Lubricating Bacteria Model for Branching growth of Bacterial Colonies

Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial cooperative self-organization. Central part of the cooperation is the collective formation of lubricant on top of the agar which enables the bacteria to swim. Hence it provides the colony means to advance towards the food. One method of modeling the colonial development is via coupled reaction-diffusion equations which describe the time evolution of the bacterial density and the concentrations of the relevant chemical fields. This idea has been pursued by a number of groups. Here we present an additional model which specifically includes an evolution equation for the lubricant excreted by the bacteria. We show that when the diffusion of the fluid is governed by nonlinear diffusion coefficient branching patterns evolves. We study the effect of the rates of emission and decomposition of the lubricant fluid on the observed patterns. The results are compared with experimental observations. We also include fields of chemotactic agents and food chemotaxis and conclude that these features are needed in order to explain the observations.Comment: 1 latex file, 16 jpeg files, submitted to Phys. Rev.

Supplementary Material for: Impact of Age on the Management of Primary Melanoma Patients

<b><i>Objectives:</i></b> Age is an understudied factor when considering treatment options for melanoma. Here, we examine the impact of age on primary melanoma treatment in a prospective cohort of patients. <b><i>Methods:</i></b> We used logistic regression models to examine the associations between age and initial treatment, using recurrence and melanoma-specific survival as endpoints. <b><i>Results:</i></b> 444 primary melanoma patients were categorized into three groups by age at diagnosis: 19-45 years (24.3%), 46-70 (50.2%), and 71-95 (25.5%). In multivariate models, older patients experienced a higher risk of recurrence (hazard ratio 3.34, 95% confidence interval, CI, 1.53-7.25; p < 0.01). No significant differences were observed in positive biopsy margin rates or extent of surgical margins across age groups. Patients in the middle age group were more likely to receive adjuvant therapy than those in the older group (odds ratio 2.78, 95% CI 1.19-6.45; p = 0.02) and showed a trend to longer disease-free survival when receiving adjuvant therapy (p = 0.09). <b><i>Conclusion:</i></b> Our data support age as an independent negative prognostic factor in melanoma. Our data suggest that age does not affect primary surgical treatment but may affect decisions of whether or not patients receive postoperative treatment(s). Further work is needed to better understand the biological variables affecting treatment decisions and efficacy in older patients