  We introduce a minimalistic model based on dynamic node deletion and node
duplication with heterodimerisation. The model is intended to capture the
essential features of the evolution of protein interaction networks. We derive
an exact two-step rate equation to describe the evolution of the degree
distribution. We present results for the case of a fixed-size network. The
results are based on the exact numerical solution to the rate equation which
are consistent with Monte Carlo simulations of the model's dynamics. Power-law
degree distributions with apparent exponents $<1$ were observed for generic
parameter choices. However, a proper finite-size scaling analysis revealed that
the actual critical exponent in such cases is equal to 1. We present a
mean-field argument to determine the asymptotic value of the average degree,
illustrating the existence of an attractive fixed point, and corroborate this
result with numerical simulations of the first moment of the degree
distribution as described by the two-step rate equation. Using the above
results, we show that the apparent exponent is determined by the
heterodimerisation probability. Our preliminary results are consistent with
empirical data for a wide range of organisms, and we believe that through
implementing some of the suggested modifications, the model could be
well-suited to other types of biological and non-biological networks.
