Understanding nucleic acid-ion interactions.

Ions surround nucleic acids in what is referred to as an ion atmosphere. As a result, the folding and dynamics of RNA and DNA and their complexes with proteins and with each other cannot be understood without a reasonably sophisticated appreciation of these ions' electrostatic interactions. However, the underlying behavior of the ion atmosphere follows physical rules that are distinct from the rules of site binding that biochemists are most familiar and comfortable with. The main goal of this review is to familiarize nucleic acid experimentalists with the physical concepts that underlie nucleic acid-ion interactions. Throughout, we provide practical strategies for interpreting and analyzing nucleic acid experiments that avoid pitfalls from oversimplified or incorrect models. We briefly review the status of theories that predict or simulate nucleic acid-ion interactions and experiments that test these theories. Finally, we describe opportunities for going beyond phenomenological fits to a next-generation, truly predictive understanding of nucleic acid-ion interactions.

Gap detection responses modelled using the Hill equation in adults with well-controlled HIV.

OBJECTIVE: This study's objective was determining whether gap detection deficits are present in a longstanding cohort of people living with HIV (PLWH) compared to those living without HIV (PLWOH) using a new gap detection modelling technique (i.e. fitting gap responses using the Hill equation and analysing the individual gap detection resulting curves with non-linear statistics). This approach provides a measure of both gap threshold and the steepness of the gap length/correct detection relationship. DESIGN: The relationship between the correct identification rate at each gap length was modelled using the Hill equation. Results were analysed using a nonlinear mixed-effect regression model. STUDY SAMPLE: 45 PLWH (age range 41-78) and 39 PLWOH (age range 38-79) were enrolled and completed gap detection testing. RESULTS: The likelihood ratio statistic comparing the full regression model with the HIV effects to the null model, assuming one population curve for both groups, was highly significant (p < 0.001), suggesting a less precise relationship between gap length and correct detection in PLWH. CONCLUSIONS: PLWH showed degraded gap detection ability compared to PLWOH, likely due to central nervous system effects of HIV infection or treatment. The Hill equation provided a new approach for modelling gap detection ability.

An Account of Models of Molecular Circuits for Associative Learning with Reinforcement Effect and Forced Dissociation.

The development of synthetic biology has enabled massive progress in biotechnology and in approaching research questions from a brand-new perspective. In particular, the design and study of gene regulatory networks in vitro, in vivo, and in silico have played an increasingly indispensable role in understanding and controlling biological phenomena. Among them, it is of great interest to understand how associative learning is formed at the molecular circuit level. Mathematical models are increasingly used to predict the behaviours of molecular circuits. Fernando's model, which is one of the first works in this line of research using the Hill equation, attempted to design a synthetic circuit that mimics Hebbian learning in a neural network architecture. In this article, we carry out indepth computational analysis of the model and demonstrate that the reinforcement effect can be achieved by choosing the proper parameter values. We also construct a novel circuit that can demonstrate forced dissociation, which was not observed in Fernando's model. Our work can be readily used as reference for synthetic biologists who consider implementing circuits of this kind in biological systems.

A New Model of Hemoglobin Oxygenation.

The study of hemoglobin oxygenation, starting from the classical works of Hill, has laid the foundation for molecular biophysics. The cooperative nature of oxygen binding to hemoglobin has been variously described in different models. In the Adair model, which better fits the experimental data, the constants of oxygen binding at various stages differ. However, the physical meaning of the parameters in this model remains unclear. In this work, we applied Hill's approach, extending its interpretation; we obtained a good agreement between the theory and the experiment. The equation in which the Hill coefficient is modulated by the Lorentz distribution for oxygen partial pressure approximates the experimental data better than not only the classical Hill equation, but also the Adair equation.

A standard operating procedure for an enzymatic activity inhibition assay.

This Standard Operating Protocol (SOP) describes the key steps of experimental setup for an inhibition assay of enzymatic activity. The protocol begins with the design of an experiment, including the choice of a catalytic reaction, optimal conditions, fraction and concentration of the active enzyme, substrate and inhibitor concentrations and the positive and negative controls. The protocol ends with the data analysis followed by a typical example of an experiment. Despite an apparently standard procedure, the assay has a number of possible pitfalls such as low fraction of the active enzyme or errors in the analysis such as application of an improper model or incorrect determination of the inhibition constant while not recognizing the dependence on enzyme concentration. The protocol provides examples of necessary steps and controls to avoid these problems and obtain highly reliable results.

Olfactory Navigation and the Receptor Nonlinearity.

The demands on a sensory system depend not only on the statistics of its inputs but also on the task. In olfactory navigation, for example, the task is to find the plume source; allocation of sensory resources may therefore be driven by aspects of the plume that are informative about source location, rather than concentration per se. Here we explore the implications of this idea for encoding odor concentration. To formalize the notion that sensory resources are limited, we considered coding strategies that partitioned the odor concentration range into a set of discriminable intervals. We developed a dynamic programming algorithm that, given the distribution of odor concentrations at several locations, determines the partitioning that conveys the most information about location. We applied this analysis to planar laser-induced fluorescence measurements of spatiotemporal odor fields with realistic advection speeds (5-20 cm/s), with or without a nearby boundary or obstacle. Across all environments, the optimal coding strategy allocated more resources (i.e., more and finer discriminable intervals) to the upper end of the concentration range than would be expected from histogram equalization, the optimal strategy if the goal were to reconstruct the plume, rather than to navigate. Finally, we show that ligand binding, as captured by the Hill equation, transforms odorant concentration into response levels in a way that approximates information maximization for navigation. This behavior occurs when the Hill dissociation constant is near the mean odor concentration, an adaptive set-point that has been observed in the olfactory system of flies.SIGNIFICANCE STATEMENT The first step of olfactory processing is receptor binding, and the resulting relationship between odorant concentration and the bound receptor fraction is a saturating one. While this Hill nonlinearity can be viewed as a distortion that is imposed by the biophysics of receptor binding, here we show that it also plays an important information-processing role in olfactory navigation. Specifically, by combining a novel dynamic-programming algorithm with physical measurements of turbulent plumes, we determine the optimal strategy for encoding odor concentration when the goal is to determine location. This strategy is distinct from histogram equalization, the strategy that maximizes information about plume concentration, and is closely approximated by the Hill nonlinearity when the binding constant is near the ambient mean.

Cooperative Binding and Stepwise Encapsulation of Drug Molecules by Sulfonylcalixarene-Based Metal-Organic Supercontainers.

The cooperative binding behavior of a face-directed octahedral metal-organic supercontainer featuring one endo cavity and six exo cavities was thoroughly examined in chloroform solution through ultraviolet-visible (UV-Vis) titration technique using two representative drug molecules as the guests. The titration curves and their nonlinear fit to Hill equation strongly suggest the efficient encapsulation of the guest molecules by the synthetic host, which exhibit interesting cooperative and stepwise binding behavior. Based on the control experiments using tetranuclear complex as a reference, it is clear that two equivalents of the guest molecules are initially encapsulated inside the endo cavity, followed by the trapping of six additional equivalents of the drug molecules through six exo cavities (1 eq. per exo cavity), and the remaining guests are entrapped by the external pockets. The results provide an in-depth understanding of the cooperative binding behavior of metal-organic supercontainers, which opens up new opportunities for designing synthetic receptors for truly biomimetic functional applications.

Thermophoresis for characterizing biomolecular interaction.

The study of biomolecular interactions is crucial to get more insight into the biological system. The interactions of protein-protein, protein-nucleic acids, protein-sugars, nucleic acid-nucleic acids and protein-small molecules are supporting therapeutics and technological developments. Recently, the development in a large number of analytical techniques for characterizing biomolecular interactions reflect the promising research investments in this field. In this review, microscale thermophoresis technology (MST) is presented as an analytical technique for characterizing biomolecular interactions. Recent years have seen much progress and several applications established. MST is a powerful technique in quantitation of binding events based on the movement of molecules in microscopic temperature gradient. Simplicity, free solutions analysis, low sample volume, short analysis time, and immobilization free are the MST advantages over other competitive techniques. A wide range of studies in biomolecular interactions have been successfully carried out using MST, which tend to the versatility of the technique to use in screening binding events in order to save time, cost and obtained high data quality.

Inter-filament spacing mediates calcium binding to troponin: A simple geometric-mechanistic model explains the shift of force-length maxima with muscle activation.

The maximum of a muscle fiber's force-length curve (FLC) shifts to shorter lengths as muscle activation increases. State-of-the-art muscle models cannot explain the mechanistic basis for this shift, which is therefore either omitted or added ad hoc in a descriptive manner. A more theoretical approach developed by Hatze, who had particularly modeled the process of muscle activation, does predict this shift but can be shown to consist of multiple mathematical attempts that are all inconsistent with their common assertion: to represent local volume constancy. What mechanism may underlie the experimentally well-known shift has thus remained unclear. We work out here that the simple assumption of sarcomere volume constancy can, first of all, indeed explain the shift in the activity-Ca2+ relation as a function of sarcomere length by the enforcement of a decrease in inter-filament spacing that must occur as sarcomere length increases. We show that physiological data of this shift are consistent with a simply linear dependency of troponin (volumetric) density on sarcomere length. Further incorporating filament overlap as a second, independent mechanism, we can moreover reproduce, by means of a single master equation, an entire set of measured FLCs from literature, which testify shifts in their maxima at different levels of activation. We conclude that both phenomena, the shift in activity-Ca2+ relations with length and the shift in the maxima of FLCs with Ca2+, can be explained by the superposition of two mechanisms immediately connected to the same sarcomere state variable length: filament overlap and inter-filament spacing.

Experimental Studies and Modeling of the Drying Kinetics of Multicomponent Polymer Films.

The process of drying thin polymer films is an important operation that influences the film structure and solid state, and the stability of the product. The purpose of this work was to study and model the drying kinetics of multicomponent films based on two polymers: hydroxypropyl methylcellulose (HPMC, amorphous) and polyvinyl alcohol (PVA, semicrystalline). The isothermal drying kinetics of the films at different temperatures (40, 60, and 80°C) were studied using thermo-gravimetric analysis (TGA) and convection oven methods. Solid-state characterization tools used in the study included polarization and hot-stage microscopy, scanning electron microscopy (SEM), and differential scanning calorimetry (DSC). The drying kinetics of HPMC and PVA films in the TGA apparatus and convection oven were comparable. The three-parameter (W max, τ, n) Hill equation successfully modeled the experimental drying kinetics. The time factor τ in the Hill equation nicely explained two drying phases in the films. Solid-state phase changes occurring in the films during dehydration had a bearing on the drying kinetics and mechanisms. TGA can be used as a simple tool to determine the end points in drying processes using ovens or tunnels. The three-parameter Hill equation explained the drying kinetics and diffusion mechanisms of the solvent through the polymer films for the first time. This study advances our understanding of film drying, in particular for pharmaceutically relevant thin films.

Single toxin dose-response models revisited.

The goal of this paper is to offer a rigorous analysis of the sigmoid shape single toxin dose-response relationship. The toxin efficacy function is introduced and four special points, including maximum toxin efficacy and inflection points, on the dose-response curve are defined. The special points define three phases of the toxin effect on mortality: (1) toxin concentrations smaller than the first inflection point or (2) larger then the second inflection point imply low mortality rate, and (3) concentrations between the first and the second inflection points imply high mortality rate. Probabilistic interpretation and mathematical analysis for each of the four models, Hill, logit, probit, and Weibull is provided. Two general model extensions are introduced: (1) the multi-target hit model that accounts for the existence of several vital receptors affected by the toxin, and (2) model with a nonzero mortality at zero concentration to account for natural mortality. Special attention is given to statistical estimation in the framework of the generalized linear model with the binomial dependent variable as the mortality count in each experiment, contrary to the widespread nonlinear regression treating the mortality rate as continuous variable. The models are illustrated using standard EPA Daphnia acute (48h) toxicity tests with mortality as a function of NiCl or CuSO4 toxin.

From Additivity to Cooperativity in Chemistry: Can Cooperativity Be Measured?

Cooperative effects can be observed in various research areas in chemistry; cooperative catalysis is well-established, the assembly of compounds on surfaces can be steered by cooperative effects, and supramolecular polymerization can proceed in a cooperative manner. In biological systems, cooperativity is observed in protein-protein, protein-lipid and protein-molecule interactions. Synergistic effects are relevant in frustrated Lewis pairs, organic multispin systems, multimetallic clusters and also in nanoparticles. However, a general approach to determine cooperativity in the different chemical systems is currently not known. In the present concept paper it is suggested that, at least for simpler systems that can be described at the molecular level, cooperativity can be defined based on energy considerations. For systems in which no chemical transformation occurs, determination of interaction energies of the whole system with respect to the interaction energies between all individual component pairs (subsystems) will allow determination of cooperativity. For systems comprising of chemical transformations, cooperativity can be evaluated by determining the activation energy of the synergistic system and by comparing this with activation energies of the corresponding subsystems that lack an activating moiety. For more complex systems, cooperativity is generally determined at a qualitative level.

A physiologically based pharmacokinetic model of vitamin D.

Despite the plethora of studies discussing the benefits of vitamin D on physiological functioning, few mathematical models of vitamin D predict the response of the body on low-concentration supplementation of vitamin D under sunlight-restricted conditions. This study developed a physiologically based pharmacokinetic (PBPK) model utilizing published human data on the metabolic cascade of orally derived, low-concentration (placebo, 5 µg and 10 µg) supplementation of vitamin D over the course of 28 days in the absence of sunlight. Vitamin D and its metabolites are highly lipophilic and binding assays of these compounds in serum may not account for binding by lipids and additional proteins. To compensate for the additional bound amounts, this study allowed the effective adipose-plasma partition coefficient to vary dynamically with the concentration of each compound in serum utilizing the Hill equation for binding. Through incorporating the optimized parameters with the adipose partition coefficient adaptation to the PBPK model, this study was able to fit serum concentration data for circulating vitamin D at all three supplementation concentrations within confidence intervals of the data. Copyright © 2017 John Wiley & Sons, Ltd.

Topologically protected states in one-dimensional continuous systems and Dirac points.

We study a class of periodic Schrödinger operators on ℝ that have Dirac points. The introduction of an "edge" via adiabatic modulation of a periodic potential by a domain wall results in the bifurcation of spatially localized "edge states," associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The bound states we construct can be realized as highly robust transverse-magnetic electromagnetic modes for a class of photonic waveguides with a phase defect. Our model captures many aspects of the phenomenon of topologically protected edge states for 2D bulk structures such as the honeycomb structure of graphene.

Evolution of optimal Hill coefficients in nonlinear public goods games.

In evolutionary game theory, the effect of public goods like diffusible molecules has been modelled using linear, concave, sigmoid and step functions. The observation that biological systems are often sigmoid input-output functions, as described by the Hill equation, suggests that a sigmoid function is more realistic. The Michaelis-Menten model of enzyme kinetics, however, predicts a concave function, and while mechanistic explanations of sigmoid kinetics exist, we lack an adaptive explanation: what is the evolutionary advantage of a sigmoid benefit function? We analyse public goods games in which the shape of the benefit function can evolve, in order to determine the optimal and evolutionarily stable Hill coefficients. We find that, while the dynamics depends on whether output is controlled at the level of the individual or the population, intermediate or high Hill coefficients often evolve, leading to sigmoid input-output functions that for some parameters are so steep to resemble a step function (an on-off switch). Our results suggest that, even when the shape of the benefit function is unknown, biological public goods should be modelled using a sigmoid or step function rather than a linear or concave function.

A Note on the use of Steady-State Fluorescence Quenching to Quantify Nanoparticle-Protein Interactions.

Steady-state fluorescence quenching is a commonly used technique to investigate the interactions between proteins and nanoparticles, providing quantitative information on binding affinity, stoichiometry and cooperativity. However, a failure to account for the limitations and pitfalls of the methodology can lead to significant errors in data analysis and interpretation. Thus, in this communication we first draw attention to a few common pitfalls in the use of fluorescence quenching to study nanoparticle-protein interactions. For example, we discuss a frequent mistake in the use of the Hill equation to determine cooperativity. We also test using both simulated and experimental data the application of a model-independent method of analysis to generate true thermodynamic nanoparticle-protein binding isotherms. This model-free approach allows for a quantitative description of the interactions independent of assumptions about the nature of the binding process [Bujalowski W, Lohman TM (1987) Biochemistry 26: 3099; Schwarz G (2000) Biophys. Chem. 86: 119].

Measuring and Statistically Testing the Size of the Effect of a Chemical Compound on a Continuous In-Vitro Pharmacological Response Through a New Statistical Model of Response Detection Limit.

Biomolecular screening research frequently searches for the chemical compounds that are most likely to make a biochemical or cell-based assay system produce a strong continuous response. Several doses are tested with each compound and it is assumed that, if there is a dose-response relationship, the relationship follows a monotonic curve, usually a version of the median-effect equation. However, the null hypothesis of no relationship cannot be statistically tested using this equation. We used a linearized version of this equation to define a measure of pharmacological effect size, and use this measure to rank the investigated compounds in order of their overall capability to produce strong responses. The null hypothesis that none of the examined doses of a particular compound produced a strong response can be tested with this approach. The proposed approach is based on a new statistical model of the important concept of response detection limit, a concept that is usually neglected in the analysis of dose-response data with continuous responses. The methodology is illustrated with data from a study searching for compounds that neutralize the infection by a human immunodeficiency virus of brain glioblastoma cells.

Modeling and Simulation of a Parametrically Resonant Micromirror With Duty-Cycled Excitation.

High frequency large scanning angle electrostatically actuated microelectromechanical systems (MEMS) mirrors are used in a variety of applications involving fast optical scanning. A 1-D parametrically resonant torsional micromirror for use in biomedical imaging is analyzed here with respect to operation by duty-cycled square waves. Duty-cycled square wave excitation can have significant advantages for practical mirror regulation and/or control. The mirror's nonlinear dynamics under such excitation is analyzed in a Hill's equation form. This form is used to predict stability regions (the voltage-frequency relationship) of parametric resonance behavior over large scanning angles using iterative approximations for nonlinear capacitance behavior of the mirror. Numerical simulations are also performed to obtain the mirror's frequency response over several voltages for various duty cycles. Frequency sweeps, stability results, and duty cycle trends from both analytical and simulation methods are compared with experimental results. Both analytical models and simulations show good agreement with experimental results over the range of duty cycled excitations tested. This paper discusses the implications of changing amplitude and phase with duty cycle for robust open-loop operation and future closed-loop operating strategies.

Radiofrequency driving antitumor effect of graphene oxide-based nanocomposites: a Hill model analysis.

Aim: This report proposes using the Hill model to assess the benchmark dose, the 50% lethal dose, the cooperativity and the dissociation constant while analyzing cell viability data using nanomaterials to evaluate the antitumor potential while combined with radiofrequency therapy. Materials & methods: A nanocomposite was synthesized (graphene oxide-polyethyleneimine-gold) and the viability was evaluated using two tumor cell lines, namely LLC-WRC-256 and B16-F10. Results: Our findings demonstrated that while the nanocomposite is biocompatible against the LLC-WRC-256 and B16-F10 cancer cell lines in the absence of radiofrequency, the application of radiofrequency enhances the cell toxicity by orders of magnitude. Conclusion: This result points to prospective studies with the tested cell lines using tumor animal models.

Mathematical models describing oxygen binding by hemoglobin.

Despite the fact that the investigation of the structural and functional properties of hemoglobin dates back more than 150 years, the topic has not lost its relevance today. The most important component of these studies is the development of mathematical models that formalize and generalize the mechanisms determining the cooperative binding of ligands based on data on the structural and functional state of the protein. In this work, we review the mathematical relationships describing oxygen binding by hemoglobin, ranging from the classical Hüfner, Hill, and Adair equations to the Szabo-Karplus and tertiary two-state mathematical models based on the Monod-Wyman-Changeux and Koshland-Némethy-Filmer concepts. The generality of the considered equations as mathematical functions, bearing in their basis a power dependence, is demonstrated. The problems and possible solutions related to approximation of experimental data by the oxygenation equations with correlated fitting parameters are noted. Attention is paid to empirical equations, extended versions of the Hill equation, where the coefficient of cooperation is modulated by Gauss and Lorentz distributions as functions of partial oxygen pressure.