Mathematical Model of Bone Remodeling Captures the Antiresorptive and Anabolic Actions of Various Therapies.

A better understanding of the molecular pathways regulating the bone remodeling process should help in the development of new antiresorptive regulators and anabolic regulators, that is, regulators of bone resorption and of bone formation. Understanding the mechanisms by which parathyroid hormone (PTH) influences bone formation and how it switches from anabolic to catabolic action is important for treating osteoporosis (Poole and Reeve in Curr Opin Pharmacol 5:612-617, 2005). In this paper we describe a mathematical model of bone remodeling that incorporates, extends, and integrates several models of particular aspects of this biochemical system (Cabal et al. in J Bone Miner Res 28(8):1830-1836, 2013; Lemaire et al. in J Theor Biol 229:293-309, 2004; Peterson and Riggs in Bone 46:49-63, 2010; Raposo et al. in J Clin Endocrinol Metab 87(9):4330-4340, 2002; Ross et al. in J Disc Cont Dyn Sys Series B 17(6):2185-2200, 2012). We plan to use this model as a bone homeostasis platform to develop anabolic and antiresorptive compounds. The model will allow us to test hypotheses about the dynamics of compounds and to test the potential benefits of combination therapies. At the core of the model is the idealized account of osteoclast and osteoblast signaling given by Lemaire et al. (J Theor Biol 229:293-309, 2004). We have relaxed some of their assumptions about the roles of osteoprotegerin, transforming growth factor [Formula: see text], and receptor activator of nuclear factor [Formula: see text]B ligand; we have devised more detailed models of the interactions of these species. We have incorporated a model of the effect of calcium sensing receptor antagonists on remodeling (Cabal et al. in J Bone Miner Res 28(8):1830-1836, 2013). We have also incorporated a basic model of the effects of vitamin D on calcium homeostasis. We have included a simple model of the mechanism proposed by Bellido et al. (2003), Ross et al. (J Disc Cont Dyn Sys Series B 17(6):2185-2200, 2012), of the influence of PTH on osteoblast apoptosis, a mechanism that accounts for the anabolic response to pulsatile PTH administration. Finally, we have devised a simple model of the administration and effects of bisphosphonates. The biomarkers in the model are procollagen type 1 amino-terminal propeptide and C-terminal telopeptide. Bone mineral density is the model's principal endpoint.

Statistical-thermodynamic model for light scattering from eye lens protein mixtures.

We model light-scattering cross sections of concentrated aqueous mixtures of the bovine eye lens proteins γB- and α-crystallin by adapting a statistical-thermodynamic model of mixtures of spheres with short-range attractions. The model reproduces measured static light scattering cross sections, or Rayleigh ratios, of γB-α mixtures from dilute concentrations where light scattering intensity depends on molecular weights and virial coefficients, to realistically high concentration protein mixtures like those of the lens. The model relates γB-γB and γB-α attraction strengths and the γB-α size ratio to the free energy curvatures that set light scattering efficiency in tandem with protein refractive index increments. The model includes (i) hard-sphere α-α interactions, which create short-range order and transparency at high protein concentrations, (ii) short-range attractive plus hard-core γ-γ interactions, which produce intense light scattering and liquid-liquid phase separation in aqueous γ-crystallin solutions, and (iii) short-range attractive plus hard-core γ-α interactions, which strongly influence highly non-additive light scattering and phase separation in concentrated γ-α mixtures. The model reveals a new lens transparency mechanism, that prominent equilibrium composition fluctuations can be perpendicular to the refractive index gradient. The model reproduces the concave-up dependence of the Rayleigh ratio on α/γ composition at high concentrations, its concave-down nature at intermediate concentrations, non-monotonic dependence of light scattering on γ-α attraction strength, and more intricate, temperature-dependent features. We analytically compute the mixed virial series for light scattering efficiency through third order for the sticky-sphere mixture, and find that the full model represents the available light scattering data at concentrations several times those where the second and third mixed virial contributions fail. The model indicates that increased γ-γ attraction can raise γ-α mixture light scattering far more than it does for solutions of γ-crystallin alone, and can produce marked turbidity tens of degrees celsius above liquid-liquid separation.

Phantom study of tear film dynamics with optical coherence tomography and maximum-likelihood estimation.

In this Letter, we implement a maximum-likelihood estimator to interpret optical coherence tomography (OCT) data for the first time, based on Fourier-domain OCT and a two-interface tear film model. We use the root mean square error as a figure of merit to quantify the system performance of estimating the tear film thickness. With the methodology of task-based assessment, we study the trade-off between system imaging speed (temporal resolution of the dynamics) and the precision of the estimation. Finally, the estimator is validated with a digital tear-film dynamics phantom.

Mathematical methods for restricted domain ternary liquid mixture free energy determination using light scattering.

We extend methods of solution of a light scattering partial differential equation for the free energy of mixing to apply to connected, isotropic ternary liquid composition domains that do not touch all three binary axes. To do so we mathematically analyze the problem of inferring needed Dirichlet boundary data, and solving for the free energy, with use of hypothetical static light scattering measurements that correspond to dielectric composition gradient vectors that have distinct directions. The physical idea behind the technique is that contrasting absorption properties of mixture components can result in such distinctly directed dielectric composition gradient vectors, due to their differing wavelength dependences of dielectric response. At suitably chosen wavelengths, contrasting light scattering efficiency patterns in the ternary composition triangle can then correspond to the same underlying free energy, and enlarge the scope of available information about the free energy, as shown here. We show how to use distinctly directed dielectric gradients to measure the free energy on both straight lines and curves within the ternary composition triangle, so as to provide needed Dirichlet conditions for light scattering partial differential equation solution. With use of Monte Carlo simulations of noisy light scattering data, we provide estimates of the overall system measurement time and sample spacing needed to determine the free energy to a desired degree of accuracy, for various angles between the assumed dielectric gradient vectors, and indicate how the measurement time depends on instrumental throughput parameters. The present analysis methods provide a way to use static light scattering to measure, directly, mixing free energies of many systems that contain such restricted liquid domains, including aqueous solutions of biological macromolecules, micellar mixtures and microemulsions, and many small molecule systems that are important in separation technology.

The GBN-dialogue model of outgroup-negative rumor transmission: group membership, belief, and novelty.

A two-step agent-based mathematical model of negative rumor spread in the context of conflicting groups is presented. The GBN-Dialogue model builds on rumor theory, focuses on person-to-person interaction characteristics,and is dynamical. The model first estimates the probability of rumor transmission between two persons based on their transmission motivation (which is a function of their Group (G) memberships), the strengths of their belief (B) in the rumor, and the Novelty (N) of the rumor for each person. Psychological and sociological research informs this Transmission Probability Function. In the second step, belief levels and rumor novelty of each participant change as a result of rumor transmission and time; literature on attitude change guides these updating functions. Empirical support is presented by comparing rumor transmission literature with results of Monte Carlo simulations on different network topologies. The validity of the model's assumptions is addressed by comparison with simpler and more complex alternatives.

On the design of experiments for determining ternary mixture free energies from static light scattering data using a nonlinear partial differential equation.

We mathematically design sets of static light scattering experiments to provide for model-independent measurements of ternary liquid mixing free energies to a desired level of accuracy. A parabolic partial differential equation (PDE), linearized from the full nonlinear PDE [D. Ross, G. Thurston, and C. Lutzer, J. Chem. Phys. 129, 064106 (2008)], describes how data noise affects the free energies to be inferred. The linearized PDE creates a net of spacelike characteristic curves and orthogonal, timelike curves in the composition triangle, and this net governs diffusion of information coming from light scattering measurements to the free energy. Free energy perturbations induced by a light scattering perturbation diffuse along the characteristic curves and towards their concave sides, with a diffusivity that is proportional to the local characteristic curvature radius. Consequently, static light scattering can determine mixing free energies in regions with convex characteristic curve boundaries, given suitable boundary data. The dielectric coefficient is a Lyapunov function for the dynamical system whose trajectories are PDE characteristics. Information diffusion is heterogeneous and system-dependent in the composition triangle, since the characteristics depend on molecular interactions and are tangent to liquid-liquid phase separation coexistence loci at critical points. We find scaling relations that link free energy accuracy, total measurement time, the number of samples, and the interpolation method, and identify the key quantitative tradeoffs between devoting time to measuring more samples, or fewer samples more accurately. For each total measurement time there are optimal sample numbers beyond which more will not improve free energy accuracy. We estimate the degree to which many-point interpolation and optimized measurement concentrations can improve accuracy and save time. For a modest light scattering setup, a sample calculation shows that less than two minutes of measurement time is, in principle, sufficient to determine the dimensionless mixing free energy of a non-associating ternary mixture to within an integrated error norm of 0.003. These findings establish a quantitative framework for designing light scattering experiments to determine the Gibbs free energy of ternary liquid mixtures.

Mathematical and computational aspects of quaternary liquid mixing free energy measurement using light scattering.

We provide a mathematical and computational analysis of light scattering measurement of mixing free energies of quaternary isotropic liquids. In previous work, we analyzed mathematical and experimental design considerations for the ternary mixture case [D. Ross, G. Thurston, and C. Lutzer, J. Chem. Phys. 129, 064106 (2008); C. Wahle, D. Ross, and G. Thurston, J. Chem. Phys. 137, 034201 (2012)]. Here, we review and introduce dimension-free general formulations of the fully nonlinear partial differential equation (PDE) and its linearization, a basis for applying the method to composition spaces of any dimension, in principle. With numerical analysis of the PDE as applied to the light scattering implied by a test free energy and dielectric gradient combination, we show that values of the Rayleigh ratio within the quaternary composition tetrahedron can be used to correctly reconstruct the composition dependence of the free energy. We then extend the analysis to the case of a finite number of data points, measured with noise. In this context the linearized PDE describes the relevant diffusion of information from light scattering noise to the free energy. The fully nonlinear PDE creates a special set of curves in the composition tetrahedron, collections of which form characteristics of the nonlinear and linear PDEs, and we show that the information diffusion has a time-like direction along the positive normals to these curves. With use of Monte Carlo simulations of light scattering experiments, we find that for a modest laboratory light scattering setup, about 100-200 samples and 100 s of measurement time are enough to be able to measure the mixing free energy over the entire quaternary composition tetrahedron, to within an L(2) error norm of 10(-3). The present method can help quantify thermodynamics of quaternary isotropic liquid mixtures.

On inferring liquid-liquid phase boundaries and tie lines from ternary mixture light scattering.

We investigate the possibility of using light scattering data in the single-phase regions of a ternary liquid mixture phase diagram to infer ternary mixture coexistence curves, and to infer tie lines joining the compositions of isotropic liquid phases in thermodynamic equilibrium. Previous analyses of a nonlinear light scattering partial differential equation (LSPDE) show that it provides for reconstruction of ternary [D. Ross, G. Thurston, and C. Lutzer, J. Chem. Phys. 129, 064106 (2008); C. Wahle, D. Ross, and G. Thurston, J. Chem. Phys. 137, 034201 (2012)] and quaternary [C. Wahle, D. Ross, and G. Thurston, J. Chem. Phys. 137, 034202 (2012)] mixing free energies from light scattering data, and that if the coexistence curves are already known, it can also yield ternary tie lines and triangles [D. Ross, G. Thurston, and C. Lutzer, J. Chem. Phys. 129, 064106 (2008)]. Here, we show that the LSPDE can be used more generally, to infer phase boundaries and tie lines from light scattering data in the single-phase region, without prior knowledge of the coexistence curve, if the single-phase region is connected. The method extends the fact that the reciprocal light scattering intensity approaches zero at the thermodynamic spinodal. Expressing the free energy as the sum of ideal and excess parts leads to a natural family of Padé approximants for the reciprocal Rayleigh ratio. To test the method, we evaluate the single-phase reciprocal Rayleigh ratio resulting from the mean-field, regular solution model on a fine grid. We then use a low-order approximant to extrapolate the reciprocal Rayleigh ratio into metastable and unstable regions. In the metastable zone, the extrapolation estimates light scattering prior to nucleation and growth of a new phase. In the unstable zone, the extrapolation produces a negative function that in the present context is a computational convenience. The original and extrapolated reciprocal light scattering are jointly used as input to solving the LSPDE to deduce the mixing free energy and its convex hull. When projected onto the composition triangle, the boundary of the convexified part of the free energy is the phase boundary, and lines on the convexified region along which the second directional derivative is zero are the tie lines. We find that the tie lines and phase boundaries so deduced agree well with their exact values. This work is a step toward developing methods for inferring phase boundaries from real light scattering intensities measured with noise, from mixtures having compositions on a coarser grid.

Phytophthora aquimorbida sp. nov. and Phytophthora taxon 'aquatilis' recovered from irrigation reservoirs and a stream in Virginia, USA.

Two distinct subgroups (L2 and A(-2)) were recovered from irrigation reservoirs and a stream in Virginia, USA. After molecular, morphological and physiological examinations, the L2 subgroup was named Phytophthora aquimorbida and the A(-2) designated as Phytophthora taxon 'aquatilis'. Both taxa are homothallic. P. aquimorbida is characterized by its noncaducous and nonpapillate sporangia, catenulate and radiating hyphal swellings and thick-walled plerotic oospores formed in globose oogonia mostly in the absence of an antheridium. P. taxon 'aquatilis' produces plerotic oospores in globose oogonia mostly with a paragynous antheridium. It has semi-papillate, caducous sporangia with variable pedicels, but it does not have hyphal swelling. Analyses of ITS, CO1, ß-tubulin and NADH1 sequences revealed that P. aquimorbida is closely related to P. hydropathica, P. irrigata and P. parsiana, and P. taxon 'aquatilis' is related to P. multivesiculata. The optimum temperature for culture growth is 30 and 20 C for P. aquimorbida and P. taxon 'aquatilis' respectively. Both taxa were pathogenic to rhododendron plants and caused root discoloration, pale leaves, wilting, tip necrosis and dieback. Their plant biosecurity risk also is discussed.

Factors that prevent roughstock rodeo athletes from wearing protective equipment.

Using a cross-sectional survey design, this study sought to determine usage rates and barriers to the use of protective equipment in roughstock athletes. Between 2004 and 2006, amateur, collegiate, and professional roughstock athletes were surveyed using national organizational mailing lists. Findings revealed that during competition, 69% never wore a helmet. Barriers were a negative effect on performance and sport persona. Conversely, 88% always wore a vest. The perception that vest usage was required encouraged roughstock athletes to wear them. Mouthpiece use results were mixed; 58% always used and 21% never used a mouthpiece. Barriers were discomfort and frequent forgetfulness. Reported injury rate was high, with users noting fewer injuries to head and ribs than nonusers, and riders agreed that protective equipment prevented injury to the head, ribs, and mouth. However, equipment usage rates varied widely by type and seemed to be underutilized because the equipment affected performance, was uncomfortable, and "not cowboy."

Zoosporic tolerance to pH stress and its implications for Phytophthora species in aquatic ecosystems.

Phytophthora species, a group of destructive plant pathogens, are commonly referred to as water molds, but little is known about their aquatic ecology. Here we show the effect of pH on zoospore survival of seven Phytophthora species commonly isolated from irrigation reservoirs and natural waterways and dissect zoospore survival strategy. Zoospores were incubated in a basal salt liquid medium at pH 3 to 11 for up to 7 days and then plated on a selective medium to determine their survival. The optimal pHs differed among Phytophthora species, with the optimal pH for P. citricola at pH 9, the optimal pH for P. tropicalis at pH 5, and the optimal pH for the five other species, P. citrophthora, P. insolita, P. irrigata, P. megasperma, and P. nicotianae, at pH 7. The greatest number of colonies was recovered from zoospores of all species plated immediately after being exposed to different levels of pH. At pH 5 to 11, the recovery rate decreased sharply (P < or = 0.0472) after 1-day exposure for five of the seven species. In contrast, no change occurred (P > or = 0.1125) in the recovery of any species even after a 7-day exposure at pH 3. Overall, P. megasperma and P. citricola survived longer at higher rates in a wider range of pHs than other species did. These results are generally applicable to field conditions as indicated by additional examination of P. citrophthora and P. megasperma in irrigation water at different levels of pH. These results challenge the notion that all Phytophthora species inhabit aquatic environments as water molds and have significant implications in the management of plant diseases resulting from waterborne microbial contamination.

On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data.

In this paper we present a method for determining the free energies of ternary mixtures from light scattering data. We use an approximation that is appropriate for liquid mixtures, which we formulate as a second-order nonlinear partial differential equation. This partial differential equation (PDE) relates the Hessian of the intensive free energy to the efficiency of light scattering in the forward direction. This basic equation applies in regions of the phase diagram in which the mixtures are thermodynamically stable. In regions in which the mixtures are unstable or metastable, the appropriate PDE is the nonlinear equation for the convex hull. We formulate this equation along with continuity conditions for the transition between the two equations at cloud point loci. We show how to discretize this problem to obtain a finite-difference approximation to it, and we present an iterative method for solving the discretized problem. We present the results of calculations that were done with a computer program that implements our method. These calculations show that our method is capable of reconstructing test free energy functions from simulated light scattering data. If the cloud point loci are known, the method also finds the tie lines and tie triangles that describe thermodynamic equilibrium between two or among three liquid phases. A robust method for solving this PDE problem, such as the one presented here, can be a basis for optical, noninvasive means of characterizing the thermodynamics of multicomponent mixtures.

A quantitative evaluation of the iron-sulfur world and its relevance to life's origins.

The significance of Wächtershäuser's iron-sulfur world to the origin of life and the limits to its notional autocatalytic cycles are examined in kinetic simulations of the chain polymerization sequence: primitive materials-->amino acids-->oligomers. The simulations were run for the formation of all oligomers up to the 20-mer over a 1 Gy interval from the end of the period of heavy bombardment, during which period life emerged. Upper-limit rate constant estimates developed from the studies of Huber and Wächtershäuser were employed. The simulations showed that oligomer production consistent with life's start within that interval emerges only with an autocatalyst exhibiting a catalytic proficiency comparable to that of contemporary enzymes. The simulations, moreover, ignored likely thermodynamic and statistical burdens which, if included, would have led to the need for catalytic capacities well in excess of those in present-day enzymes. Prebiotic oligomers with such levels of activity are clearly not likely, and it is apparent that the iron-sulfur scheme could not have played a role in life's beginnings.

Model for screened, charge-regulated electrostatics of an eye lens protein: Bovine gammaB-crystallin.

We model screened, site-specific charge regulation of the eye lens protein bovine gammaB-crystallin (γB) and study the probability distributions of its proton occupancy patterns. Using a simplified dielectric model, we solve the linearized Poisson-Boltzmann equation to calculate a 54×54 work-of-charging matrix, each entry being the modeled voltage at a given titratable site, due to an elementary charge at another site. The matrix quantifies interactions within patches of sites, including γB charge pairs. We model intrinsic pK values that would occur hypothetically in the absence of other charges, with use of experimental data on the dependence of pK values on aqueous solution conditions, the dielectric model, and literature values. We use Monte Carlo simulations to calculate a model grand-canonical partition function that incorporates both the work-of-charging and the intrinsic pK values for isolated γB molecules and we calculate the probabilities of leading proton occupancy configurations, for 4

Dry/Wet Cycling and the Thermodynamics and Kinetics of Prebiotic Polymer Synthesis.

The endoergic nature of protein and nucleic acid assembly in aqueous media presents two questions that are fundamental to the understanding of life's origins: (i) how did the polymers arise in an aqueous prebiotic world; and (ii) once formed in some manner, how were they sufficiently persistent to engage in further chemistry. We propose here a quantitative resolution of these issues that evolved from recent accounts in which RNA-like polymers were produced in evaporation/rehydration cycles. The equilibrium Nm + Nn ↔ Nm+n + H2O is endoergic by about 3.3 kcal/mol for polynucleotide formation, and the system thus lies far to the left in the starting solutions. Kinetic simulations of the evaporation showed that simple Le Châtelier's principle shifts were insufficient, but the introduction of oligomer-stabilizing factors of 5-10 kcal/mol both moved the process to the right and respectively boosted and retarded the elongation and hydrolysis rates. Molecular crowding and excluded volume effects in present-day cells yield stabilizing factors of that order, and we argue here that the crowded conditions in the evaporites generate similar effects. Oligomer formation is thus energetically preferred in those settings, but the process is thwarted in each evaporation step as diffusion becomes rate limiting. Rehydration dissipates disordered oligomer clusters in the evaporites, however, and subsequent dry/wet cycling accordingly "ratchets up" the system to an ultimate population of kinetically trappedthermodynamically preferred biopolymers.

Preclinical Experimental and Mathematical Approaches for Assessing Effective Doses of Inhaled Drugs, Using Mometasone to Support Human Dose Predictions.

BACKGROUND: Understanding the relationship between dose, lung exposure, and drug efficacy continues to be a challenging aspect of inhaled drug development. An experimental inhalation platform was developed using mometasone furoate to link rodent lung exposure to its in vivo pharmacodynamic (PD) effects. METHODS: We assessed the effect of mometasone delivered directly to the lung in two different rodent PD models of lung inflammation. The data obtained were used to develop and evaluate a mathematical model to estimate drug dissolution, transport, distribution, and efficacy, following inhaled delivery in rodents and humans. RESULTS: Mometasone directly delivered to the lung, in both LPS and Alternaria alternata rat models, resulted in dose dependent inhibition of BALf cellular inflammation. The parameters for our mathematical model were calibrated to describe the observed lung and systemic exposure profiles of mometasone in humans and in animal models. We found that physicochemical properties, such as lung fluid solubility and lipophilicity, strongly influenced compound distribution and lung retention. CONCLUSIONS: Presently, we report on a novel and sophisticated mathematical model leading to improvements in a current inhaled drug development practices by providing a quantitative understanding of the relationship between PD effects and drug concentration in lungs.

Exchange of tears under a contact lens is driven by distortions of the contact lens.

We studied the flow of the post-lens tear film under a soft contact lens to understand how the design parameters of contact lenses can affect ocular health. When a soft contact lens is inserted, the blinking eyelid causes the lens to stretch in order to conform to the shape of the eye. The deformed contact lens acts to assume its un-deformed shape and thus generates a suction pressure in the post-lens tear film. In consequence, the post-lens tear fluid moves; it responds to the suction pressure. The suction pressure may draw in fresh fluid from the edge of the lens, or it may eject fluid there, as the lens reassumes its un-deformed shape. In this article, we develop a mathematical model of the flow of the post-lens tear fluid in response to the mechanical suction pressure of a deformed contact lens. We predict the amount of exchange of fluid exchange under a contact lens and we explore the influence of the eye's shape on the rate of exchange of fluid.

Action in the event tent! Medical-legal issues facing the volunteer event physician.

CONTEXT: Physicians need to consider medical-legal issues when volunteering their time to assist with community mass-participation and athletic events. This article also reviews medical-legal aspects of the volunteer physician's out-of-state practice. Seven cases illustrate the importance of expertise and planning to avoid legal issues for the volunteer event physician. EVIDENCE ACQUISITION: Relevant studies, expert opinion, medical-legal legislation, and medical-legal cases were reviewed. RESULTS: Physicians typically make 4 common assumptions regarding these types of events: Good Samaritan legislation, event liability insurance, personal liability insurance, and waivers. We discuss the intent of these assumptions and the reality of how, or how not, they provide any protection to the volunteer event physician. CONCLUSION: The intent of this article is to make physicians aware of medial-legal issues when volunteering their time for community and athletic events.