The biophysical basis of bacterial colony growth.

Bacteria often attach to surfaces and grow densely-packed communities called biofilms. As biofilms grow, they expand across the surface, increasing their surface area and access to nutrients. Thus, the overall growth rate of a biofilm is directly dependent on its "range expansion" rate. One factor that limits the range expansion rate is vertical growth; at the biofilm edge there is a direct trade-off between horizontal and vertical growth-the more a biofilm grows up, the less it can grow out. Thus, the balance of horizontal and vertical growth impacts the range expansion rate and, crucially, the overall biofilm growth rate. However, the biophysical connection between horizontal and vertical growth remains poorly understood, due in large part to difficulty in resolving biofilm shape with sufficient spatial and temporal resolution from small length scales to macroscopic sizes. Here, we experimentally show that the horizontal expansion rate of bacterial colonies is controlled by the contact angle at the biofilm edge. Using white light interferometry, we measure the three-dimensional surface morphology of growing colonies, and find that small colonies are surprisingly well-described as spherical caps. At later times, nutrient diffusion and uptake prevent the tall colony center from growing exponentially. However, the colony edge always has a region short enough to grow exponentially; the size and shape of this region, characterized by its contact angle, along with cellular doubling time, determines the range expansion rate. We found that the geometry of the exponentially growing biofilm edge is well-described as a spherical-cap-napkin-ring, i.e., a spherical cap with a cylindrical hole in its center (where the biofilm is too tall to grow exponentially). We derive an exact expression for the spherical-cap-napkin-ring-based range expansion rate; further, to first order, the expansion rate only depends on the colony contact angle, the thickness of the exponentially growing region, and the cellular doubling time. We experimentally validate both of these expressions. In line with our theoretical predictions, we find that biofilms with long cellular doubling times and small contact angles do in fact grow faster than biofilms with short cellular doubling times and large contact angles. Accordingly, sensitivity analysis shows that biofilm growth rates are more sensitive to their contact angles than to their cellular growth rates. Thus, to understand the fitness of a growing biofilm, one must account for its shape, not just its cellular doubling time.

Ossifying bone marrow explant culture as a three-dimensional mechanoresponsive in vitro model of osteogenesis.

Mechanical cues play an important role in bone regeneration and affect production and secretion dynamics of growth factors (GFs) involved in osteogenesis. The in vitro models for investigating the mechanoresponsiveness of the involvement of GFs in osteogenesis are limited to two-dimensional monolayer cell culture studies, which do not effectively embody the physiological interactions with the neighboring cells of different types and the interactions with a natural extracellular matrix. Natural bone formation is a complex process that necessitates the contribution of multiple cell types, physical and chemical cues in a three-dimensional (3D) setting. There is a need for in vitro models that represent the physiological diversity and characteristics of bone formation to realistically study the effects of mechanical cues on this process. In vitro cultures of marrow explants inherently ossify and they embody the multicellular and 3D nature of osteogenesis. Therefore, the aim of this study was to assess the mechanoresponsiveness of the scaffold-free, multicellular, and 3D model of osteogenesis based on inherent marrow ossification and to investigate the effects of mechanical loading on the osteoinductive GF production dynamics of this model. These aims were achieved by (1) culturing rat bone marrow explants for 28 days under basal conditions that facilitate inherent ossification, (2) employing mechanical stimulation (compressive loading) between days 12 and 26, and (3) quantifying the final ossified volume (OV) and the production levels of bone morphogenetic protein-2, vascular endothelial growth factor, insulin-like growth factor-1, and transforming growth factor-ß1. The results showed that the final OV of the marrow explants increased by about fourfold in mechanically stimulated samples. Further, mechanical stimulation sustained the production level of vascular endothelial growth factor (starting day 21), which otherwise declined temporally under static conditions. The production levels of insulin-like growth factor-1 and transforming growth factor-ß1 were enhanced under the effect of loading after day 21. In addition, significant correlations were observed between the final OV and the levels of GFs analyzed. In conclusion, this study demonstrates that the scaffold-free, multicellular, and 3D model of bone formation based on inherent ossification of marrow tissue is mechanoresponsive and mechanical loading improves in vitro osteogenesis in this model with sustaining or enhancing osteoinductive GF production levels, which otherwise would decline with increasing time.