CNRS, LIEC (Laboratoire Interdisciplinaire des Environnements Continentaux), UMR7360, Vandoeuvre-lès-Nancy, F-54501, France.
Phys Chem Chem Phys. 2013 May 28;15(20):7873-88. doi: 10.1039/c3cp00002h. Epub 2013 Apr 22.
A theory is proposed for the dynamics of metal uptake by a spherical microorganism whose peripheral structure consists of a charged bioactive surface surrounded by a soft (ion-permeable) charged layer. The formalism explicitly considers the concomitant steady-state conductive diffusion transport of metals from bulk medium to the bioactive surface and the kinetics of intracellular metal internalisation described by a Michaelis-Menten mechanism. The spatial distribution of metals at the microorganism/solution interphase is derived from an explicit solution of the Nernst-Planck equation with differentiated metal diffusion coefficients inside and outside the microorganism soft surface layer. The metal concentration profile involves the interphasial electrostatic potential distribution governed by the Poisson-Boltzmann equation accounting for the dielectric permittivity gradient across the soft layer/solution interface. The resulting metal uptake flux is rationalized in terms of dimensionless metal-biosurface affinity and the ratio between limiting uptake flux and limiting conductive diffusion flux. Both parameters depend on background electrolyte concentration, microorganism soft surface composition and geometry via their connection to a Boltzmann surface term and a factor expressing the electrostatically-driven retardation or acceleration of metal diffusion. Illustrations demonstrate how metal transport dynamics impacts biouptake depending on electrolyte concentration and on the key bio-physico-chemical properties of the biointerphase. The mathematical framework is then applied to practical situations where a swarm of charged microorganisms deplete metals under steady-state transport conditions. Several depletion kinetic regimes are evaluated as a function of medium salinity and microorganism electrostatic features. Expressions of their characteristic timescales are derived and analogies with equivalent electrochemical circuits are formulated.
提出了一种用于描述金属被带电荷的生物活性表面包围的球形微生物摄取的动力学理论。该理论的形式体系明确考虑了金属从主体介质到生物活性表面的稳态导电扩散传输以及米氏动力学（Michaelis-Menten kinetics）描述的细胞内金属内化过程。微生物/溶液界面处的金属空间分布是通过纳恩斯特-普朗克（Nernst-Planck）方程的显式解推导出来的，该方程考虑了微生物软表面层内外不同的金属扩散系数。金属浓度分布涉及到由泊松-玻尔兹曼（Poisson-Boltzmann）方程控制的相间静电势分布，该方程考虑了软层/溶液界面处的介电常数梯度。所得的金属摄取通量可以用无量纲金属-生物表面亲和力和限制摄取通量与限制导电扩散通量之比来合理化。这两个参数取决于背景电解质浓度、微生物软表面的组成和几何形状，通过它们与玻尔兹曼表面项和表示静电驱动金属扩散延迟或加速的因子的关系来实现。实例说明了金属传输动力学如何根据电解质浓度以及生物相间的关键生物物理化学特性来影响生物摄取。然后将数学框架应用于带电微生物在稳态传输条件下耗尽金属的实际情况。评估了几种耗尽动力学状态，作为介质盐度和微生物静电特性的函数。推导出了它们的特征时间尺度的表达式，并制定了与等效电化学电路的类比。
