Mathematical modeling of the effects of CK2.3 on mineralization in osteoporotic bone

Abstract

Osteoporosis is caused by decreased bone mineral density (BMD) and new treatments for this disease are desperately needed. Bone morphogenetic protein 2 (BMP2) is crucial for bone formation. The mimetic peptide CK2.3 acts downstream of BMP2 and increases BMD when injected systemically into the tail vein of mice. However, the most effective dosage needed to induce BMD in humans is unknown. We developed a mathematical model for CK2.3-dependent bone mineralization. We used a physiologically based pharmacokinetic (PBPK) model to derive the CK2.3 concentration needed to increase BMD. Based on our results, the ideal dose of CK2.3 for a healthy individual to achieve the maximum increase of mineralization was about 409 µM injected in 500 µL volume, while dosage for osteoporosis patients was about 990 µM. This model showed that CK2.3 could increase the average area of bone mineralization in patients and in healthy adults.

Figure 1

(a) Differentiation potential of mesenchymal stem cells. (b) 1. BMP2 binds to the BMP receptors on the plasma membrane causing the release of CK2 from three distinct sites on BMPRIa. This allows BMPRIa to release a signal along several pathways such as Smad, ERK, mTOR. 2. CK2.3 acts intracellular and inhibits binding of CK2 to BMPRIa leading to the activation of the ERK signaling pathway.15, 22 Shown here is the pathway by which CK2.3 increases osteogenesis.

Figure 2

(a) Mineralization areas for various dosages of CK2.3. (a) statistically significant difference from control. (b) statistically significant difference from 50 nM. (c) statistically significant difference from 75 nM. (d) statistically significant difference from 100 nM. (e) statistically significant difference from 250 nM. (f) statistically significant difference from 500 nM. (b) Mineralization areas for various BMPRIa signal quantities.

Figure 3

BMPRIa signal released and the mineralization constant derived from the experimental data and the PBPK model. The points were fit to the cubic equation y(x).

Figure 4

(a) Sample dose–response curve for CK2.3 from 200 to 1000 µM. (b) Sample dose‐response curve for CK2.3 from 600 µM to 1.6 mM in osteoporotic bone.

Figure 5

(a) CK2.3 concentration (in pM/L) in the blood, kidney, liver, heart, and brain, run over 500 min, when the subject receives 409 µM CK2.3 in 500 µL of CK2.3. (b) BMPRIa signal over time.