MATHEMATICAL METHODS IN GEL ELECTROPHORESIS

电泳法是生物学中广泛使用的一种分离技术， 对大分子和颗粒的复杂混合物进行分类和研究 (如DNA)。我们已经将数学方法和技术应用于 电泳法中的问题。特别是，我们开发了一些模型 描述大分子和病毒大小的颗粒在 凝胶。我们定义了一个分解函数，它很好地适应于 微粒的电泳法分离，如DNA。的模型。 运动，与分辨率函数一起，使我们能够预测 求解复杂问题的最短时间和最优偏移路径 混合物，例如在DNA测序中遇到的那些混合物。我们还有 开发了评估各种聚合物的效率的方法 不同大小的大分子的分离。为此，我们 定义了分离效率函数，以及分离效率函数 分辨率效率函数。这些函数用于评估 不同的聚合物彼此相对。这些技术为我们提供了一个 选择最有效筛分聚合物的实用方法 针对特定分子大小的解决方案。最后，我们实现了 在分析中使用的数学算法是一种用户友好的 在个人计算机上使用的软件包。

Electrophoresis is a technique widely used in biology to separate, classify, and study complex mixtures of macromolecules and particles (such as DNA). We have applied mathematical methods and techniques to problems in electrophoresis. In particular, we have developed models describing the motion of macromolecules and virus-sized particles in gels. We have defined a resolution function which is well adapted to electrophoretic separation of particles such as DNA. The models of motion, together with the resolution function, allow us to predict the minimal time and optimal migration path for the resolution of complex mixtures, such as those encountered in DNA sequencing. We have also developed methods for evaluating the efficiency of various polymers in the separation of macromolecules of various sizes. For this purpose, we have defined the separation efficiency function, as well as the resolution efficiency function. These functions are used to evaluate different polymers relative to one another. These techniques give us a practical means by which to select the most efficiently sieving polymer solution for a particular molecular size. Finally, we have implemented the mathematical algorithms used in the analyses in a user-friendly software package for use on a personal computer.