Mathematical and computational modelling of biochemical mechanisms

我的研究重点是建立和分析数学和计算模型，以阐明各种生化现象背后的机制。只要有可能，我就与收集定量数据的实验学家密切合作，这些数据的分析需要开发新的方法。用这些方法研究的两个理想系统是细菌细胞分裂调节蛋白MinCDE和atp结合盒（ABC）转运蛋白。******* atp结合盒（ABC）转运蛋白形成了广泛的跨膜蛋白，促进糖、离子、脂质、氨基酸、肽和各种药物跨细胞膜的单向运输。abc转运体氯离子通道的突变是囊性纤维化的潜在原因。细菌对抗生素的耐药性和癌细胞对某些药物治疗的耐药性都是由ABC转运蛋白促进的。在过去的几年中，对这些转运体的生物化学的详细了解逐渐出现，但对这些蛋白质功能的机制的全面和定量的描述仍然是一个重要的研究目标。******* Min蛋白MinC、MinD和MinE是细菌细胞分裂的重要空间调控因子，它们在膜上相互作用，产生振荡的空间交替的极对极定位。空间格局的形成最近被重建在体外的平面支撑膜和细胞形状的微制造室。在支撑膜上观察到行波和螺旋波，在细胞状腔室中观察到类似体内的振荡。尽管在过去的15年里发表了许多模型，但对于蛋白质相互作用的精确细节仍然没有共识，也没有一个定量准确的模型可以概括体内和体外生化时间过程水平的实验观察。*******我为处理这类问题而建立的数学模型有多种形式，包括普通方程、偏微分方程、积分微分方程、离散映射、随机过程、基于代理的模拟等。在分析数据和模型时出现的一些较常见的技术是渐近分析、分岔分析、数值方法、参数估计（非线性回归、模型松弛等）、模型选择（f检验、AIC等）、图像处理和分析

My research focusses on building and analysing mathematical and computational models to elucidate the mechanisms underlying various biochemical phenomena. Whenever possible, I work closely with experimentalists who gather quantitative data, the analysis of which requires the development of novel methods. Two systems ideal for study with these methods are the bacterial cell-division-regulating proteins MinCDE and the ATP-binding cassette (ABC) transporters.*******ATP-binding cassette (ABC) transporters form a broad class of transmembrane proteins that facilitate unidirectional transport of sugars, ions, lipids, amino acids, peptides and various drugs across cell membranes. Mutations in an ABC-transporter chloride ion channel are the underlying cause of cystic fibrosis. Bacterial resistance to antibiotics and cancer-cell resistance to certain drug treatments are both facilitated by ABC transporters. A detailed understanding of the biochemistry of these transporters has been emerging gradually over the last few years but a comprehensive and quantitative picture of the mechanisms by which these proteins function remains an important research goal.*******The Min proteins, MinC, MinD and MinE, form an important spatial regulator of cell division in bacteria, where they interact on the membrane to generate an oscillatory spatially alternating pole-to-pole localization. Spatial pattern formation has recently been reconstituted in vitro on flat supported membrane and in cell-shaped micro-fabricated chambers. Traveling waves and spiral waves on supported membrane and in vivo-like oscillations in cell-shaped chambers have been observed. Despite the publication of numerous models over the last decade and a half, there is still no consensus on the precise details of the protein interactions and no single quantitatively accurate model that recapitulates experimental observations both in vivo and in vitro at the level of biochemical time courses.*******The mathematical models I formulate to work on these types of problems come in many forms including ordinary, partial and integro- differential equations, discrete maps, stochastic processes, agent-based simulations and others. Some of the more common techniques that arise in analyzing the data and models are asymptotic analysis, bifurcation analysis, numerical methods, parameter estimation (nonlinear regression, model relaxation, etc.), model selection (F-test, AIC, etc.), image processing and analysis.**