Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Absolute quantification of human tear lactoferrin using multiple reaction monitoring technique with stable-isotopic labeling

The mass spectrometry technique of multiple reaction monitoring (MRM) was used to quantify and compare the expression level of lactoferrin in tear films among control, prostate cancer (CaP), and benign prostate hyperplasia (BPH) groups. Tear samples from 14 men with CaP, 15 men with BPH, and 14 controls were analyzed in the study. Collected tears (2 μl) of each sample were digested with trypsin overnight at 37 °C without any pretreatment, and tear lactoferrin was quantified using a lactoferrin-specific peptide, VPSHAVVAR, both using natural/light and isotopic-labeled/heavy peptides with MRM. The average tear lactoferrin concentration was 1.01 ± 0.07 μg/μl in control samples, 0.96 ± 0.07 μg/μl in the BPH group, and 0.98 ± 0.07 μg/μl in the CaP group. Our study is the first to quantify tear proteins using a total of 43 individual (non-pooled) tear samples and showed that direct digestion of tear samples is suitable for MRM studies. The calculated average lactoferrin concentration in the control group matched that in the published range of human tear lactoferrin concentration measured by enzyme-linked immunosorbent assay (ELISA). Moreover, the lactoferrin was stably expressed across all of the samples, with no significant differences being observed among the control, BPH, and CaP groups.