Local probes and heterogeneous catalysis: A case study of a mitochondria-luciferase-hexokinase coupled system

Biological systems are characterized by a high degree of structural organization. In the intracellular context, this introduces physical constraints which are not considered in the standard biochemical analysis of isolated systems, aimed towards mechanistic studies. A major challenge in cellular biology is thus to integrate the structural and mechanistic information and reach an adequate representation of the modes of operation in situ. We present an approach to this problem which takes advantage of a localized probe to study heterogeneous coupled system, as minimal models for cellular operation. The system consists of ATP production at the surface of mitochondria, and ATP consumption in solution by the hexokinase reaction. Soluble or biologically localized firefly luciferase is used to continuously monitor ATP concentration either in the bulk solution or at the surface of the organelle, respectively. The general system of a surface source and a bulk sink is mathematically modeled, and an analytic steady-state solution for local and bulk ATP is presented. The results are validated by experiment and differ from the expected behavior of an equivalent homogeneous system in solution. The model is further adapted to evaluate the effect of mixing. In addition, two limiting cases of heterogeneous distribution of hexokinase are analyzed, in which the soluble enzyme adsorbs non-specifically to mitochondria, or binds selectively to the site of ATP appearance on the membrane. The results are discussed in terms of their significance to the analysis of bulk measurements in vitro and their relevance to better description of cellular situations.