DISTING: A web application for fast algorithmic computation of alternative indistinguishable linear compartmental models.

BACKGROUND AND OBJECTIVES: We describe and illustrate use of DISTING, a novel web application for computing alternative structurally identifiable linear compartmental models that are input-output indistinguishable from a postulated linear compartmental model. Several computer packages are available for analysing the structural identifiability of such models, but DISTING is the first to be made available for assessing indistinguishability. METHODS: The computational algorithms embedded in DISTING are based on advanced versions of established geometric and algebraic properties of linear compartmental models, embedded in a user-friendly graphic model user interface. Novel computational tools greatly speed up the overall procedure. These include algorithms for Jacobian matrix reduction, submatrix rank reduction, and parallelization of candidate rank computations in symbolic matrix analysis. RESULTS: The application of DISTING to three postulated models with respectively two, three and four compartments is given. The 2-compartment example is used to illustrate the indistinguishability problem; the original (unidentifiable) model is found to have two structurally identifiable models that are indistinguishable from it. The 3-compartment example has three structurally identifiable indistinguishable models. It is found from DISTING that the four-compartment example has five structurally identifiable models indistinguishable from the original postulated model. This example shows that care is needed when dealing with models that have two or more compartments which are neither perturbed nor observed, because the numbering of these compartments may be arbitrary. CONCLUSIONS: DISTING is universally and freely available via the Internet. It is easy to use and circumvents tedious and complicated algebraic analysis previously done by hand.

Alternative to Ritt's pseudodivision for finding the input-output equations of multi-output models.

Differential algebra approaches to structural identifiability analysis of a dynamic system model in many instances heavily depend upon Ritt's pseudodivision at an early step in analysis. The pseudodivision algorithm is used to find the characteristic set, of which a subset, the input-output equations, is used for identifiability analysis. A simpler algorithm is proposed for this step, using Gröbner Bases, along with a proof of the method that includes a reduced upper bound on derivative requirements. Efficacy of the new algorithm is illustrated with several biosystem model examples.

Simulation of post-thyroidectomy treatment alternatives for triiodothyronine or thyroxine replacement in pediatric thyroid cancer patients.

BACKGROUND: As in adults, thyroidectomy in pediatric patients with differentiated thyroid cancer is often followed by (131)I remnant ablation. A standard protocol is to give normalizing oral thyroxine (T(4)) or triiodothyronine (T(3)) after surgery and then withdraw it for 2 to 6 weeks. Thyroid remnants or metastases are treated most effectively when serum thyrotropin (TSH) is high, but prolonged withdrawals should be avoided to minimize hypothyroid morbidity. METHODS: A published feedback control system model of adult human thyroid hormone regulation was modified for children using pediatric T(4) kinetic data. The child model was developed from data for patients ranging from 3 to 9 years old. We simulated a range of T(4) and T(3) replacement protocols for children, exploring alternative regimens for minimizing the withdrawal period, while maintaining normal or suppressed TSH during replacement. The results are presented with the intent of providing a quantitative basis to guide further studies of pediatric treatment options. Replacement was simulated for up to 3 weeks post-thyroidectomy, followed by various withdrawal periods. T(4) vs. T(3) replacement, remnant size, dose size, and dose frequency were tested for effects on the time for TSH to reach 25 mU/L (withdrawal period). RESULTS: For both T(3) and T(4) replacement, higher doses were associated with longer withdrawal periods. T(3) replacement yielded shorter withdrawal periods than T(4) replacement (up to 3.5 days versus 7-10 days). Higher than normal serum T(3) concentrations were required to normalize or suppress TSH during T(3) monotherapy, but not T(4) monotherapy. Larger remnant sizes resulted in longer withdrawal periods if T(4) replacement was used, but had little effect for T(3) replacement. CONCLUSIONS: T(3) replacement yielded withdrawal periods about half those for T(4) replacement. Higher than normal hormone levels under T(3) monotherapy can be partially alleviated by more frequent, smaller doses (e.g., twice a day). LT(4) may be the preferred option for most children, given the convenience of single daily dosing and familiarity of pediatric endocrinologists with its administration. Remnant effects on withdrawal period highlight the importance of minimizing remnant size.

Finding identifiable parameter combinations in nonlinear ODE models and the rational reparameterization of their input-output equations.

When examining the structural identifiability properties of dynamic system models, some parameters can take on an infinite number of values and yet yield identical input-output data. These parameters and the model are then said to be unidentifiable. Finding identifiable combinations of parameters with which to reparameterize the model provides a means for quantitatively analyzing the model and computing solutions in terms of the combinations. In this paper, we revisit and explore the properties of an algorithm for finding identifiable parameter combinations using Gröbner Bases and prove useful theoretical properties of these parameter combinations. We prove a set of M algebraically independent identifiable parameter combinations can be found using this algorithm and that there exists a unique rational reparameterization of the input-output equations over these parameter combinations. We also demonstrate application of the procedure to a nonlinear biomodel.

Predicting chemical impacts on vertebrate endocrine systems.

Animals have evolved diverse protective mechanisms for responding to toxic chemicals of both natural and anthropogenic origin. From a governmental regulatory perspective, these protective responses complicate efforts to establish acceptable levels of chemical exposure. To explore this issue, we considered vertebrate endocrine systems as potential targets for environmental contaminants. Using the hypothalamic-pituitary-thyroid (HPT), hypothalamic-pituitary-gonad (HPG), and hypothalamic-pituitary-adrenal (HPA) axes as case examples, we identified features of these systems that allow them to accommodate and recover from chemical insults. In doing so, a distinction was made between effects on adults and those on developing organisms. This distinction was required because endocrine system disruption in early life stages may alter development of organs and organ systems, resulting in permanent changes in phenotypic expression later in life. Risk assessments of chemicals that impact highly regulated systems must consider the dynamics of these systems in relation to complex environmental exposures. A largely unanswered question is whether successful accommodation to a toxic insult exerts a fitness cost on individual animals, resulting in adverse consequences for populations. Mechanistically based mathematical models of endocrine systems provide a means for better understanding accommodation and recovery. In the short term, these models can be used to design experiments and interpret study findings. Over the long term, a set of validated models could be used to extrapolate limited in vitro and in vivo testing data to a broader range of untested chemicals, species, and exposure scenarios. With appropriate modification, Tier 2 assays developed in support of the U.S. Environmental Protection Agency's Endocrine Disruptor Screening Program could be used to assess the potential for accommodation and recovery and inform the development of mechanistically based models.

TSH regulation dynamics in central and extreme primary hypothyroidism.

BACKGROUND: Thyrotropin (TSH) changes in extreme primary hypothyroidism include increased secretion, slowed degradation, and diminished or absent TSH circadian rhythms. Diminished rhythms are also observed in central hypothyroid patients and have been speculated to be a cause of central hypothyroidism. We examined whether TSH secretion saturation, previously suggested in extreme primary hypothyroidism, might explain diminished circadian rhythms in both disorders. METHODS: We augmented and extended the range of our published feedback control system model to reflect nonlinear changes in extreme primary hypothyroidism, including putative TSH secretion saturation, and quantified and validated it using multiple clinical datasets ranging from euthyroid to extreme hypothyroid (postthyroidectomy). We simulated central hypothyroidism by reducing overall TSH secretion and also simulated normal TSH secretion without circadian oscillation, maintaining plasma TSH at constant normal levels. We also utilized the validated model to explore thyroid hormone withdrawal protocols used to prepare remnant ablation in thyroid cancer patients postthyroidectomy. RESULTS: Both central and extreme primary hypothyroidism simulations yielded low thyroid hormone levels and reduced circadian rhythms, with simulated daytime TSH levels low-to-normal for central hypothyroidism and increased in primary hypothyroidism. Simulated plasma TSH showed a rapid rise immediately following triiodothyronine (T(3)) withdrawal postthyroidectomy, compared with a slower rise after thyroxine withdrawal or postthyroidectomy without replacement. CONCLUSIONS: Diminished circadian rhythms in central and extreme primary hypothyroidism can both be explained by pituitary TSH secretion reaching maximum capacity. In simulated remnant ablation protocols using the extended model, TSH shows a more rapid rise after T(3) withdrawal than after thyroxine withdrawal postthyroidectomy, supporting the use of replacement with T(3) prior to (131)I treatment.

An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Gröbner Bases.

The parameter identifiability problem for dynamic system ODE models has been extensively studied. Nevertheless, except for linear ODE models, the question of establishing identifiable combinations of parameters when the model is unidentifiable has not received as much attention and the problem is not fully resolved for nonlinear ODEs. Identifiable combinations are useful, for example, for the reparameterization of an unidentifiable ODE model into an identifiable one. We extend an existing algorithm for finding globally identifiable parameters of nonlinear ODE models to generate the 'simplest' globally identifiable parameter combinations using Gröbner Bases. We also provide sufficient conditions for the method to work, demonstrate our algorithm and find associated identifiable reparameterizations for several linear and nonlinear unidentifiable biomodels.

TSH-based protocol, tablet instability, and absorption effects on L-T4 bioequivalence.

BACKGROUND: FDA Guidance for pharmacokinetic (PK) testing of levothyroxine (L-T(4)) for interbrand bioequivalence has evolved recently. Concerns remain about efficacy and safety of the current protocol, based on PK analysis following supraphysiological L-T(4) dosing in euthyroid volunteers, and recent recalls due to intrabrand manufacturing problems also suggest need for further refinement. We examine these interrelated issues quantitatively, using simulated what-if scenarios testing efficacy of a TSH-based protocol and tablet stability and absorption, to enhance precision of L-T(4) bioequivalence methods. METHODS: We use an updated simulation model of human thyroid hormone regulation quantified and validated from data that span a wide range of normal and abnormal thyroid system function. Bioequivalence: We explored a TSH-based protocol, using normal replacement dosing in simulated thyroidectomized patients, switching brands after 8 weeks of full replacement dosing. We simulated effects of tablet potency differences and intestinal absorption differences on predicted plasma TSH, T(4), and triiodothyronine (T(3)) dynamics. Stability: We simulated effects of potency decay and lot-by-lot differences in realistic scenarios, using actual tablet potency data spanning 2 years, comparing the recently reduced 95-105% FDA-approved potency range with the original 90-110% range. RESULTS: A simulated decrease as small as 10-15% in L-T(4) or its absorption generated TSH concentrations outside the bioequivalence target range (0.5-2.5 mU/L TSH), whereas T(3) and T(4) plasma levels were maintained normal. For a 25% reduction, steady-state TSH changed 300% (from 1.5 to 6 mU/L) compared with <25% for both T(4) and T(3) (both within their reference ranges). Stability: TSH, T(4), and T(3) remained within normal ranges for most potency decay scenarios, but tablets of the same dose strength and brand were not bioequivalent between lots and between fresh and near-expired tablets. CONCLUSIONS: A pharmacodynamic TSH-measurement bioequivalence protocol, using normal L-T(4) replacement dosing in athyreotic volunteers, is likely to be more sensitive and safer than current FDA Guidance based on T(4) PK. The tightened 95-105% allowable potency range for L-T(4) tablets is a significant improvement, but otherwise acceptable potency differences (whether due to potency decay or lot-by-lot inconsistencies) may be problematic for some patients, for example, those undergoing high-dose L-T(4) therapy for cancer.

Extensions, validation, and clinical applications of a feedback control system simulator of the hypothalamo-pituitary-thyroid axis.

BACKGROUND: We upgraded our recent feedback control system (FBCS) simulation model of human thyroid hormone (TH) regulation to include explicit representation of hypothalamic and pituitary dynamics, and updated TH distribution and elimination (D&E) parameters. This new model greatly expands the range of clinical and basic science scenarios explorable by computer simulation. METHODS: We quantified the model from pharmacokinetic (PK) and physiological human data and validated it comparatively against several independent clinical data sets. We then explored three contemporary clinical issues with the new model: combined triiodothyronine (T(3))/thyroxine (T(4)) versus T(4)-only treatment, parenteral levothyroxine (L-T(4)) administration, and central hypothyroidism. RESULTS: Combined T(3)/T(4) therapy--In thyroidectomized patients, the L-T(4)-only replacement doses needed to normalize plasma T(3) or average tissue T(3) were 145 microg L-T(4)/day or 165 microg L-T(4)/day, respectively. The combined T(4) + T(3) dosing needed to normalize both plasma and tissue T(3) levels was 105 microg L-T(4) + 9 microg T(3) per day. For all three regimens, simulated mean steady-state plasma thyroid-stimulating hormone (TSH), T(3), and T(4) was within normal ranges (TSH: 0.5-5 mU/L; T(4): 5-12 microg/dL; T(3): 0.8-1.9 ng/mL). Parenteral T(4) administration--800 microg weekly or 400 microg twice weekly normalized average tissue T(3) levels both for subcutaneous (SC) and intramuscular (IM) routes of administration. TSH, T(3), and T(4) levels were maintained within normal ranges for all four of these dosing schemes (1x vs. 2x weekly, SC vs. IM). Central hypothyroidism--We simulated steady-state plasma T(3), T(4), and TSH concentrations in response to varying degrees of central hypothyroidism, reducing TSH secretion from 50% down to 0.1% of normal. Surprisingly, TSH, T(3), and T(4) plasma concentrations remained within normal ranges for TSH secretion as low as 25% of normal. CONCLUSIONS: Combined T(3)/T(4) treatment--Simulated standard L-T(4)-only therapy was sufficient to renormalize average tissue T(3) levels and maintain normal TSH, T(3), and T(4) plasma levels, supporting adequacy of standard L-T(4)-only treatment. Parenteral T(4) administration-TSH, T(3), and T(4) levels were maintained within normal ranges for all four of these dosing schemes (1x vs. 2x weekly, SC vs. IM), supporting these therapeutic alternatives for patients with compromised L-T(4) gut absorption. Central hypothyroidism--These results highlight how highly nonlinear feedback in the hypothalamic-pituitary-thyroid axis acts to maintain normal hormone levels, even with severely reduced TSH secretion.

A two-tiered physiologically based model for dually labeled single-chain Fv-Fc antibody fragments.

Monoclonal antibodies (mAb) are being used at an increasing rate in the treatment of cancer, with current efforts focused on developing engineered antibodies that exhibit optimal biodistribution profiles for imaging and/or radioimmunotherapy. We recently developed the single-chain Fv-Fc (scFv-Fc) mAb, which consists of a single-chain antibody Fv fragment (light-chain and heavy-chain variable domains) coupled to the IgG1 Fc region. Point mutations that attenuate binding affinity to FcRn were introduced into the Fc region of the wild-type scFv-Fc mAb, resulting in several new antibodies, each with a different half-life. Here, we describe the construction of a two-tiered physiologically based pharmacokinetic model capable of simulating the apparent biodistribution of both (111)In- and (125)I-labeled scFv-Fc mAbs, where (111)In-labeled metabolites from degraded (111)In-labeled mAbs tend to become trapped within the lysosomal compartment, whereas free (125)I from degraded (125)I-labeled mAbs is quickly eliminated via the urinary pathway. The different concentration-time profiles of (111)In- and (125)I-labeled mAbs permits estimation of the degradation capacity of each organ and elucidates the dependence of cumulative degradation in liver, muscle, and skin on FcRn affinity and tumor mass. Liver is estimated to account for approximately 50% of all degraded mAb when tumor is small (approximately 0.1 g) and drops to about 35% when tumor mass is larger (approximately 0.3 g). mAb degradation in residual carcass (primarily skin and muscle) decreases from approximately 45% to 16% as FcRn affinity of the three mAb variants under consideration increases. In addition, elimination of a small amount of mAb in the kidneys is shown to be required for a successful fit of model to data.

W3MAMCAT: a world wide web based tool for mammillary and catenary compartmental modeling and expert system distinguishability.

W(3)MAMCAT is a new web-based and interactive system for building and quantifying the parameters or parameter ranges of n-compartment mammillary and catenary model structures, with input and output in the first compartment, from unstructured multiexponential (sum-of-n-exponentials) models. It handles unidentifiable as well as identifiable models and, as such, provides finite parameter interval solutions for unidentifiable models, whereas direct parameter search programs typically do not. It also tutorially develops the theory of model distinguishability for same order mammillary versus catenary models, as did its desktop application predecessor MAMCAT+. This includes expert system analysis for distinguishing mammillary from catenary structures, given input and output in similarly numbered compartments. W(3)MAMCAT provides for universal deployment via the internet and enhanced application error checking. It uses supported Microsoft technologies to form an extensible application framework for maintaining a stable and easily updatable application. Most important, anybody, anywhere, is welcome to access it using Internet Explorer 6.0 over the internet for their teaching or research needs. It is available on the Biocybernetics Laboratory website at UCLA: www.biocyb.cs.ucla.edu.

Role of endosomal trafficking dynamics on the regulation of hepatic insulin receptor activity: models for Fao cells.

Evidence indicates that endosomal insulin receptor (IR) trafficking plays a role in regulating insulin signal transduction. To evaluate its importance, we developed a series of biokinetic models for quantifying activated surface and endosomal IR dynamics from published experimental data. Starting with a published two-compartment Fao hepatoma model, a four-pool model was formulated that depicts IR autophosphorylation after receptor binding, IR endosomal internalization/trafficking, insulin dissociation from and dephosphorylation of internalized IR, and recycling of unliganded, dephosphorylated IR to the plasma membrane. Quantification required three additional data sets, two measured, but unmodeled by the same group. A five-pool model created to include endosomal trafficking of the nonphosphorylated insulin-IR complex was fitted using the same data sets, augmented with another published data set. Creation of a six-pool model added the physiologically relevant dissociation of insulin ligand from the activated endosomal IR. More importantly, all three models, validated against additional data not used in model fitting, predict that, mechanistically, internalization of activated IR is a rate-limiting step, at least under the receptor saturating conditions of the fitting data. This rate includes the transit time to a site where insulin dissociation from and/or dephosphorylation of the IR occurs by docking with protein-tyrosine phosphatases (PTPases), or where a sufficient conformational change occurs in the IR, perhaps due to insulin-IR dissociation, where associated PTPases may complete IR dephosphorylation. Our new models indicate that key events in endosomal IR trafficking have significance in mediating IR activity, possibly serving to regulate insulin signal transduction.

L-T4 bioequivalence and hormone replacement studies via feedback control simulations.

FDA Guidance for testing bioequivalence of levothyroxine (L-T(4)) preparations has been challenged by several groups, based on multiple issues. The efficacy of single versus combined hormone therapy also is receiving additional scrutiny. To examine these concerns, we developed a new nonlinear feedback system simulation model of whole-body regulation mechanisms involving dynamics of T(3), T(4), TSH, plasma protein binding, extravascular regulatory enzyme systems, and the hypothalamic-pituitary-thyroid axis, all quantified from human data. To address bioequivalence, we explored how to best account for varying and unmeasured endogenous T(4) following dosing with exogenous oral L-T(4) in euthyroid volunteers in required pharmacokinetic (PK) studies, by simulating various dosing scenarios and developing a new and simple correction method. We computed and assessed dosing error effects and baseline corrections using simulator-predicted endogenous T(4) level variations, due to actual closed-loop effects, and compared these with approximate corrections computed directly from PK data. Predicted dose-responses were quite linear, and for constant baseline, 7-day half-life, and our new formula-correction methods, we established some bounds on bioequivalent dosages. Simulated replacement after thyroidectomy required 141 microg L-T(4) only to normalize T(3) tissue levels and 162 microg L-T(4) to normalize plasma T(3) levels. A combined dose of approximately 103 microg L-T(4) plus approximately 6 microg T(3) ( approximately 18:1 ratio) was needed to normalize both plasma T(3) and T(4) and average tissue T(3) levels. However, simulated average tissue T(3) levels were normalized with standard L-T(4)-only therapy, and plasma T(3) levels were still within the normal range. We suggest a simple and more accurate correction for endogenous T(4) in PK studies. Current standard L-T(4)-only treatment is supported for routine replacement needs.

A predictive model of therapeutic monoclonal antibody dynamics and regulation by the neonatal Fc receptor (FcRn).

We constructed a novel physiologically-based pharmacokinetic (PBPK) model for predicting interactions between the neonatal Fc receptor (FcRn) and anti-carcinoembryonic antigen (CEA) monoclonal antibodies (mAbs) with varying affinity for FcRn. Our new model, an integration and extension of several previously published models, includes aspects of mAb-FcRn dynamics within intracellular compartments not represented in previous PBPK models. We added mechanistic structure that details internalization of class G immunoglobulins by endothelial cells, subsequent FcRn binding, recycling into plasma of FcRn-bound IgG and degradation of free endosomal IgG. Degradation in liver is explicitly represented along with the FcRn submodel in skin and muscle. A variable tumor mass submodel is also included, used to estimate the growth of an avascular, necrotic tumor core, providing a more realistic picture of mAb uptake by tumor. We fitted the new multiscale model to published anti-CEA mAb biodistribution data, i.e. concentration-time profiles in tumor and various healthy tissues in mice, providing new estimates of mAb-FcRn related kinetic parameters. The model was further validated by successful prediction of F(ab')2 mAb fragment biodistribution, providing additional evidence of its potential value in optimizing intact mAb and mAb fragment dosing for clinical imaging and immunotherapy applications.

Automated expert multiexponential biomodeling interactively over the Internet.

DIMSUM, an acronym for DIMension of a SUM of exponentials, is a highly automated expert system for fitting multiexponential models of increasing dimension to time series data. Up to now, a researcher has needed an individual copy of DIMSUM on his or her own computer as well as support to learn how to use it. W3DIMSUM, a new implementation of DIMSUM, is web-based, new territory for interactive biomodeling, allowing interactive multiexponential model building and model discrimination over the Internet. The algorithms used are numerically intensive, so we have implemented a distributed system, with numerical processing done on our server. Only the user interface is run on the client machine, but users can load and save data and results on their machines, facilitated by our use of Java WebStart.

W3MCSim: an online and reconfigurable Monte Carlo simulator for interactive probabilistic/statistical modeling.

We have implemented a Monte Carlo simulator (W3MCSim) as an Internet software tool, primarily for interactive use by students, educators, life and other physical scientists, as well as other practitioners of probabilistic and statistical modeling. Interested users download, install and run W3MCSim by visiting the application website. This application incorporates three freely available Microsoft web technologies, namely the Internet Explorer web browser, the Component Object Model software framework and the JScript web page script interpreter. We define the software architecture here, as a web application model, and show how incorporation of these technologies provides an efficient solution to W3MCSim software deployment. We demonstrate the usability and versatility of this simulator with three distinct tutorial examples: simulating the sum of six-sided dice, estimating intersection frequency in "Buffon's needle problem", and testing an animal experiment design model a priori. We also show how the program components can be reconfigured into other programs.

Thyroid hormone production rates in rat liver and intestine in vivo: a novel graph theory and experimental solution.

We develop a novel method for finding sufficient experimental conditions for discriminating and quantifying individual biomolecule production sources in distributed, inhomogeneous multisource systems in vivo, and we apply it experimentally to a complex, unsolved problem in endocrinology. The majority of hormonal triiodothyronine (T3) is produced from prohormone thyroxine (T4) in numerous nonthyroidal organs and, with one exception, the T3 production rate has not been fully resolved in any single extrathyroidal organ of any species. Using a readily generalized graphic method called cut-set analysis, we show here that measured steady-state responses in several organs to three independent tracer infusions, two into blood and one directly into the organ(s) of interest, are sufficient to resolve this problem for organs fully accessible to direct infusion in vivo. We evaluated local T3 production in rat liver and intestine, which also required T3 bile flux measurements, and we found that liver produces approximately 31% and whole intestine approximately 6% of whole body T3 from T4. With thyroidal production included, liver contributes approximately 15% and intestine approximately 3% of whole rat T3 production. This new methodology is broadly applicable, especially to biosystems that include molecular interconversions at multiple sites.