A mass action model of a fibroblast growth factor signaling pathway and its simplification

We consider a kinetic law of mass action model for Fibroblast Growth Factor (FGF) signaling, focusing on the induction of the RAS-MAP kinase pathway via GRB2 binding. Our biologically simple model suffers a combinatorial explosion in the number of differential equations required to simulate the system. In addition to numerically solving the full model, we show that it can be accurately simplified. This requires combining matched asymptotics, the quasi-steady state hypothesis, and the fact subsets of the equations decouple asymptotically. Both the full and simplified models reproduce the qualitative dynamics observed experimentally and in previous stochastic models. The simplified model also elucidates both the qualitative features of GRB2 binding and the complex relationship between SHP2 levels, the rate SHP2 induces dephosphorylation and levels of bound GRB2. In addition to providing insight into the important and redundant features of FGF signaling, such work further highlights the usefulness of numerous simplification techniques in the study of mass action models of signal transduction, as also illustrated recently by Borisov and co-workers (Borisov et al. in Biophys. J. 89, 951–66, 2005, Biosystems 83, 152–66, 2006; Kiyatkin et al. in J. Biol. Chem. 281, 19925–9938, 2006). These developments will facilitate the construction of tractable models of FGF signaling, incorporating further biological realism, such as spatial effects or realistic binding stoichiometries, despite a more severe combinatorial explosion associated with the latter

A solute gradient in the tear meniscus I. A hypothesis to explain Marx's line

Marx's line is a line of mucosal staining behind the mucocutaneous junction. It can be demonstrated throughout life in all normal lids by staining with lissamine green and related dyes. Of all the body orifices, only the mucosae of the eye and mouth are directly exposed to the atmosphere. In this paper, we suggest that for the eye, this exposure leads to the formation of Marx's line. The tear meniscus thins progressively toward its apex, where it is pinned at the mucocutaneous junction of the lid. It also thins toward the black line, which segregates the meniscus from the tear film after the blink. We predict that, because of the geometry of the tear meniscus, evaporation generates a solute gradient across the meniscus profile in the anteroposterior plane, which peaks at the meniscus apices at the end of the interblink. One outcome would be to amplify the level of tear molarity at these sites so that they reach hyperosmolar proportions. Preliminary mathematical modeling suggests that dilution of this effect by advection and diffusion of solute away from the meniscus apex at the mucocutaneous junction will be restricted by spatial constraints, the presence of tear and surface mucins at this site, and limited fluid flow. We conclude that evaporative water loss from the tear meniscus may result in a physiological zone of hyperosmolar and related stresses to the occlusal conjunctiva, directly behind the mucocutaneous junction. We hypothesize that this stimulates a high epithelial cell turnover at this site, incomplete epithelial maturation, and a failure to express key molecules such as MUC 16 and galectin-3, which, with the tight junctions between surface epithelial cells, are necessary to seal the ocular surface and prevent penetration of dyes and other molecules into the epithelium. This is proposed as the basis for Marx's line. In Part II of this paper (also published in this issue of The Ocular Surface), we address additional pathophysiological consequences of this mechanism, affecting lid margins

A solute gradient in the tear meniscus II. implications for lid margin disease, including meibomian gland dysfunction

We have hypothesized previously that evaporation from the tears generates a solute gradient across the tear meniscus, which delivers hyperosmolar stress to the mucocutaneous junction (MCJ) of the lid margin. This is proposed as the basis for Marx's line, a line of staining with topically applied dyes that lies directly behind the MCJ. In this article, we consider the implications of this hypothesis for progressive damage to the lid margin as an age-related phenomenon, its amplification in dry eye states, and its possible role in the etiology of meibomian gland dysfunction (MGD). It is suggested that a hyperosmolar or related stimulus, acting behind the MCJ over a lifetime, promotes the anterior migration of the MCJ, which is a feature of the aging lid margin. This mechanism would be amplified in dry eye states, not only by reason of increased tear molarity at the meniscus apex but also by raising the concentration of inflammatory peptides at this site. This could explain the increased width and irregularity of Marx's line in dry eye. While the presence of stem cells at the lid margin may equip this region to respond to such stress, their depletion could be the basis of irreversible lid margin damage. It is further proposed, given the proximity of the MCJ to the meibomian gland orifices, that the solute gradient mechanism could play a role in the initiation of MGD by delivering hyperosmolar and inflammatory stresses to the terminal ducts and orifices of the glands. By the same token, the presence of a zone of increased epithelial permeability in this region may provide a back door route for the delivery of drugs in the treatment of MGD

A mass and solute balance model for tear volume & osmolarity in the normal and the dry eye

Tear hyperosmolarity is thought to play a key role in the mechanism of dry eye, a common symptomatic condition accompanied by visual disturbance, tear film instability, inflammation and damage to the ocular surface. We have constructed a model for the mass and solute balance of the tears, with parameter estimation based on extensive data from the literature which permits the influence of tear evaporation, lacrimal flux and blink rate on tear osmolarity to be explored. In particular the nature of compensatory events has been estimated in aqueous-deficient (ADDE) and evaporative (EDE) dry eye.\ud \ud The model reproduces observed osmolarities of the tear meniscus for the healthy eye and predicts a higher concentration in the tear film than meniscus in normal and dry eye states. The differential is small in the normal eye, but is significantly increased in dry eye, especially for the simultaneous presence of high meniscus concentration and low meniscus radius. This may influence the interpretation of osmolarity values obtained from meniscus samples since they need not fully reflect potential damage to the ocular surface caused by tear film hyperosmolarity.\ud \ud Interrogation of the model suggests that increases in blink rate may play a limited role in compensating for a rise in tear osmolarity in ADDE but that an increase in lacrimal flux, together with an increase in blink rate, may delay the development of hyperosmolarity in EDE. Nonetheless, it is predicted that tear osmolarity may rise to much higher levels in EDE than ADDE before the onset of tear film breakup, in the absence of events at the ocular surface which would independently compromise tear film stability. Differences in the predicted responses of the pre-ocular tears in ADDE compared to EDE or hybrid disease to defined conditions suggest that no single, empirically-accessible variable can act as a surrogate for tear film concentration and the potential for ocular surface damage. This emphasises the need to measure and integrate multiple diagnostic indicators to determine outcomes and prognosis. Modelling predictions in addition show that further studies concerning the possibility of a high lacrimal flux phenotype in EDE are likely to be profitable

Report from the pandemic influenza project: expert panel meetings

This report was prepared by the Indiana University Center for Bioethics under contract with the Indiana State Department of Health as a part of the project “Translating Ethics Advice into Practice: Public and Professional Outreach about Pandemic Influenza Planning in Indiana.” The views expressed in this document are those of the authors and may not necessarily reflect the opinions of the Center for Bioethics, Indiana University, or the Indiana State Department of Health.The Indiana University Center for Bioethics convened expert panels for each of the four topics of the Technical Advisory Documents (TADs): altered standards of care, triage, vaccine and antiviral allocation, and healthcare workforce management. The goal of each meeting was to assess the relevance and applicability of the recommendations put forth by the TADs. Participants were encouraged to apply the seven ethical points and assess the feasibility of the recommendations by examining case studies intended to portray real world ethical dilemmas. Engagement from the public was critical for each panel to learn the full ethical and social implications of pandemic influenza preparedness and planning.Indiana University Center for Bioethics; Indiana State Department of Healt

Incorporating spatial correlations into multispecies mean-field models

In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modeling interactions between such species, we often make use of the mean-field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean-field approximation is only used in appropriate settings. In circumstances where the mean-field approximation is unsuitable, we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper, we provide a method that overcomes many of the failures of the mean-field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multispecies case and show results specific to a two-species problem. We compare averaged discrete results to both the mean-field approximation and our improved method, which incorporates spatial correlations. We note that the mean-field approximation fails dramatically in some cases, predicting very different behavior from that seen upon averaging multiple realizations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behavior in all cases, thus providing a more reliable modeling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques

Measurement of cone dark adaptation: a comparison of four psychophysical methods

Purpose: Dark adaptometry is an important clinical tool for the diagnosis of a range of conditions, including age-related macular degeneration (AMD). In order to identify the most robust, clinically applicable technique for the measurement of cone dark adaptation, the repeatability and agreement of four psychophysical methods were assessed. Methods: Data were obtained from 31 healthy adults on two occasions, using four psychophysical methods. Participants’ pupils were dilated and 96% of cone photopigment was bleached before threshold was monitored in the dark using one of the techniques, selected at random. This procedure was repeated for each of the remaining methods. An exponential recovery function was fitted to all threshold recovery data. The co-efficient of repeatability (CoR) was calculated to assess the repeatability of the methods and a repeated measures analysis of variance (ANOVA) was used to compare mean recovery parameters. Results: All four methods demonstrated a similar level of inter-session repeatability for measurement of cone recovery, yielding CoRs between 1.18 and 1.56 minutes. There were no statistically significant differences in estimates of mean time constant of cone recovery (cone τ) between the four methods (p = 0.488), however significant differences initial and final cone thresholds were reported (p < 0.005). Conclusions: All of the techniques were capable of monitoring the rapid changes in visual threshold that occur during cone dark adaptation and the repeatability of the techniques was similar. This indicates that, despite the respective advantages and disadvantages of these psychophysical techniques, all four methods would be suitable for measuring cone dark adaptation in clinical practice

The effect of pre-adapting light intensity on dark adaptation in early age-related macular degeneration

Background This study aimed to identify the pre-adapting light intensity that generated the maximum separation in the parameters of dark adaptation between participants with early age-related macular degeneration (AMD) and healthy control participants in the minimum recording time. Methods Cone dark adaptation was monitored in 10 participants with early AMD and 10 age-matched controls after exposure to three pre-adapting light intensities, using an achromatic annulus (12° radius) centred on the fovea. Threshold recovery data were modelled, and the time constant of cone recovery (τ), final cone threshold, and time to rod-cone-break (RCB) were determined. The diagnostic potential of these parameters at all pre-adapting intensities was evaluated by constructing receiver operating characteristic (ROC) curves. Results There were significant differences between those with early AMD and healthy controls in cone τ and time to RCB (p < 0.05) at all pre-adapting ‘bleaching’ intensities. ROC curves showed that the diagnostic potential of dark adaptometry was high following exposure to all three pre-adapting intensities, generating an area under the curve in excess of 0.87 ± 0.08 for cone τ and time to RCB for all conditions. Conclusions Dark adaptation was shown to be highly diagnostic for early AMD across a range of pre-adapting light intensities, and therefore, the lower pre-adapting intensities evaluated in this study may be used to expedite dark adaptation measurement in the clinic without compromising the integrity of the data obtained. This study reinforces the suggestion that cone and rod dark adaptation are good candidate biomarkers for early AMD

Roll-to-roll dip coating of three different PIMs for Organic Solvent Nanofiltration

PIM-1, PIM-7, and PIM-8 composite membranes have been fabricated for Organic Solvent Nanofiltration (OSN) on two different support membranes. Both support membranes, PAN and crosslinked Ultem 1000, displayed pore sizes within the range of 20–25 nm as characterised by gas liquid porometry. PIM layers of < 500 nm thickness were formed from dip coating on a roll-to-roll pilot line. The resultant composite membranes exhibited typical MWCOs in the region of 500–800 g mol−1. The quality of coating obtained on the crosslinked Ultem 1000 support membrane was consistently higher for all three PIMs than that obtained on the PAN membrane. The PIM composite membranes coated on to crosslinked Ultem 1000 were stable in a wider range of solvents than those on the PAN support. OSN testing in a model system with isomeric alkane solutes verified that manipulated changes to the molecular architecture of the polymer backbone resulted in a higher separation factor between straight and branched alkane isomers

Blade loss transient dynamics analysis, volume 2. Task 2: Theoretical and analytical development. Task 3: Experimental verification

The component element method was used to develop a transient dynamic analysis computer program which is essentially based on modal synthesis combined with a central, finite difference, numerical integration scheme. The methodology leads to a modular or building-block technique that is amenable to computer programming. To verify the analytical method, turbine engine transient response analysis (TETRA), was applied to two blade-out test vehicles that had been previously instrumented and tested. Comparison of the time dependent test data with those predicted by TETRA led to recommendations for refinement or extension of the analytical method to improve its accuracy and overcome its shortcomings. The development of working equations, their discretization, numerical solution scheme, the modular concept of engine modelling, the program logical structure and some illustrated results are discussed. The blade-loss test vehicles (rig full engine), the type of measured data, and the engine structural model are described