The chemical master equation (CME) represents the accepted stochastic description of chemical reaction kinetics in mesoscopic systems. As its exact solution—which gives the corresponding probability density function—is possible only in very simple cases; there is a clear need for approximation techniques. Here, we propose a novel perturbative three-step approach, which draws heavily on graph theory: (i) we expand the eigenvalues of the transition state matrix in the CME as a series in a nondimensional parameter that depends on the reaction rates and the reaction volume; (ii) we derive an analogous series for the corresponding eigenvectors via a graph-based algorithm; (iii) we combine the resulting expansions into an approximate solution to the CME. We illustrate our approach by applying it to a reversible dimerization reaction; then we formulate a set of conditions, which ensure its applicability to more general reaction networks, and we verify those conditions for two common catalytic mechanisms. Comparing our results with the linear-noise approximation (LNA), we find that our methodology is consistently more accurate for sufficiently small values of the nondimensional parameter. This superior accuracy is particularly evident in scenarios characterized by small molecule numbers, which are typical of conditions inside biological cells.
Background
Achalasia is a rare esophageal motor disorder. Laparoscopic Heller-Dor myotomy (LHD) is among the most effective treatments. The use of nasogastric tube (NGT) following LHD is still controversial. The aim of our study was to evaluate the role of NGT in achalasia patients undergoing LHD.
Methods
We prospectively enrolled achalasia patients treated with LHD from January 2019 until June 2022 at our institution and randomly assigned them to two groups: one group with NGT and group without (noNGT). Perioperative outcomes were compared between the two groups. ClinicalTrials.gov Identifier: NCT05729971.
Results
Seventy-nine patients who underwent LHD myotomy were prospectively enrolled. Patients were divided in two groups: 38 with NGT and 41 noNGT. There were no significant differences between two groups in terms of demographic data, preoperative characteristics, length of stay, start of liquid and solid diet, intraoperative and postoperative complications. First flatus was shorter in the noNGT group (p: 0.03).
Conclusion
Nasogastric tube placement following LHD myotomy does not reduce nausea, vomiting and chest pain, while it increased patients discomfort and time of first flatus.
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