Modeling and Analysis of the Molecular Basis of Pain in Sensory Neurons

Intracellular calcium dynamics are critical to cellular functions like pain transmission. Extracellular ATP plays an important role in modulating intracellular calcium levels by interacting with the P2 family of surface receptors. In this study, we developed a mechanistic mathematical model of ATP-induced P2 mediated calcium signaling in archetype sensory neurons. The model architecture, which described 90 species connected by 162 interactions, was formulated by aggregating disparate molecular modules from literature. Unlike previous models, only mass action kinetics were used to describe the rate of molecular interactions. Thus, the majority of the 252 unknown model parameters were either association, dissociation or catalytic rate constants. Model parameters were estimated from nine independent data sets taken from multiple laboratories. The training data consisted of both dynamic and steady-state measurements. However, because of the complexity of the calcium network, we were unable to estimate unique model parameters. Instead, we estimated a family or ensemble of probable parameter sets using a multi-objective thermal ensemble method. Each member of the ensemble met an error criterion and was located along or near the optimal trade-off surface between the individual training data sets. The model quantitatively reproduced experimental measurements from dorsal root ganglion neurons as a function of extracellular ATP forcing. Hypothesized architecture linking phosphoinositide regulation with P2X receptor activity explained the inhibition of P2X-mediated current flow by activated metabotropic P2Y receptors. Sensitivity analysis using individual and the whole system outputs suggested which molecular subsystems were most important following P2 activation. Taken together, modeling and analysis of ATP-induced P2 mediated calcium signaling generated qualitative insight into the critical interactions controlling ATP induced calcium dynamics. Understanding these critical interactions may prove useful for the design of the next generation of molecular pain management strategies

The Gracilis Myocutaneous Free Flap: A Quantitative Analysis of the Fasciocutaneous Blood Supply and Implications for Autologous Breast Reconstruction

BACKGROUND: Mastectomies are one of the most common surgical procedures in women of the developed world. The gracilis myocutaneous flap is favoured by many reconstructive surgeons due to the donor site profile and speed of dissection. The distal component of the longitudinal skin paddle of the gracilis myocutaneous flap is unreliable. This study quantifies the fasciocutaneous vascular territories of the gracilis flap and offers the potential to reconstruct breasts of all sizes. METHODS: Twenty-seven human cadaver dissections were performed and injected using lead oxide into the gracilis vascular pedicles, followed by radiographic studies to identify the muscular and fasciocutaneous perforator patterns. The vascular territories and choke zones were characterized quantitatively using the 'Lymphatic Vessel Analysis Protocol' (LVAP) plug-in for Image J® software. RESULTS: We found a step-wise decrease in the average vessel density from the upper to middle and lower thirds of both the gracilis muscle and the overlying skin paddle with a significantly higher average vessel density in the skin compared to the muscle. The average vessel width was greater in the muscle. Distal to the main pedicle, there were either one (7/27 cases), two (14/27 cases) or three (6/27 cases) minor pedicles. The gracilis angiosome was T-shaped and the maximum cutaneous vascular territory for the main and first minor pedicle was 35 × 19 cm and 34 × 10 cm, respectively. CONCLUSION: Our findings support the concept that small volume breast reconstructions can be performed on suitable patients, based on septocutaneous perforators from the minor pedicle without the need to harvest any muscle, further reducing donor site morbidity. For large reconstructions, if a 'T' or tri-lobed flap with an extended vertical component is needed, it is important to establish if three territories are present. Flap reliability and size may be optimized following computed tomographic angiography and surgical delay