Modeling the effect of cell-associated polymeric fluid layers on force spectroscopy measurements. Part I: model...

The mechanical response, the force-indentation relationship, in normal force spectroscopy measurements carried out on individual polysaccharide encapsulated bacteria is modeled using three increasingly refined approaches that consider the elastic response of the bacterium and cantilever in combination with a fluid (hydrodynamic) model for the polysaccharide layer. For the hydrodynamic description of the polysaccharide layer, several increasingly realistic models are described in detail, together with numerical solution techniques. These models range from one-dimensional, Newtonian, to two-dimensional, axisymmetric, fully viscoelastic (Phan-Thien/Tanner). In all cases, the models rigorously consider the time-dependent rheological-mechanical coupling between the elastic and fluid viscoelastic physical components of the experimental setup. Effects of inherent variability in geometrical and material properties of the bacterium and polysaccharide layer on the measurable response are quantified. A parametric investigation of the force-indentation relationship highlights the importance of accurate knowledge of the rheology of the extracellular polysaccharides. We also draw conclusions about the design and evaluation of force spectroscopy experiments on single encapsulated bacteria. Supported by model calculations, we also point the way to methods of in vivo rheological characterization of the extracellular polysaccharide as a preferable alternative to characterization after its removal from the native environment.