Modeling, identification and parameter estimation of bilirubin kinetics in normal, hemolytic and Gilbert's states

On finding and using identifiable parameter combinations in nonlinear dynamic systems biology models and COMBOS: a novel web implementation

Parameter identifiability problems can plague biomodelers when they reach the quantification stage of development, even for relatively simple models. Structural identifiability (SI) is the primary question, usually understood as knowing which of P unknown biomodel parameters p1,…, pi,…, pP are-and which are not-quantifiable in principle from particular input-output (I-O) biodata. It is not widely appreciated that the same database also can provide quantitative information about the structurally unidentifiable (not quantifiable) subset, in the form of explicit algebraic relationships among unidentifiable pi. Importantly, this is a first step toward finding what else is needed to quantify particular unidentifiable parameters of interest from new I-O experiments. We further develop, implement and exemplify novel algorithms that address and solve the SI problem for a practical class of ordinary differential equation (ODE) systems biology models, as a user-friendly and universally-accessible web application (app)-COMBOS. Users provide the structural ODE and output measurement models in one of two standard forms to a remote server via their web browser. COMBOS provides a list of uniquely and non-uniquely SI model parameters, and-importantly-the combinations of parameters not individually SI. If non-uniquely SI, it also provides the maximum number of different solutions, with important practical implications. The behind-the-scenes symbolic differential algebra algorithms are based on computing Gröbner bases of model attributes established after some algebraic transformations, using the computer-algebra system Maxima. COMBOS was developed for facile instructional and research use as well as modeling. We use it in the classroom to illustrate SI analysis; and have simplified complex models of tumor suppressor p53 and hormone regulation, based on explicit computation of parameter combinations. It's illustrated and validated here for models of moderate complexity, with and without initial conditions. Built-in examples include unidentifiable 2 to 4-compartment and HIV dynamics models.

The origins and kinetics of bilirubin in healthy dogs, in comparison with man

The origins and the kinetics of unconjugated bilirubin were assessed in 25 healthy dogs. Bilirubin kinetics were measured by the analysis of the plasma disappearance of [3H]bilirubin in a two-compartment model. The relative bilirubin productions from erythrocyte haem degradation and early labeled bilirubin were determined by measuring the incorporation of [14C]glycine in erythrocyte haem and in fecal stercobilin. The incorporation of this relation into the model permitted the quantitation of the bilirubin production from erythrocyte destruction, ineffective erythropoiesis and the catabolism of hepatic haemoproteins. The contribution of the three bilirubin sources to the plasma concentration was derived from the calculated fraction reflux into the plasma of bilirubin produced in the liver from hepatic haemoproteins. Other calculated model-dependent and -independent parameters were plasma bilirubin clearance, hepatic bilirubin extraction efficiency, pool sizes, and the fractional transfer rates which reflect the hepatic uptake process, reflux from liver to the plasma, and the conjugating enzyme activity. In plasma of healthy dogs only unconjugated bilirubin was detected. It averaged 0.68 mumol/l, which is far below levels in man. This is probably due to the 20-fold higher hepatic clearance rate in dogs (median 32.2; range 21.6-43.9 ml/kg per min). In addition, fasting hyperbilirubinaemia could not be documented in the dog. The total bilirubin turnover was 14.9 (12.6-17.1) mumol/kg (median and 95% range), with 67 (60-70)% derived from erythrocyte degradation, 5.3 (4.7-5.5)% from ineffective erythropoiesis and 27.7 (24.5-35.3)% from hepatic haemoproteins. The figures for the plasma bilirubin turnover were 12.3 (10.3-14.2) mumol/kg per day, 79 (75-84)%, 6.3 (6.0-6.6)% and 14.8 (9.2-18.9)%, respectively. The presented model permits the simultaneous quantitation of both the origins and the kinetics of bilirubin. The application of this approach in pathological conditions is expected to provide better insight in the pathophysiology of acquired hyperbilirubinaemia.

Abnormal hepatic uptake of low doses of sulfobromophthalein in Gilbert's syndrome: the role of reduced affinity of the plasma membrane carrier of organic anions

The plasma disappearance rate of sulfobromophthalein (VBSP; mumol/kg/min) was measured in 15 Gilbert's syndrome patients and 12 control subjects after intravenous injection of two different doses (0.59 and 5.90 mumol/kg) of the dye. Plasma disappearance rate was significantly reduced in Gilbert's syndrome patients after administration of 0.59 mumol sulfobromophthalein/kg (0.119 +/- 0.016 vs. 0.146 +/- 0.018 mumol/kg/min; mean +/- S.D.; p less than 0.001), whereas no difference was found with the higher dose (0.754 +/- 0.040 vs. 0.767 +/- 0.072 mumol/kg/min). Significant reduction was also found after administration to four Gilbert's syndrome patients and four control subjects of 0.29 and 2.95 mumol sulfobromophthalein (0.060 +/- 0.005 mumol/kg/min vs. 0.077 +/- 0.07 mumol/kg/min and 0.480 +/- 0.012 mumol/kg/min vs. 0.591 +/- 0.015 mumol/kg/min, respectively; p less than 0.01). Competition studies with combined administration of sulfobromophthalein (0.59 mumol/kg) and different doses of rifamycin SV (0.59, 1.47 and 2.95 mumol/kg) showed a significant (p less than 0.001) reduction in plasma disappearance rate in Gilbert's syndrome patients but not in controls. The rifamycin SV dose at which a 50% inhibition in plasma disappearance rate was observed was 0.8 mumol/kg. The apparent affinity (Km) of the hepatic transport was higher in Gilbert's syndrome patients than in control subjects (3.61 +/- 0.37 mumol sulfobromophthalein/kg vs. 2.76 +/- 0.29 mumol sulfobromophthalein/kg, mean +/- S.D.; p less than 0.01), whereas no difference was found in Vmax (0.95 +/- 0.11 mumol sulfobromophthalein/kg vs. 0.93 +/- 0.10 mumol sulfobromophthalein/kg/min, mean +/- S.D.; N.S.).(ABSTRACT TRUNCATED AT 250 WORDS)

Optimal input design: case study of the metabolic process

An optimal input of nutrients into the metabolic process of the individual subject so as to effect desired therapeutic results is particularly important for the critically ill. A patient-related, individualized nutrients optimization procedure is proposed here. The procedure is applicable to any time-invariant and deterministic metabolic model that is bound by one or more quantitative limiting criteria. As a case in hand, the procedure is used to optimize the individual metabolic needs of critically ill patients. The results indicate that, given a proper metabolic model, the patient may be treated on an individual appropriateness basis rather than on the traditional statistical intuitive approach.

A model of the distribution and metabolism of corticotropin-releasing factor

The aim of this study is the selection of the number of compartments required for a model to represent the distribution and metabolism of corticotropin-releasing factor (CRF) in rats. The dynamics of labeled rat CRF were measured in plasma for seven rats after a rapid injection. The sampling schedule resulted from the combination of the two D-optimal sampling sets of times corresponding to both rival models. This protocol improved the numerical identifiability of the parameters and consequently facilitated the selection of the relevant model. A three-compartment model fits adequately to the seven individual dynamics and better represents four of them compared with the lower-order model. It was demonstrated, using simulations in which the measurement errors and the interindividual variability of the parameters are included, that his four-to-seven ratio of data sets is consistent with the relevance of the three-compartment model for every individual kinetic data set. Kinetic and metabolic parameters were then derived for each individual rat, their values being consistent with the prolonged effects of CRF on pituitary-adrenocortical secretion.

Sex differences of nicotinate-induced hyperbilirubinemia in Gilbert's syndrome. Implication of bilitranslocase function

Intravenous administration of nicotinic acid (NA) is followed by an increase in serum unconjugated bilirubin level. This effect is higher in Gilbert's syndrome (GS) and this test has been used in the diagnosis of the syndrome. After administration of 5.9 mumol NA/kg body weight, the maximal increment of serum unconjugated bilirubin and the area under the bilirubin concentration time curve (AUC) were significantly higher (P less than 0.01) in GS males than in GS females. The half-life of the first fast slope of plasma disappearance curve of the drug was also significantly prolonged in GS males as compared to GS females (15.91 +/- 1.12 vs 9.13 +/- 1.25 min, mean +/- SEM, P less than 0.005). The maximal bilirubin increment and AUC were linearly correlated (P less than 0.01) with NA plasma half-life. Purified preparations of bilitranslocase, a liver plasma-membrane protein involved in bilirubin and sulfobromophthalein (BSP) transport, specifically bound NA and the drug competitively inhibited BSP uptake in rat liver plasma membrane vesicles (Ki = 50 nM). These data suggest that, in addition to the hemolytic effect of the drug, NA-induced hyperbilirubinaemia could be also due to a competition between the two anions at the sinusoidal plasma membrane level. A possible implication of bilitranslocase in GS is considered.

The hepatic excretion of 131I-rose bengal and 99mTc-IDA derivatives in Rotor's syndrome

Bilirubin kinetics and hepatobiliary excretion of some exogenous anions (BSP, 131I-rose bengal, diethyl and parabutly-IDA labeled with 99mTc) were studied in three patients presenting with Rotor's syndrome. Two were brothers; a nonjaundiced fraternal twin of one of them was also evaluated. The hepatic clearance of the radiopharmaceuticals was impaired in the affected patients but the degree of impairment was different among the tested anions, i.e., maximal for 99mTc-diethyl-IDA and minimal for 131I-rose bengal. Parabutyl-IDA was cleared better than the diethyl derivative. The metabolic derangement seems to be at the level of transfer from plasma to liver and of the hepatic storage, rather than at the level of hepatocyte excretory pathways, as in the case of Dubin-Johnson syndrome.

Prognosis, trend and prediction in patient management

A survey was conducted to get to know the 'state of the art' in trend prediction as a basis for optimal therapy, with emphasis on research being done in the countries of the European Community. Special areas of interest are quantitative prognosis (prognostic indices), the detection and use of trends in the patient's state, the use of models in prediction and their possible use for deciding which therapy is optimal for a specific patient. An extensive list of centres working in these fields as well as an extensive reference list is included.

New insights into the classification and mechanisms of hereditary, chronic, non-haemolytic hyperbilirubinaemias

Gilbert's syndrome is typically associated with a deficiency in hepatic bilirubin UDP-glucuronosyltransferase activity (B-GTA). The overproduction of bilirubin that is often found in this condition could be a fortuitous coincidence that leads to the unmasking of the disease, which otherwise often remains latent. Some cases of chronic unconjugated hyperbilirubinaemia could, however, be related to a defect in hepatic uptake, as reflected by alterations in BSP kinetics. Severe deficiencies of hepatic B-GTA exist in all types of Crigler-Najjar disease. An increased proportion of bilirubin monoglucuronide is always found in bile when a B-GTA deficiency is present. This observation strongly suggests a common biochemical defect in Gilbert's syndrome and in Crigler-Najjar disease, and thus renders the suggestion that the latter condition may be separated into two groups somewhat inappropriate. There is, however, no doubt that further knowledge of the conjugating enzyme, or enzymes, is required: such information may lead to the characterisation of several types of enzymic defects. Whereas little is new as far as the Dubin-Johnson syndrome is concerned, Rotor's syndrome can no longer be considered to be a variant of the former. The transport defect which is involved in most cases of Rotor's syndrome, if not in all, is an impairment of hepatic storage, thus distinguishing it from the impairment of excretion which is involved in the Dubin-Johnson syndrome. The distinct patterns of urinary coproporphyrin excretion, which were recently reported in Dubin-Johnson and Rotor's syndromes, offer additional evidence for a clear differentiation between these two entities.