Chan V, Graves D J, McKenzie S E
Department of Chemical Engineering, University of Pennsylvania, Philadelphia, USA.
Biophys J. 1995 Dec;69(6):2243-55. doi: 10.1016/S0006-3495(95)80095-0.
A mathematical model based on receptor-ligand interactions at a cell surface has been modified and further developed to represent heterogeneous DNA-DNA hybridization on a solid surface. The immobilized DNA molecules with known sequences are called probes, and the DNA molecules in solution with unknown sequences are called targets in this model. Capture of the perfectly complementary target is modeled as a combined reaction-diffusion limited irreversible reaction. In the model, there are two different mechanisms by which targets can hybridize with the complementary probes: direct hybridization from the solution and hybridization by molecules that adsorb nonspecifically and then surface diffuse to the probe. The results indicate that nonspecific adsorption of single-stranded DNA on the surface and subsequent two-dimensional diffusion can significantly enhance the overall reaction rate. Heterogeneous hybridization depends strongly on the rate constants for DNA adsorption/desorption in the non-probe-covered regions of the surface, the two-dimensional (2D) diffusion coefficient, and the size of probes and targets. The model shows that the overall kinetics of DNA hybridization to DNA on a solid support may be an extremely efficient process for physically realistic 2D diffusion coefficients, target concentrations, and surface probe densities. The implication for design and operation of a DNA hybridization surface is that there is an optimal surface probe density when 2D diffusion occurs; values above that optimum do not increase the capture rate. Our model predicts capture rates in agreement with those from recent experimental literature. The results of our analysis predict that several things can be done to improve heterogeneous hybridization: 1) the solution phase target molecules should be about 100 bases or less in size to speed solution-phase and surface diffusion; 2) conditions should be created such that reversible adsorption and two-dimensional diffusion occur in the surface regions between DNA probe molecules; 3) provided that 2) is satisfied, one can achieve results with a sparse probe coverage that are equal to or better than those obtained with a surface totally covered with DNA probes.
基于细胞表面受体 - 配体相互作用的数学模型已被修改并进一步发展，以描述固体表面上的异质DNA - DNA杂交。在该模型中，具有已知序列的固定化DNA分子称为探针，溶液中具有未知序列的DNA分子称为靶标。完美互补靶标的捕获被建模为反应 - 扩散受限的不可逆反应。在该模型中，靶标与互补探针杂交有两种不同机制：从溶液中直接杂交以及非特异性吸附然后在表面扩散到探针的分子进行杂交。结果表明，单链DNA在表面的非特异性吸附以及随后的二维扩散可显著提高整体反应速率。异质杂交强烈依赖于表面未被探针覆盖区域中DNA吸附/解吸的速率常数、二维扩散系数以及探针和靶标的大小。该模型表明，对于实际的二维扩散系数、靶标浓度和表面探针密度，固体支持物上DNA杂交的整体动力学可能是一个极其高效的过程。DNA杂交表面设计和操作的意义在于，当发生二维扩散时存在最佳表面探针密度；高于该最佳值不会提高捕获率。我们的模型预测的捕获率与近期实验文献中的结果一致。我们的分析结果预测，可以采取以下几种方法来改善异质杂交：1）溶液相靶标分子的大小应约为100个碱基或更小，以加快溶液相和表面扩散；2）应创造条件，使DNA探针分子之间的表面区域发生可逆吸附和二维扩散；3）只要满足2），稀疏探针覆盖度就能获得与完全被DNA探针覆盖的表面相同或更好的结果。
