Elsevier

Bone

Volume 45, Issue 5, November 2009, Pages 1017-1023
Bone

The dependency of solute diffusion on molecular weight and shape in intact bone

https://doi.org/10.1016/j.bone.2009.07.076Get rights and content

Abstract

Solute transport through the bone lacunar–canalicular system (LCS) is essential for osteocyte survival and function, but quantitative data on the diffusivity of various biological molecules in the LCS are scarce. Using our recently developed approach based on fluorescence recovery after photobleaching (FRAP), diffusion coefficients of five exogenous fluorescent tracers (sodium fluorescein, dextran-3k, dextran-10k, parvalbumin, and ovalbumin) were measured in murine tibiae in situ. These tracers were chosen to test the dependency of solute diffusion on molecular weight (376–43,000 Da) and shape (linear vs. globular). Among the five tracers, no fluorescence recovery (and thus mobility) was detected for dextran-10k and the diffusion coefficients (DLCS) of the other four tracers were 295 ± 46, 128 ± 32, 157 ± 88, 65 ± 21 μm2 s 1 in the LCS, respectively. Overall, the rate of solute diffusion in the bone LCS showed strong dependency on molecular size and shape. Diffusivity decreased with increasing molecular weight for both linear and globular molecules, with the linear molecules decreasing at a faster rate. Compared with free diffusion (Dfree) in aqueous solutions, the relative diffusivities (DLCS / Dfree) of the four tracers were not significantly different for sodium fluorescein, dextran-3k, parvalbumin, and ovalbumin (55.0 ± 8.6%, 68.1 ± 17.0%, 79.7 ± 44.7%, 61.0 ± 19.6%, respectively). This result did not agree with the homogenous molecular sieve model proposed for the osteocytic pericellular matrix structure. Instead, a heterogeneous porous model of the pericellular matrix may account for the observed solute transport in the LCS. In summary, the present study provides quantitative data on diffusion of various nutrients and signaling molecules in the LCS that are important for bone metabolism and mechanotransduction.

Introduction

Osteocytes, the most abundant cells in bone, are believed to serve as mechanical sensors and as modulators of other bone cells during bone adaptation and remodeling [1], [2], [3], [4], [5]. Recent evidence suggests that osteocytes play more active roles in bone physiology through matrix maintenance and modification and the regulation of systemic phosphate metabolism [1], [3]. These interconnected osteocytes are encased within the lacunar–canalicular pore system (LCS) [6] where they may detect external mechanical loading (in terms of substrate deformation, load-induced fluid flow, pressure, as well as secondary signals such as streaming potentials and chemo-transport [1], [2], [3], [4], [5], [7], [8]) and subsequently transduce biochemical response signals to other osteocytes or effector cells either intracellularly via gap junctions [9], [10] or extracellularly via the pericellular space [7]. Osteocytes express a variety of secretory molecules that could fulfill these regulatory functions such as adenosine-5′-triphosphate (ATP) [11], nitric oxide [12], [13], prostaglandin E2 [14], [15], osteoprotegerin (OPG) and its soluble ligand (sRANKL) [16], [17], [18], dentin matrix protein-1 (DMP-1) [19], sclerostin [20], and fibroblasts growth factor (FGF23) [1]. Transport of these signaling molecules, along with nutrients and metabolic wastes, is essential for the survival and proper functioning of osteocytes [21], [22]. However, it remains difficult to quantitatively measure molecular transport in situ and in vivo due to i) the small dimensions of the osteocyte LCS, and ii) the presence of mineralized tissue.

With a newly developed in situ imaging method based on fluorescence recovery after photobleaching [23], measurement of in situ and real-time solute diffusion has become feasible. Utilizing the optical sectioning capability and the high spatial resolution of laser scanning confocal microscopy, solute diffusivity in the tiny canalicular channels (order 0.5 micron in diameter) can be quantified by time series imaging of the fluorescence recovery after photobleaching of individual osteocyte lacuna (order 10 μm in linear dimension) [23]. Compared with the few previous studies attempted to measure dynamic transport in bone utilizing the solute desorption method [24], [25], FRAP has the obvious advantages of high speed (i.e., measurement can be completed within minutes vs. hours and days in the desorption methods [24], [25]), high spatial resolution (i.e., at the lacunar–canalicular level vs. at mm level of the tissue blocks [24], [25]), and minimal invasiveness (i.e., no sectioning is needed) [21], [26]. Using this FRAP technique, we have previously quantified diffusion of a small molecule (sodium fluorescein, 376 Da) in murine tibia in situ and in real-time by fitting the FRAP data to a two-compartment model [23].

The objective of the present study was to quantify diffusion of molecules with varying molecular weight and shape in the bone LCS using the established FRAP approach. Representative fluorescent tracers, as surrogates of the biological signaling molecules or nutrients found in bone, were selected with a range of molecular weights and of either linear or globular shape. Our hypothesis was that solute diffusion in the bone LCS decreases with increasing molecular weight and this relationship varies with molecular shape. We also explored mechanisms such as steric exclusion to explain retarded tracer diffusion in LCS as compared to free diffusion in aqueous solutions. These systemic studies yielded quantitative data on the mobility of various molecules that are important in bone mechanotransduction and metabolism. The results can also help mapping the distribution of some commonly used drugs such as anti-resorptive bisphosphonates and parathyroid hormone segments in bone. The knowledge of how molecules move in bone provides design guidelines for the formulation of pharmaceutical agents and their carrier systems to ensure effective transport into the bone tissue.

Section snippets

Fluorescent tracers

Five fluorescent tracers including sodium fluorescein, dextrans-3k conjugated with fluorescein, dextran-10k conjugated with fluorescein, parvalbumin conjugated with Alexa Fluor 488, and ovalbumin conjugated with Texas Red were selected, thereby permitting the testing of tracers with various molecular weights (from 376 to 43,000 Da) of either linear (for dextrans) or globular shape (Table 1). Tracers were purchased from Molecular Probes/Invitrogen Corp., (Eugene, OR) except for sodium

Diffusion in the bone LCS

Overall, solute diffusion showed a strong dependence on the molecular weight (size) and the shape of the fluorescent molecule (Fig. 2, Table 2). The diffusion coefficient measured in the bone LCS decreased with increasing molecular weight for both linear and globular molecules, and the linear dextrans moved slower than globular proteins of comparable molecular weights. For instance, diffusion of dextran-10k was barely measurable in the LCS, while the globular parvalbumin of comparable molecular

Discussion

The present study aimed to quantify diffusion of molecules of various size and shape in the bone lacunar–canalicular system within an intact long bone. Transport of functional molecules is critical for bone's mechanosensation and metabolism, because these molecules are involved in cell-to-cell signaling and tissue nutrition (some example molecules are shown in Table 4). Using our newly developed FRAP approach [23], we have injected five exogenous fluorescent tracers to mimic the functional

Acknowledgments

This study was supported by grants from NIH (AR054385 and P20RR016458 (to LW), AR41210 (to MBS)) and Canadian National Sciences and Engineering Research Council (NSERC 341704-08, to LY). The authors thank the valuable comments and technical help from Drs. Chris Price, Randy Duncan, Mary C. Farach-Carson, Xinqiao Jia, and Ms. Sue Seta of University of Delaware. We also thank Dr. Junmin Zhu from the Western Case Reserve University for running molecular simulations on dextrans.

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