  Bivalency confers several concentration-dependent phenomena, including
avidity, competitive exchange and multi-site competitive exchange. Since these
concepts are crucial for a wide variety of topics in cell and molecular
biology, their extension, modification and/or re-purposing is also increasingly
important for the design and construction of de-novo synthetic systems at the
nanoscale. In this context, we draw upon classical techniques of statistical
physics to revisit bivalency, highlighting that receptor site geometry offers a
design modality independent of the chemistry of the individual binding
interfaces themselves. Recasting the problem in terms of many-body
coordination, we explore extended, translationally-invariant chains and
lattices of receptor sites. This not only brings clarity to behaviours
associated with simpler motifs, but also enables us to distil core principles
for the rational design of concentration-dependent kinetics in synthetic
soft-systems, which centre on the notion of geometric frustration. In doing so,
we also reveal the possibility of other tunable spatio-temporal features, such
as correlation lengths, mean-squared displacements and percolation-like
transitions.
