An intrinsic compartmentalization code for peripheral membrane proteins in photoreceptor neurons.

In neurons, peripheral membrane proteins are enriched in subcellular compartments, where they play key roles, including transducing and transmitting information. However, little is known about the mechanisms underlying their compartmentalization. To explore the roles of hydrophobic and electrostatic interactions, we engineered probes consisting of lipidation motifs attached to fluorescent proteins by variously charged linkers and expressed them in Xenopus rod photoreceptors. Quantitative live cell imaging showed dramatic differences in distributions and dynamics of the probes, including presynapse and ciliary OS enrichment, depending on lipid moiety and protein surface charge. Opposing extant models of ciliary enrichment, most probes were weakly membrane bound and diffused through the connecting cilium without lipid binding chaperone protein interactions. A diffusion-binding-transport model showed that ciliary enrichment of a rhodopsin kinase probe occurs via recycling as it perpetually leaks out of the ciliary OS. The model accounts for weak membrane binding of peripheral membrane proteins and a leaky connecting cilium diffusion barrier.

Modeling solute reactivity in a phreatic solution conduit penetrating a karst aquifer.

A two-dimensional model for solute migration, transformation, and deposition in a phreatic solution conduit penetrating a karst aquifer is presented in which the solute is anthropogenic to the natural system. Transformation of a reacting solute in a solution conduit has generally been accepted as likely occurring but actual physical measurements and mathematical analyses of the suspected process have been generally minimally investigated, primarily because of the logistical difficulties and complexities associated with solute transport through solution conduits. The model demonstrates how a reacting solute might decay or be transformed to a product solute some of which then migrates via radial dispersion to the conduit wall where it may become adsorbed. Model effects vary for laminar flow and turbulent flow in the axial direction. Dispersion in the radial direction also exhibits marked differences for both laminar flow and turbulent flow. Reaction zones may enhance subsequent reactions due to some overlap resulting from the longitudinal dispersion caused by flow in the axial direction. Simulations showed that varying the reaction rate coefficient strongly affects solute reactions, but that varying deposition coefficients had only minimal impacts. The model was applied to a well-known tracer test that used the tracer dye, Rhodamine WT, which readily converts to deaminoalkylated Rhodamine WT after release, to illustrate how the model may be used to suggest one possible cause, in addition to other possible causes, for less than 100 tracer-mass recovery. In terms of pollutants in a karst aquifer the model also suggests one possible mechanism for pollutant transformation in a solution conduit.

Methadone Recycling Sustains Drug Reservoir in Tissue.

We hypothesize that there is a tissue store of methadone content in humans that is not directly accessible, but is quantifiable. Further, we hypothesize the mechanism by which methadone content is sustained in tissue stores involves methadone uptake, storage, and release from tissue depots in the body (recycling). Accordingly, we hypothesize that such tissue stores, in part, determine plasma methadone levels. We studied a random sample of six opioid-naïve healthy subjects. We performed a clinical trial simulation in silico using pharmacokinetic modeling. We found a large tissue store of methadone content whose size was much larger than methadone's size in plasma in response to a single oral dose of methadone 10 mg. The tissue store measured 13-17 mg. This finding could only be explained by the contemporaneous storage of methadone in tissue with dose recycling. We found that methadone recycles 2-5 times through an inaccessible extravascular compartment (IAC), from an accessible plasma-containing compartment (AC), before exiting irreversibly. We estimate the rate of accumulation (or storage) of methadone in tissue was 0.029-7.29 mg/h. We predict 39 ± 13% to 83 ± 6% of methadone's tissue stores "spillover" into the circulation. Our results indicate that there exists a large quantifiable tissue store of methadone in humans. Our results support the notion that methadone in humans undergoes tissue uptake, storage, release into the circulation, reuptake from the circulation, and re-release into the circulation, and that spillover of methadone from tissue stores, in part, maintain plasma methadone levels in humans.

In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis.

BACKGROUND: There is a need to have a model to study methadone's losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. AIM: To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). METHODOLOGY: We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone's overall intradialytic mass transfer rate coefficient, km ; and, methadone's removal rate, j ME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. RESULTS: The ODE/PDE model revealed a significant increase in the change of methadone's mass transfer with increased dialysate flow rate, %Δkm =18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone's mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone's removal during dialysis. The absolute value of the prediction errors for methadone's extraction and throughput were less than 2%. CONCLUSION: ODE/PDE modeling of methadone's hemodialysis is a new approach to study methadone's removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone's mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model predictive control during dialysis in humans.

CYP2D6 phenotype-specific codeine population pharmacokinetics.

Codeine's metabolic fate in the body is complex, and detailed quantitative knowledge of it, and that of its metabolites is lacking among prescribers. We aimed to develop a codeine pharmacokinetic pathway model for codeine and its metabolites that incorporates the effects of genetic polymorphisms. We studied the phenotype-specific time courses of plasma codeine, codeine-6-glucoronide, morphine, morphine-3-glucoronide, and morphine-6-glucoronide. A codeine pharmacokinetic pathway model accurately fit the time courses of plasma codeine and its metabolites. We used this model to build a population pharmacokinetic codeine pathway model. The population model indicated that about 10% of a codeine dose was converted to morphine in poor-metabolizer phenotype subjects. The model also showed that about 40% of a codeine dose was converted to morphine in EM subjects, and about 51% was converted to morphine in ultrarapid-metabolizers. The population model further indicated that only about 4% of MO formed from codeine was converted to morphine-6-glucoronide in poor-metabolizer phenotype subjects. The model also showed that about 39% of the MO formed from codeine was converted to morphine-6-glucoronide in extensive-metabolizer phenotypes, and about 58% was converted in ultrarapid-metabolizers. We conclude, a population pharmacokinetic codeine pathway model can be useful because beyond helping to achieve a quantitative understanding the codeine and MO pathways, the model can be used for simulation to answer questions about codeine's pharmacogenetic-based disposition in the body. Our study suggests that pharmacogenetics for personalized dosing might be most effectively advanced by studying the interplay between pharmacogenetics, population pharmacokinetics, and clinical pharmacokinetics.

Organ-specific microcirculatory mass transport of oxycodone in humans: clinical implications for therapeutic use.

OBJECTIVES: To begin to address the problem of heterogeneity of distribution of oxycodone (OC) in humans, we developed an organ-specific microcirculatory capillary-tissue exchange 2-compartment model for studying regional OC mass transport. MATERIALS AND METHODS: The model was developed in silico. It quantifies OC's organ-specific mass transport rates, clearances and recycling, and it considers the effects of blood flow on OC's convective and diffusive transport. RESULTS: What is new is the finding that OC undergoes local recycling at the level of organ-specific capillary-tissue exchange units in humans. Results indicate recycled OC occurs in sufficient amounts to function as a reusable source of circulating OC; which has important implications for OC dosing. Results show the brain, which is central to OC effects only receives about 8% of OC delivered to all organs via the microcirculation. This suggests that differential regulation of receptor binding, trafficking, internalization, or desensitization in the brain likely plays a dominant role in OC's central analgesic effects. DISCUSSION: Organ-specific OC mass transport kinetics provide new information for OC dosing in pain management. The model promotes patient safety in opioid prescribing because it allows predictions to be made about the relative contribution that OC recycling makes to circulating OC levels. The model indicates that pharmacologic modulation of the microcirculation may give way to site-specific delivery of opioids in the future. Our study demonstrates that translation of bench in silico research data into clinical practice, although still challenging, is feasible and can assist in OC dose regimen design for patient safety.

ODE/PDE analysis of corneal curvature.

The starting point for this paper is a nonlinear, two-point boundary value ordinary differential equation (BVODE) that defines corneal curvature according to a static force balance. A numerical solution to the BVODE is computed by first converting the BVODE to a parabolic partial differential equation (PDE) by adding an initial value (t, pseudo-time) derivative to the BVODE. A numerical solution to the PDE is then computed by the method of lines (MOL) with the calculation proceeding to a sufficiently large value of t such that the derivative in t reduces to essentially zero. The PDE solution at this point is also the solution for the BVODE. This procedure is implemented in R (an open source scientific programming system) and the programming is discussed in some detail. A series approximation to the solution is derived from which an estimate for the rate of convergence is obtained. This is compared to a fitted exponential model. Also, two linear approximations are derived, one of which leads to a closed form solution. Both provide solutions very close to that obtained from the full nonlinear model. An estimate for the cornea radius of curvature is also derived. The paper concludes with a discussion of the features of the solution to the ODE/PDE system.

Oxycodone recycling: a novel hypothesis of opioid tolerance development in humans.

We hypothesize that oxycodone (OC) recycling promotes sustained synaptic OC content, which prolongs OC's exposure to local µ-opioid receptors (µORs). In that way, OC recycling gives rise to OC tolerance in humans. To pilot test our hypothesis, we developed a whole-body OC mass transport tolerance recovery model. The model derived quantifiable measure of tolerance is TΩ. TΩ estimates OC's tolerance recovery in days; It is defined as the rate of recovery of OC's pharmacologic response after OC is stopped. We studied a random sample of five opioid intolerant healthy male subjects with no history of opioid or illicit drug use, or comorbidities in silico. Subjects were age 24.5 ± 2.3 yr (all values mean ± SD), weight 93 ± 20 kg, and CYP2D6 EM phenotype. Each subject was studied under two experimental conditions: (1) administration of a single oral dose of OC 12 ± 7 mg; and, after complete washout of OC from the intravascular pool, (2) administration of repetitive oral OC doses every 4h for 5 half-lives (t1/2 = 4.5h)-after which time steady-state was assumed. Repetitive OC dose TΩ fell 61% compared to single OC dose TΩ (5.2 ± 1.1 vs. 3.5 ± 0.7 days, p = 0.001). The fall in TΩ was associated with a significant 3-fold increase in extravascular OC content, which was accompanied by 2-fold increase in OC spillover from the extravascular pool, into the intravascular pool. Thus, the model predicted that a single dose of orally administered OC could give rise to tolerance. This is consistent with the widely held view of acute opioid tolerance. In addition, the dynamic changes accompanying repetitive OC dosing suggested that local unbound OC gave rise to both higher extravascular OC content and increased OC spillover. This reflects that OC stimulated endocytosis of µORs was accompanied by a reduction in the availability OC responsive neuroeffector cell surface µOR binding sites. We conclude that our hypothesis extends current concepts of opioid tolerance development to include OC recycling. OC recycling is a novel hypothesis of OC tolerance development in humans.

A transit compartment model unmasks OxyContin's reflective pharmacokinetics from urine measurements in humans.

The absorption pattern of orally administered OxyContin (OXC) reflected in urine indicates that its appearance into systemic circulation undergoes transit absorption delays. The authors developed an OXC transit-delay compartment model that identified a new source of oxycodone hydrochloride (OC): the rate of appearance of OC due to OXC tablet dissolution in transit through the gastrointestinal (GI) tract (R(a)(GI)), which is due to disintegration of OXC's AcroContin delivery system. R(a)(GI) is independent of the biphasic dissolution and release of OC from the delivery system. The authors conclude that an OXC transit-delay compartment model can be of value in the interpretation of OXC pharmacokinetics.

Impact of signaling microcompartment geometry on GPCR dynamics in live retinal photoreceptors.

G protein-coupled receptor (GPCR) cascades rely on membrane protein diffusion for signaling and are generally found in spatially constrained subcellular microcompartments. How the geometry of these microcompartments impacts cascade activities, however, is not understood, primarily because of the inability of current live cell-imaging technologies to resolve these small structures. Here, we examine the dynamics of the GPCR rhodopsin within discrete signaling microcompartments of live photoreceptors using a novel high resolution approach. Rhodopsin fused to green fluorescent protein variants, either enhanced green fluorescent protein (EGFP) or the photoactivatable PAGFP (Rho-E/PAGFP), was expressed transgenically in Xenopus laevis rod photoreceptors, and the geometries of light signaling microcompartments formed by lamellar disc membranes and their incisure clefts were resolved by confocal imaging. Multiphoton fluorescence relaxation after photoconversion experiments were then performed with a Ti-sapphire laser focused to the diffraction limit, which produced small sub-cubic micrometer volumes of photoconverted molecules within the discrete microcompartments. A model of molecular diffusion was developed that allows the geometry of the particular compartment being examined to be specified. This was used to interpret the experimental results. Using this unique approach, we showed that rhodopsin mobility across the disc surface was highly heterogeneous. The overall relaxation of Rho-PAGFP fluorescence photoactivated within a microcompartment was biphasic, with a fast phase lasting several seconds and a slow phase of variable duration that required up to several minutes to reach equilibrium. Local Rho-EGFP diffusion within defined compartments was monotonic, however, with an effective lateral diffusion coefficient D(lat) = 0.130 ± 0.012 µm(2)s(-1). Comparison of rhodopsin-PAGFP relaxation time courses with model predictions revealed that microcompartment geometry alone may explain both fast local rhodopsin diffusion and its slow equilibration across the greater disc membrane. Our approach has for the first time allowed direct examination of GPCR dynamics within a live cell signaling microcompartment and a quantitative assessment of the impact of compartment geometry on GPCR activity.

Diffusion of a soluble protein, photoactivatable GFP, through a sensory cilium.

Transport of proteins to and from cilia is crucial for normal cell function and survival, and interruption of transport has been implicated in degenerative and neoplastic diseases. It has been hypothesized that the ciliary axoneme and structures adjacent to and including the basal bodies of cilia impose selective barriers to the movement of proteins into and out of the cilium. To examine this hypothesis, using confocal and multiphoton microscopy we determined the mobility of the highly soluble photoactivatable green fluorescent protein (PAGFP) in the connecting cilium (CC) of live Xenopus retinal rod photoreceptors, and in the contiguous subcellular compartments bridged by the CC, the inner segment (IS) and the outer segment (OS). The estimated axial diffusion coefficients are D(CC) = 2.8 +/- 0.3, D(IS) = 5.2 +/- 0.6, and D(OS) = 0.079 +/- 0.009 microm(2) s(-1). The results establish that the CC does not pose a major barrier to protein diffusion within the rod cell. However, the results also reveal that axial diffusion in each of the rod's compartments is substantially retarded relative to aqueous solution: the axial diffusion of PAGFP was retarded approximately 18-, 32- and 1,000-fold in the IS, CC, and OS, respectively, with approximately 20-fold of the reduction in the OS attributable to tortuosity imposed by the lamellar disc membranes. Previous investigation of PAGFP diffusion in passed, spherical Chinese hamster ovary cells yielded D(CHO) = 20 microm(2) s(-1), and estimating cytoplasmic viscosity as D(aq)/D(CHO) = 4.5, the residual 3- to 10-fold reduction in PAGFP diffusion is ascribed to sub-optical resolution structures in the IS, CC, and OS compartments.

Light-driven translocation of signaling proteins in vertebrate photoreceptors.

The dynamic localization of proteins within cells is often determined by environmental stimuli. In retinal photoreceptors, light exposure results in the massive translocation of three key signal transduction proteins, transducin, arrestin and recoverin, into and out of the outer segment compartment where phototransduction takes place. This phenomenon has rapidly taken the center stage of photoreceptor cell biology, thanks to the introduction of new quantitative and transgenic approaches. Here, we discuss evidence that intracellular protein translocation contributes to adaptation of photoreceptors to diurnal changes in ambient light intensity and summarize the current debate on whether it is driven by diffusion or molecular motors.