  Large multidimensionality of high-throughput datasets pertaining to cell
signaling and gene regulation renders it difficult to extract mechanisms
underlying the complex kinetics involving various biochemical compounds (e.g.,
proteins, lipids). Data-driven models often circumvent this difficulty by using
pair correlations of the protein expression levels to produce a small numbers
(<10) of principal components, each a linear combination of the concentrations,
to successfully model how cells respond to different stimuli. However, it is
not understood if this reduction is specific to a particular biological system
or to nature of the stimuli used in these experiments. We study temporal
changes in pair correlations described by the covariance matrix between
different molecular species that evolve following deterministic mass action
kinetics in large biologically relevant reaction networks and show that this
dramatic reduction of dimensions (from hundreds to <5) arises from the strong
correlations between different species at any time and is in sensitive of the
form of the nonlinear interactions, network architecture and values of rate
constants and concentrations over a wide range. We relate temporal changes in
the eigenvalue spectrum of the covariance matrix to low-dimensional, local
changes in directions of the trajectory embedded in much larger dimensions
using elementary differential geometry. We illustrate how to extract
biologically relevant insights such as identifying significant time scales and
groups of correlated chemical species from our analysis. Our work provides for
the first time a theoretical underpinning for the successful experimental
analysis and points to way to extract mechanisms from large- scale high
throughput data sets.
