Phenomenological parameters from a mathematical model of cell motility are used to quantitatively characterize chemosensory migration responses of rat alveolar macrophages migrating to C5a in the linear under-agarose assay, simultaneously at the levels of both single cells and cell populations. This model provides theoretical relationships between single-cell and cell-population motility parameters. Our experiments offer a critical test of these theoretical linking relationships, by comparison of results obtained at the cell population level to results obtained at the single-cell level. Random motility of a cell population is characterized by the random motility coefficient, mu (analogous to a particle diffusion coefficient), whereas single-cell random motility is described by cell speed, s, and persistence time, P (related to the period of time that a cell moves in one direction before changing direction). Population chemotaxis is quantified by the chemotactic sensitivity, chi 0, which provides a measure of the minimum attractant gradient necessary to elicit a specified chemotactic response. Single-cell chemotaxis is characterized by the chemotactic index, CI, which ranges from 0 for purely random motility to 1 for perfectly directed motility. Measurements of cell number versus migration distance were analyzed in conjunction with the phenomenological model to determine the population parameters while paths of individual cells in the same experiment were analyzed in order to determine the single-cell parameters. The parameter mu shows a biphasic dependence on C5a concentration with a maximum of 1.9 x 10(-8) cm2/sec at 10(-11) M C5a and relative minima of 0.86 x 10(-8) cm2/sec at 10(-7) M C5a and 1.1 x 10(-8) cm2/sec in the absence of Ca; s and P remain fairly constant with C5a concentration, with s ranging from 2.1 to 2.5 microns/min and P varying from 22 to 32 min. chi 0 is equal to 1.0 x 10(-6) cm/receptor for all C5a concentrations tested, corresponding to 60% correct orientation for a difference of 500 bound C5a receptors across a 20 microns cell length. The maximum CI measured was 0.2. Values for the population parameters mu and chi 0 were calculated from single-cell parameter values using the aforementioned theoretical linking relationships. The values of mu and chi 0 calculated from single-cell parameters agreed with values of mu and chi 0 determined independently from population migrations, over the full range of C5a concentrations, confirming the validity of the linking equations. Experimental confirmation of such relationships between single-cell and cell-population parameters has not previously been reported.

译文

来自细胞运动数学模型的现象学参数用于定量表征在线性下琼脂糖测定中同时在单细胞和细胞群体水平上迁移到C5a的大鼠肺泡巨噬细胞的化学感觉迁移反应。该模型提供了单细胞和细胞群体运动参数之间的理论关系。通过将在细胞群体水平上获得的结果与在单细胞水平上获得的结果进行比较,我们的实验为这些理论联系关系提供了严格的测试。细胞群的随机运动的特征是随机运动系数mu (类似于粒子扩散系数),而单细胞随机运动则由细胞速度,s和持续时间描述,P (与单元格在改变方向之前沿一个方向移动的时间段有关)。群体趋化性通过趋化敏感性chi 0来量化,chi 0提供了引起指定趋化反应所需的最小引诱剂梯度的量度。单细胞趋化性的特征是趋化指数CI,其范围从纯随机运动的0到完全定向运动的1。结合现象学模型分析了细胞数量与迁移距离的测量结果,以确定种群参数,同时分析了同一实验中单个细胞的路径,以确定单细胞参数。参数mu显示了对C5a浓度的双相依赖性,在10(-11) M C5a时最大值为1.9 × 10(-8) cm2/秒,在10(-7) M C5a和1.1 × 10(-10) 相对最小值为0.86 × 10(-8) cm2/秒。8) 在没有Ca的情况下cm2/sec; s和P在C5a浓度下保持相当恒定,s的范围为2.1至2.5微米/分钟,P的变化范围为22至32分钟。对于所有测试的C5a浓度,chi 0等于1.0x10(-6) cm/受体,对应于跨越20微米细胞长度的500结合C5a受体的差异的60% 正确取向。测量的最大CI为0.2。使用上述理论链接关系,根据单细胞参数值计算种群参数mu和chi 0的值。在整个C5a浓度范围内,由单细胞参数计算出的mu和chi 0的值与独立于种群迁移而确定的mu和chi 0的值一致,从而证实了链接方程的有效性。以前尚未报道过单细胞和细胞群体参数之间这种关系的实验证实。

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