${C}_{i}^{f}$ or ${c}_{i}^{f}$

Metabolic control coefficients as defined in (3). f is the system function of interest (i.e. a particular flux, J_{
j
}, or a metabolite concentration X). Lowercase c is used to represent control within a local network (e.g. supply module). The index i refers the process that is controlling.

${H}_{i}^{f}$

Hierarchical control coefficient. Its mathematical definition is in the same form as metabolic control coefficients in (3), but the system under study can be more general. MCA only studies the control in a metabolic pathway or a signal transduction cascade, but not their combination. HCA investigates the control in a hierarchical regulatory network with interactions at different levels, i.e. metabolic, signal transduction, and geneexpression.

${\Re}_{i}^{f}$

MCA (or HCA) based robustness coefficient.

${\Re}_{i}^{f}\equiv \frac{1}{\left(\frac{\partial lnf}{\partial ln{e}_{i}}\right)}\equiv \frac{1}{{C}_{i}^{f}}\phantom{\rule{0.5em}{0ex}}\mathit{or}\phantom{\rule{0.5em}{0ex}}\frac{1}{{H}_{i}^{f}}$.

${F}_{i}^{f}$

Fragility coefficient. It is the inverse of the robustness coefficient and identical to the control coefficient.
${F}_{i}^{f}\equiv \frac{\partial lnf}{\partial ln{e}_{i}}\equiv \frac{1}{{\Re}_{i}^{f}}\equiv {C}_{i}^{f}\phantom{\rule{0.5em}{0ex}}\mathit{or}\phantom{\rule{0.5em}{0ex}}{H}_{i}^{f}.$

${\u03f5}_{{x}_{i}}^{{v}_{j}}$

Elasticity coefficient defined in MCA. It denotes the immediate influences of metabolite x_{
i
} with respect to the reaction rate in the j^{th} step in the presteady state.

${\u03f5}_{{x}_{i}}^{s}$ or ${\u03f5}_{{x}_{i}}^{d}$

Elasticity coefficient of metabolite x_{
i
} with respect to the metabolic supply (s) or demand (d) module, as defined in (4).

$*{\u03f5}_{{x}_{i}}^{{v}_{j}}$, $*{\u03f5}_{{x}_{i}}^{s}$ (or$*{\u03f5}_{{x}_{i}}^{d}$)

The overall elasticity (see[32]) for a reaction step under both metabolic and gene expression regulation, or the overall elasticity in a hierarchical supply or demand module.

v_{Trsc} or v_{Trnl}

Reaction rate of transcription or translation

v_{RD} or v_{ED}

Reaction rate of mRNA or protein degradation

k_{RD} or k_{ED}

mRNA or protein degradation rate constant

${k}_{\text{proteolysis}}^{i}$

Rate constant of i^{th} order proteolysis

μ

The cells’ specific growth (division) rate

E

Concentration of enzyme

X or x
_{
i
}

Concentration of intermediate metabolite

R

Concentration of mRNA

r

Reference signal.
