaction (DeltaG degrees ' = +16 kJ.mol-1). By analyzing the concentration ratios between formyl-methanofuran and methanofuran in the cells, free energy changes under experimental conditions (DeltaG') were found to range between +10 and +35 kJ.mol-1 depending on the pH2 applied. The comparison with the sodium motive force indicated that the reaction should be driven by the import of a variable number of two to four sodium ions. Heterodisulfide reduction (DeltaG degrees ' = -40 kJ.mol-1) was associated with free energy changes as high as -55 to -80 kJ.mol-1. The values were determined by analyzing the concentrations of CoM-S-S-CoB, HS-CoM and HS-CoB in methane-forming cells operating under a variety of hydrogen partial pressures. Free energy changes were in equilibrium with the proton motive force to the extent that three to four protons could be translocated out of the cells per reaction. Remarkably, an apparent proton translocation stoichiometry of three held for cells that had been grown at pH2<0.12 bar, whilst the number was four for cells grown above that concentration. The shift occurred within a narrow pH2 span around 0.12 bar. The findings suggest that the methanogens regulate the bioenergetic machinery involved in CoM-S-S-CoB reduction and proton pumping in response to the environmental hydrogen concentrations.