Mathematical models in biology: from molecules to life

Defining the optimal lymphadenectomy cut-off value in epithelial ovarian cancer staging surgery utilizing a mathematical model of validation

OBJECTIVE

Since 1985 International Federation of Gynecology and Obstetrics includes pelvic and aortic lymphadenectomy as part of the surgical staging in epithelial ovarian cancer (EOC). There is no consensus on the overall number of nodes needed in a systematic lymphadenectomy. The aim of this study is to calculate the optimal cut-off value using a mathematical modeling approach.

METHODS

Data was collected retrospectively, from 1996 to 2000, of 120 consecutive Mayo Clinic patients with EOC and positive nodes. All patients was underwent pelvic and/or aortic lymphadnectomy during surgical staging. To mathematically predict the probability of a positive node in EOC patients we used a predictive mathematical model (PMM). The mathematical analysis consisted: creation of a new PMM according to our purposes, application of PMM to describe the experimental data in order to build the polynomial regression curves in each lymphatic area and determine the optimal point for each curve.

RESULTS

The mean number of lymph nodes and metastatic nodes removed were 35 and 7.8, respectively; the mean percentage of positive nodes was 28.3%. The optimal point of each fitting curves were: 7 nodes for unilateral aortic nodal sampling (at least 3 infrarenal or 5 inframesenteric) and 15 nodes for unilateral pelvic lymphadenectomy (at least 5 external iliac).

CONCLUSIONS

We can mathematically predict the probability to obtain a positive node in EOC surgical staging. Our results have shown the need to obtain at least 22 lymph nodes between pelvic and aortic lymphadenectomy.

proTeOn and proTeOff, new protein devices that inducibly activate bacterial gene expression

Using an original workflow, we have modeled, constructed, and characterized two new molecular devices that inducibly activate gene expression in Escherichia coli. The devices, prokaryotic-TetOn and prokaryotic-TetOff, were built by fusing an inducible DNA-binding protein domain to a transcription activation domain and constructing a complementary synthetic promoter sequence through which they could control downstream gene expression. In particular, the transactivators were built using variants of the tetracycline repressor, TetR, and the transactivating domain of the LuxR activator. The complementary promoter sequence included TetR's operator, tetO, and elements of the lux promoter. These specific protein domains and their operator sites were chosen as they have been thoroughly studied and well characterized. First, our methodology began with optimizing the geometry of the molecular components using molecular modeling. We did so to achieve an unprecedented combination of controllable and transactivating function in bacterial organisms. The devices were then built to activate the expression of green fluorescent protein. Their unique function was found to be robustly tight and activating many-fold increases of expressed gene levels, as measured by flow cytometry experiments. The devices were further characterized with stochastic kinetic models. The new devices presented herein may become useful additions to the molecular toolboxes used by biologists to control bacterial gene expression. The methodology used may also be a foundation for the design, development, and characterization of a library of such devices and more complex gene regulatory networks.