## 1 Introduction  
Proteins are the main biomolecules that perform and control most biological processes in all living cells, tissues and organisms. Proteins exhibit their biological functions through selective interactions with other molecules, which could also be proteins and/or DNA. So far, the rules governing protein ability to selectively interact with other biomolecules have not been completely understood. The protein functions are exhibited through protein interactions and mostly through interactions between proteins and their receptors, which are proteins or complexes of proteins that selectively drive specific biological pathways. Currently, the interactions between proteins and their receptors are investigated mostly using 3D matching between interacting proteins, which is not explicit enough to explain the specificity of these interactions. Experimentally, protein functions and protein/receptor interactions are investigated by a number of techniques, including X-ray, MRI, spectroscopy, etc. However, although all these techniques are very expensive and time consuming, they still are not providing a complete understanding of the selectivity of protein interactions. Thus, there is a need for a theoretical/computational approach based on molecular biophysics that can investigate the specificity of protein/receptor interactions with more accuracy than 3D matching. Here, we used parathyroid hormone as an example to present the ability of the Resonant Recognition Model (RRM), which is a computational model based on molecular biophysics and mathematics, to investigate the specificity of protein functions and protein/receptor recognitions and interactions. The RRM is based on findings that certain periodicities (frequencies) within the distribution of free electron energies along the protein macromolecule are critical for its biological function and protein ability for selective recognitions and interactions. On the other hand, there is an emerging need to use tissue engineering based on living cells as an alternative to tissue or organ transplantation. There is particular interest to differentiate stem cells into osteoblasts for bone regeneration, bone healing and bone transplantation. Parathyroid hormone (PTH) is involved in the stimulation of bone remodelling and in the induction of differentiation of bone marrow mesenchymal stromal/stem cells by enhancing bone morphogenetic protein signalling [1]. The PTH is the principal regulator of calcium homeostasis in the human body and has been shown to influence and expand the bone marrow stem cell niche with both self-renewal and differentiation. As it has been shown that the population of pluripotent stem cells highly express parathyroid hormone type 1 receptors, it was postulated that parathyroid hormone has similar action as stromal cell-derived factor-1 (SDF-1\(\alpha\)), which is crucial for the recruitment of stem cells to a number of diseased organs [2]. Moreover, it has been shown that PhotoBioModulation (PBM) of specific blue and green light wavelengths initiates osteoblastic differentiation of human adipose-derived stem cells [3]. The research described in reference [3] presents the effect of PBM on both proliferation and differentiation of osteogenic stem cells. The effects of four different wavelengths (420 nm, 540 nm, 660 nm and 810 nm) were measured and it has been shown that wavelengths of 420 nm and 540 nm were more efficient in stimulating osteoblast differentiation compared to wavelengths of 660 nm and 810 nm [3]. Here, we hypothesised that stimulation of osteoblast differentiation by specific blue and green light wavelengths is related to activation of proteins involved in osteoblast differentiation like PTH and SDF-1\(\alpha\). For this purpose, we have utilised the RRM model, which proposes that protein activation and function are based on specific wavelengths (frequencies) of electromagnetic radiation within ultra-violet, visible, infra-red and far infra-red light.