Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling

Komarova, Svetlana V.; Smith, Robert J.; Dixon, S. Jeffrey; Sims, Stephen M.; Wahl, Lindi M.

doi:10.1016/s8756-3282(03)00157-1

Cited by 269 publications

(369 citation statements)

References 25 publications

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“…Recently, models of the PK/PD relationship for sCT have described the interactions between osteoclasts and osteoblasts [40]. Compartmental models have been previously used to describe the kinetics of sCT [21], and the present work confirms that the PK of free sCT can be well characterized with a two-compartmental model after i.v.…”

Section: Discussionsupporting

confidence: 75%

PK/PD modelling of comb-shaped PEGylated salmon calcitonin conjugates of differing molecular weights

Ryan

Frías²,

Wang

et al. 2011

Journal of Controlled Release

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Salmon calcitonin (sCT) was conjugated via cysteine-1 to novel combed-shaped endfunctionalised poly(PEG) methyl ether methacrylate) (sCT-P) comb-shaped polymers, to yield conjugates of total molecular weights (MW) inclusive of sCT: 6.5, 9.5, 23 and 40 kDa. The conjugates were characterised by HPLC and their in vitro and in vivo bioactivity was measured by cAMP assay on human T47D cells and following intravenous (i.v.) injection to rats, respectively. Stability against endopeptidases, rat serum and liver homogenates was assessed. There were linear and exponential relationships between conjugate MW with potency and efficacy respectively, however the largest MW conjugate still retained 70% of E max and an EC 50 of 3.7 nM. In vivo, while free sCT and the conjugates reduced serum [calcium] to a maximum of 15-30 % over 240 min, the half life (T½) was increased and the area under the curve (AUC) was extended in proportion to conjugate MW. Likewise, the polymer conferred protection on sCT against attack by trypsin, chymotrypsin, elastase, rat serum and liver homogenates, with the best protection afforded by sCT-P (40 kDa). Mathematical modelling accurately predicted the MW relationships to in vitro efficacy, potency, in vivo PK and enzymatic stability. With a significant increase in T½ for sCT, the 40 kDa MW comb-shaped PEG conjugate of sCT may have potential as a long-acting injectable formulation.

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Section: Discussionsupporting

confidence: 75%

PK/PD modelling of comb-shaped PEGylated salmon calcitonin conjugates of differing molecular weights

Ryan

Frías²,

Wang

et al. 2011

Journal of Controlled Release

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“…Recently in [8], an interesting mathematical study was performed which indicates that the paracrine and autocrine relations are very important parts of the cellular model of the bone remodelling cycle. However, different paracrine mechanisms could be involved and the approach of present work differs from study [8] in an important molecular respect that we tried to study the possibility to change the focus by giving cell relationships based on the formal allosteric form, starting from Michaelis-Menten (M-M) one-site molecular control and extending the study to the well known Hill, Monod-Wyman-Changeux (MWC) and KoshlandNemethy-Filmer (KNF) patterns.…”

Section: Accepted M Manuscriptmentioning

confidence: 99%

“…However, different paracrine mechanisms could be involved and the approach of present work differs from study [8] in an important molecular respect that we tried to study the possibility to change the focus by giving cell relationships based on the formal allosteric form, starting from Michaelis-Menten (M-M) one-site molecular control and extending the study to the well known Hill, Monod-Wyman-Changeux (MWC) and KoshlandNemethy-Filmer (KNF) patterns. All these forms of control have the potential to represent allosteric regulation and this could be very interesting when studying the RANKL/OPG balance regulation, for example [9].…”

Section: Accepted M Manuscriptmentioning

confidence: 99%

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Allosteric control model of bone remodelling containing periodical modes

Moroz¹,

Wimpenny²

2007

Biophysical Chemistry

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To help to understand the modelling process that occurs when a scaffold is implanted it is vital to understand the rather complex bone remodelling process prevalent in native bone.We have formulated a mathematical model that predicts osteoactivity both in scaffolds, as well as in bone in vivo and could set a basis for the more detailed allosteric models. The model is extended towards a bio-cybernetic vision of basic multicellular unit (BMU) action, when some of the regulation loops have been modified to reflect the allosteric control mechanisms, developed by Michaels-Menten, Hill, Koshland-Nemethy-Filmer, Monod-Wyman-Changeux.By implementation of this approach a four-dimensional system was obtained that shows steady cyclic behaviour using a wide range of constants with clear biological meaning. We have observed that a local steady-state appears as a limiting cycle in multidimensional phase space and this is discussed in this paper. Physiological interpretation of this limiting four-dimension cycle possibly related to a conservative-like value has been proposed. Analysis and simulation of the model has shown an analogy between this conservative value, as a kind of substrateenergy regenerative potential of the bone remodelling system with a molecular nature, and to the classical physical value -energy. This dynamic recovery potential is directed against both mechanical and biomechanical damage to the bone. Furthermore, the current model has credibility when compared to the normal bone remodelling process. In the framework of widely recognised Hill mechanisms of allosteric regulation the cyclic attractor, described formerly for a pure cellular model, prevails for different forms of feedback control. This result indicates the viability of the proposed existence of a conservative value (analogous to energy) that characterises the recovery potential of the bone remodelling cycle. Linear stability analysis has been performed in order to determine the robustness of the basic state, however, additional work is required to study a wider range of constants.

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“…In particular, macrophages and mesenchymal stem cells (MSCs) have been discovered to be decisive for controlling inflammation by cleaning up debris, releasing anti-inflammatory cytokines, and suppressing inflammatory immune cells functions, respectively [15,7]. However, the exact mechanisms and functions of the immune cells present at the fracture site are still not completely understood [15].…”

Section: Introductionmentioning

confidence: 99%

Modeling the effects of inflammation in bone fracture healing

Kojouharov¹,

Trejo²,

Chen-Charpentier³

2017

AIP Conference Proceedings

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Abstract.A new mathematical model is presented to study the early inflammatory effects in bone healing. It consists of a system of nonlinear ordinary differential equations that represents the interactions among macrophages, mesenchymal stem cells, and osteoblasts. A qualitative analysis of the model is performed to determine the equilibria and their corresponding stability properties. A set of numerical simulations is performed to support the theoretical results. The model is also used to numerically monitor the evolution of a broken bone for different types of fractures and to explore possible treatments to accelerate bone healing by administrating anti-inflammatory drugs.

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Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling

Cited by 269 publications

References 25 publications

PK/PD modelling of comb-shaped PEGylated salmon calcitonin conjugates of differing molecular weights

PK/PD modelling of comb-shaped PEGylated salmon calcitonin conjugates of differing molecular weights

Allosteric control model of bone remodelling containing periodical modes

Modeling the effects of inflammation in bone fracture healing

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