Proctor2016 - Circadian rhythm of PTH and the dynamics of signalling molecules on bone remodelling

November 2018, model of the month by Sarubini Kananathan
Original model: BIOMD0000000612

Introduction

Bone is an organ that is under a continuous process of remodelling since birth. Old bone cells get reabsorbed and replaced with new bone cells to repair micro-fractures and maintain mineral homeostasis [1]. This process is maintained by osteoclasts (cells that absorbs bone tissue during growth and healing) and osteoblasts (cells that secretes the substance of bone). Osteoclasts and osteoblasts are regulated through various network signalling pathways such as: Wnt signalling, parathyroid hormone (PTH), RANK ligand/osteoprotegrin, and TGF-β in response to a stimulus (mechanical loading) [2]. Aging causes a gradual decrease of bone mass due to the disruption of the signalling pathways which then causes the loss of homeostasis. This results in the remaining bone to have more micro-fractures increasing the possibility of a fracture upon an accident. The authors aimed to model the bone remodelling process with the signalling pathways to see the effects of mechanical loading and how different interventions can help prevent the loss of bone mass.

Biological Background

Figure 1

Figure 1. Network diagram of the model with the four signalling pathways: Wnt signalling, parathyroid hormone (PTH), RANK ligand/osteoprotegrin, and TGF-β. Figure taken from [2].

Osteoblast originates from mesenchymal stem cells (MSCs) and after fulfilling their bone formation purpose, they either mature into osteocytes (which forms the lining cells) or undergo apoptosis. Osteoclast originates from hematopoietic stem cells (HSCs). For the conversion of HSCs into progenitor cells, it requires macrophage colony-stimulation factor (MCSF’) which is secreted by osteoblast and MSCs. For the progenitor cells to mature further into mature osteoclasts, it requires the RANK ligand (RANK) to attach to the receptor activator of NFκB (RANK) receptors. After osteocytes finishes the resorption process they undergo apoptosis as well. Osteocytes have an important role in maintaining the bone homeostasis as they respond to the mechanical stimuli. When it is not present osteocytes undergo apoptosis.

As stated before there are several pathways involved in the process of bone remodelling:

Pathway Mechanism
RANK-RANKL-OPG A decoy ligand osteoprotegrin (OPG) binds with RANKL to prevent RANKL from binding with the RANK receptors. Therefore, the ratio of RANKL/OPG is important when it comes to maintaining the homeostasis. RANKL is secreted by MSCs, mature (Ob_m) and precursor (Ob_p) osteoblast cells and osteocytes. Osteoblasts also secretes OPG. Mature (Precursor) osteoblast cells secretes low (high) levels of RANKL and high (low) levels of OPG. This causes the ratio to change during osteoblast differentiation. During the early stages of differentiation osteoclastogenesis is promoted and then inhibited later.
TGF-β signalling Osteoblasts produces and secretes TGF-β. It is required for the differentiation of MSCs into osteoblast precursors, but it inhibits at the later stage.
Wnt signalling Wnt promotes the proliferation and differentiation of osteoblasts. Wnt signalling can be inhibited by sclerostin which is secreted by inactive osteocytes. Apoptosis of osteocytes do not take place when Wnt signalling is activated.
Signalling via PTH PTH leads to activation of osteocytes which is useful when there is a lack of mechanical stimulus. Osteoblasts and osteocytes have PTH receptors. PTH signalling increases the RANKL/OPG ratio (Inhibition of OPG and increases in RANKL secretion) which leads to more bone resorption. Osteocytes are activated by PTH signalling which leads to an increase in Wnt Signalling. This lowers the level of Sclerostin. When PTH binds to the receptors on osteoblasts it activates a signalling cascade (phosphorylation of CREB) which inhibits osteoblasts apoptosis.

Model

Several models to depict the bone remodelling process has been created ([3]-[9]) however they do not include the dynamics of the signalling pathways. Instead the dynamics were represented as parameters in reaction rates. The authors aimed to integrate majority of the pathways with assumptions however to decrease the complexity some assumptions were disregarded. The model consists of 37 species, 76 reactions with 72 global quantities. For majority of the equations mass action kinetics was used and for second order reactions Hill kinetics was used. The mechanical loading and PTH cycle were included in the model as events. The model was encoded in SBML.

Results

With the encoded model, the authors varied the parameters to represent different situations to see its effect on the bone mass. Figure 2 shows that to maintain the bone mass it requires two regular intermittent loading (30 min exercise per day) and a normal PTH circadian rhythm (two peaks per day). As age increases the amount of physical activity one does decreases and there is more disruption on the circadian rhythm. To show this the authors ran simulations by withdrawing load levels and PTH levels which can be seen in Figure 2. From these simulations, they concluded that the absence of loading and/or a complete disruption of the PTH circadian rhythm results in severe bone loss [2].

The authors then experimented in changing the rate of the global parameters to find possible treatments to reduce bone loss while ageing. To portray ageing and the reduced physical activity only 1 loading event and one PTH peak per day was used in the simulations.

Simulation of Result
RANKL Inhibition There was a gradual increase in bone mass. With the lowest value for the rate of RANKL binding to its receptors on osteoclasts, the bone mass returns to its normal value.
Sost Inhibition The bone mass increased rapidly initially and the flattened off which suggests that this treatment will only have a maximal effect.
PTH Injections Simulations were run for 1/2/3 injections per day. One injection was insufficient to restore bone mass whereas two injections with amount of 200 was enough to restore bone mass. 3 injections can also be used with lower amounts of PTH.
Continuous PTH Continuous PTH lead to a decrease in bone mass. This suggests having high levels of PTH is counterproductive.
Effects of Bisphophonates Bone mass increases.
Additional Loading The model was run with 0/1/2/3 loads per day. When there was only one PTH peak, three mechanical loading was needed to recover the original bone mass. One factor that determined the output was the timing of the additional loads.

The authors had found through sensitivity analysis that bone remodelling is mainly affected by components involved in Wnt and PTH Pathways.

Figure 2

Figure 2. (A) Shows the model simulation output with 2 loading events per day and a normal circadian rhythm of PTH with 2 peaks/day. (B) Shows the model simulation output with 1 loading event per day and a normal circadian rhythm of PTH with 2 peaks/day. (C) Shows the model simulation output with 2 loading events per day and a circadian rhythm of PTH with 1 peak/day. (D) Shows the model simulation output with 1 loading event per day and a circadian rhythm of PTH with 1 peak/day. The simulation was performed in COPASI 4.24 (Build 197).

Conclusion

The authors built a mathematical model including pathways, that help maintain the homeostasis, to see the effects loading and PTH circadian rhythm has. They found that declining loading or having a disruption to the PTH cycle led to the bone mass decreasing. This was mainly due to the levels of sclerostin increasing which inhibited Wnt signalling. OPG levels were also increased, which lowered the RANKL/OPG ratio resulting in Ob_m :Ocl_m ratio to be increased. This led to more bone mass formation. Through sensitivity analysis they also found the most affected parameter to be involved with the lifespan of osteoblasts and osteoclasts and their differentiation. From which they were able to conclude that interventions should target more than one aspect of the process. This requires more research and study into recognising which combinations of parameters will have the maximal effect. As continuous PTH levels led to a decrease in bone mass, patient’ PTH circadian rhythm must be checked before any interventions can be applied to prevent the risk of bone tumours. Future directions to improve the model would be to look at the effects of different loading regimes and prior existing damaged bone cells.

 

References

  1. Dimitrios J. Hadjidakis and Ioannis I. Androulakis (2006). Bone Remodeling. New York Academy of Sciences. , 385-396. doi: 10.1196/annals.1365.035.
  2. Proctor CJ and Gartland A (2016). Simulated Interventions to Ameliorate Age-Related Bone Loss Indicate the Importance of Timing. Front. Endocrinol. , 7:61. doi: 10.3389/fendo.2016.00061.
  3. Buenzli PR, Pivonka P, Gardiner BS, Smith DW (2012). Modelling the anabolic response of bone using a cell population model. J Theor Biol, 307:42-52. doi:10.1016/j.jtbi.2012.04.019.
  4. Graham JM, Ayati BP, Holstein SA, Martin JA. (2013). The role of osteocytes in targeted bone remodeling: a mathematical model. PLoS One , 8:E63884. doi:10.1371/journal.pone.0063884.
  5. Komarova SV. (2005). Mathematical model of paracrine interactions between osteoclasts and osteoblasts predicts anabolic action of parathyroid hormone on bone. Endocrinology, 146:3589-95. doi:10.1210/en.2004-1642.
  6. Lemaire V, Tobin FL, Greller LD, Cho CR, Suva LJ. (2004). Modeling the interactions between osteoblast and osteoclast activities in bone remodeling. J Theor Biol , 229:293-309. doi:10.1016/j.jtbi.2004.03.023.
  7. Pivonka P, Zimak J, Smith DW, Gardiner BS, Dunstan CR, Sims NA, et al.(2008). Model structure and control of bone remodeling: a theoretical study. Bone, 43:249-63. doi:10.1016/j.bone.2008.03.025.
  8. Pivonka P, Zimak J, Smith DW, Gardiner BS, Dunstan CR, Sims NA, et al. (2010). Theoretical investigation of the role of the RANK-RANKL-OPG system in bone remodeling. J Theor Biol, 262:306-16. doi:10.1016/j.jtbi.2009.09.021.
  9. Kroll MH.(2000). Parathyroid hormone temporal effects on bone formation and resorption. Bull Math Biol , 62:163-88. doi:10.1006/bulm.1999.0146.