  Enzyme-substrate kinetics form the basis of many biomolecular processes. The
interplay between substrate binding and substrate geometry can give rise to
long-range interactions between enzyme binding events. Here, we study a general
model of enzyme-substrate kinetics with restricted long-range interactions
described by an exponent $-\lambda$. We employ a coherent-state path integral
and renormalization group approach to calculate the first moment and two-point
correlation function of the enzyme-binding profile. We show that starting from
an empty substrate the average occupancy follows a power law with an exponent
$1/(1-\lambda)$ over time. The correlation function decays algebraically with
two distinct spatial regimes characterized by exponents $-\lambda$ on short
distances and $-(2/3)(2-\lambda)$ on long distances. The crossover between both
regimes scales inversely with the average substrate occupancy. Our work allows
to associate experimental measurements of bound enzyme locations with their
binding kinetics and the spatial confirmation of the substrate.
