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Nikolaev et al., (2005). Mathematical model of binding of albumin-bilirubin complex to the surface of carbon pyropolymer.

October 2012, model of the month by Vijayalakshmi Chelliah
Original model: BIOMD0000000291

Erythrocytes (red blood cells), as they get old and damaged are disposed of in the spleen. Hemoglobin, the principal component of red blood cells, is broken down into heme, as the globin part is turned into amino acids and recycled. The heme initially breaks apart into biliverdin, a green pigment which is rapidly reduced to bilirubin (unconjugated bilirubin - not soluble in water), an orange-yellow pigment (Figure 1). Bilirubin binds to albumin and is transported to the liver, where it is conjugated by reacting with glucuronic acid catalysed by enzyme glucuronyltransferase. The conjugated bilirubin (water soluble) goes into the bile from where it finds its way for excretion.

Dysregulation in the bilirubin pathway that leads to the accumulation of excess bilirubin in the blood is the cause of Jaundice. Many diseases can cause jaundice and there are different kinds of Jaundice. Hemolytic jaundice occurs when there is a rapid break down of too many red blood cells, which leads to overproduction of bilirubin. This type of jaundice occurs in patients suffering from malaria, sickle-cell anemia, septicemia or blood poisoning. Hepatocellular jaundice occurs in patients having liver diseases, where the liver fails to remove bilirubin from blood. This type of jaundice commonly occurs in hepatitis, cirrhosis and liver cancer. Obstructive jaundice occurs when the bile duct from the gallbladder to the small intestine is completely or partially blocked, causing bilirubin to back up and accumulate in the blood. This type of jaundice may result from gall-stones, tumours, or inflammation that affects the bile ducts. Physiologic jaundice occurs when newborns have too much of bilirubin in the blood that is caused due to immature liver.

Figure 2

Figure 2 Crystal structure of human serum albumin complexed with bilirubin (2VUE).

Figure 3

Figure 3 Adsorption mechanism of albumin and bilirubin on the surface of CPP. Figure taken from [1.

Other similar studies: In order to remove substantial quantities of albumin-bound toxins in an effective and biocompatible manner, a form of artificial liver support MARS (Molecular Adsorbent Recirculating Systems) was developed [2]. Magosso et al. [3], proposed a first mathematical model of toxin removal by MARS. MARS, although is very effective in removing water-soluble and protein-bound toxins, is complicated and expensive, which limits its clinical applications.

Recently, as a functional replacement for human serum albumin used in MARS, Wang et al. [4,5], developed an inexpensive water-soluble adsorbent (beta-cyclodextrin-grafted polyethyleneimine), to remove bilirubin from plasma of hyperbilirubinemia patient. Developing mathematical models describing the mechanism of these water-soluble adsorbent would be useful for further studies.

Figure 1

Figure 1 Heme catabolism.

Bilirubin is a surrogate marker of albumin-bound toxins, and it is frequently used to access the severity of liver disease. As the removal of bilirubin from blood improves patient's condition, many studies on bilirubin adsorbents used in plasma perfusion system have been carried out. Nikolaev et al. [1, BIOMD0000000291] proposed a mathematical model and estimated the parameters of adsorption of albumin-bilirubin complex to the surface of carbon pyropolymer (CPP). CPP obtained by pyrolysis and heat activation of synthetic copolymer vinyl pyridine styrene divinyl benzene (VP-SDVB) retain mechanical strength and surface smoothness of granules typical of a precursor polymer. Several methods of medicinal treatment are based on the removal of protein-bound substances from ascitic fluid, blood plasma, and whole blood by using these adsorbents.

The variables considered in the model are Al (albumin), B (unconjugated bilirubin), C (CPP adsorption sites for bilirubin), AlB (albumin-bilirubin complex, high affinity site), AlB2 (albumin-bilirubin complex, low affinity site), AlCn (albumin-CPP complex), BC (bilirubin-CPP complex). The reactions that describe the following processes are taken into account. Firstly, the binding of unconjugated bilirubin to albumin is considered. Albumin has two binding sites for bilirubin, and hence the model assumes that the binding to low affinity site proceeds when the high affinity site is occupied (equations 1 to 4 of [1]). Figure 2 shows the crystal structure of 4Z,15E-bilirubin-IXα isomer bound to the primary site of human serum albumin (PDB:2vue). Secondly, the binding of bilirubin and albumin to CPP sites are considered (equations 5 to 8 of [1]). The molecule of albumin has a greater molecular weight than bilirubin and hence the area accessible to bilirubin is probably several times greater compared to that of albumin on the surface of CPP. Also, as albumin has a three-domain structure with flexible bonds between domains, they can exist in various spatial conformations. The model has been constructed taking into account the mean number of sites accessible to bilirubin and overlapped by albumin molecules. Figure 3 shows the adsorption mechanism of albumin and bilirubin on the surface of CPP. Finally, the binding of albumin-bilirubin complex to the surface of CPP is considered (equations 9 and 10 of [1]). It is assumed that albumin undergoes reversible and partial denaturation on the surface of CPP that lead to the disintegration of the complex. These changes are followed by consecutive release of bilirubin bound to the low and high affinity sites of albumin and get adsorbed on the surface of CPP. The variable (n) denotes the mean number of bilirubin-binding sites blocked by one molecule of albumin on the surface of CPP.

Figure 4 shows the adsorption of albumin-bilirubin complex on the surface of CPP, with mean number of sites occupied with one albumin molecule being one (i.e. n=1). The analysis is done with two 2 initial concentrations of bilirubin (10mg% and 30mg%) at an initial albumin concentration of 30g/l. The maximum concentration of bound bilirubin was determined by its initial concentration and number of CPP sites, whereas the concentration of bound albumin remains the same (0.2mM) irrespective of its initial concentration.

Due to a difference in the size of albumin and bilirubin molecules and fractal characteristics of the CPP surface, large molecules of albumin bind to surface sites on CPP granules. The sites located inside CPP pores remain accessible to lower linear size molecule bilirubin. However, these sites are inaccessible to additional albumin or albumin-bilirubin complexes. On the whole, the model has proposed to account for fractal properties of the surface of CPP.

Figure 4

Figure 4 Adsorption of albumin-bilirubin complex on the surface of CPP. Simulation result taken from BIOMD0000000291.

Bibliographic References

  1. Nikolaev et al. Mathematical model of binding of albumin-bilirubin complex to the surface of carbon pyropolymer. Bull Exp Biol Med. 2005; Sep ;140(3):365-9 [PMID:16307060]
  2. Boyle et al. Equipment review: The molecular adsorbents recirculating system (MARS). Crit Care. 2004; Aug ;8(4):280-6 [PMID:15312211]
  3. Magosso et al. A modeling study of bilirubin kinetics during Molecular Adsorbent Recirculating System sessions. Artif Organs. 2006; Apr ;30(4):285-300 [PMID:16643387]
  4. Wang et al. Bilirubin adsorption properties of water-soluble adsorbents with different cyclodextrin cavities in plasma dialysis system. Colloids Surf B Biointerfaces. 2012a; Feb 1 ;90:248-53 [PMID:22037476]
  5. Wang et al. Water-soluble adsorbent β-cyclodextrin-grafted polyethyleneimine for removing bilirubin from plasma. Transfus Apher Sci. 2012; Oct ;42(2):159-65 [PMID:22836125]