Basic Principles Underlying Cellular Processes
Daniel M. Zuckerman

Notation

$ \newcommand{\avg}[1]{\langle #1 \rangle} \newcommand{\cc}[1]{[\mathrm{#1}]^{\mathrm{cell}}} \newcommand{\cgdp}{\mathrm{C \! \cdot \! GDP}} \newcommand{\cgtp}{\mathrm{C \! \cdot \! GTP}} \newcommand{\comb}[1]{{#1}^{\mathrm{comb}}} \newcommand{\conc}[1]{[\mathrm{#1}]} \newcommand{\conceq}[1]{[\mathrm{#1}]^{\mathrm{eq}}} \newcommand{\concss}[1]{[\mathrm{#1}]^{\mathrm{ss}}} \newcommand{\conctot}[1]{[\mathrm{#1}]_{\mathrm{tot}}} \newcommand{\cu}{\conc{U}} \newcommand{\dee}{\partial} \newcommand{\dgbind}{\Delta G_0^{\mathrm{bind}}} \newcommand{\dgdp}{\mathrm{D \! \cdot \! GDP}} \newcommand{\dgtp}{\mathrm{D \! \cdot \! GTP}} \newcommand{\dmu}{\Delta \mu} \newcommand{\dphi}{\Delta \Phi} \newcommand{\dplus}[1]{\mbox{#1}^{++}} \newcommand{\eq}[1]{{#1}^{\mathrm{eq}}} \newcommand{\fidl}{F^{\mathrm{idl}}} \newcommand{\idl}[1]{{#1}^{\mathrm{idl}}} \newcommand{\inn}[1]{{#1}_{\mathrm{in}}} \newcommand{\ka}{k_a} \newcommand{\kcat}{k_{\mathrm{cat}}} \newcommand{\kf}{k_f} \newcommand{\kfc}{k_{fc}} \newcommand{\kftot}{k_f^{\mathrm{tot}}} \newcommand{\kd}{K_{\mathrm{d}}} \newcommand{\kdt}{k_{\mathrm{dt}}} \newcommand{\kdtsol}{k^{\mathrm{sol}}_{\mathrm{dt}}} \newcommand{\kgtp}{K_{\mathrm{GTP}}} \newcommand{\kij}{k_{ij}} \newcommand{\kji}{k_{ji}} \newcommand{\kkeq}{K^{\mathrm{eq}}} \newcommand{\kmmon}{\kon^{\mathrm{ES}}} \newcommand{\kmmoff}{\koff^{\mathrm{ES}}} \newcommand{\kconf}{k_{\mathrm{conf}}} \newcommand{\konf}{k^{\mathrm{on}}_{\mathrm{F}}} \newcommand{\koff}{k_{\mathrm{off}}} \newcommand{\kofff}{k^{\mathrm{off}}_{\mathrm{F}}} \newcommand{\konu}{k^{\mathrm{on}}_{\mathrm{U}}} \newcommand{\koffu}{k^{\mathrm{off}}_{\mathrm{U}}} \newcommand{\kon}{k_{\mathrm{on}}} \newcommand{\kr}{k_r} \newcommand{\ks}{k_s} \newcommand{\ku}{k_u} \newcommand{\kuc}{k_{uc}} \newcommand{\kutot}{k_u^{\mathrm{tot}}} \newcommand{\ktd}{k_{\mathrm{td}}} \newcommand{\ktdsol}{k^{\mathrm{sol}}_{\mathrm{td}}} \newcommand{\minus}[1]{\mbox{#1}^{-}} \newcommand{\na}{N_A} \newcommand{\nai}{N_A^i} \newcommand{\nao}{N_A^o} \newcommand{\nb}{N_B} \newcommand{\nbi}{N_B^i} \newcommand{\nbo}{N_B^o} \newcommand{\nc}{N_{C}} \newcommand{\nl}{N_L} \newcommand{\nltot}{N_L^{\mathrm{tot}}} \newcommand{\nr}{N_R} \newcommand{\nrl}{N_{RL}} \newcommand{\nrtot}{N_R^{\mathrm{tot}}} \newcommand{\out}[1]{{#1}_{\mathrm{out}}} \newcommand{\plus}[1]{\mbox{#1}^{+}} \newcommand{\rall}{\mathbf{r}^N} \newcommand{\rn}[1]{\mathrm{r}^N_{#1}} \newcommand{\rdotc}{R \!\! \cdot \! C} \newcommand{\rstarc}{R^* \! \! \cdot \! C} \newcommand{\rstard}{R^* \! \! \cdot \! D} \newcommand{\rstarx}{R^* \! \! \cdot \! X} \newcommand{\ss}{\mathrm{SS}} \newcommand{\totsub}[1]{{#1}_{\mathrm{tot}}} \newcommand{\totsup}[1]{{#1}^{\mathrm{tot}}} \newcommand{\ztot}{Z^{\mathrm{tot}}} % Rate notation: o = 1; w = two; r = three; f = four \newcommand{\aow}{\alpha_{f}} \newcommand{\awo}{\alpha_{u}} \newcommand{\kow}{\kf} % {\kf(12)} \newcommand{\kwo}{\ku} % {\ku(21)} \newcommand{\kor}{\conc{C} \, \konu} % \konu(13)} \newcommand{\kwf}{\conc{C} \, \konf} % \konf(24)} \newcommand{\kro}{\koffu} % {\koffu(31)} \newcommand{\kfw}{\kofff} % {\kofff(42)} \newcommand{\krf}{\kfc} % {\kfc(34)} \newcommand{\kfr}{\kuc} % {\kuc(43)} \newcommand{\denom}{ \krf \, \kfw + \kro \, \kfw + \kro \, \kfr } $

Notation and Technical Terminology

Symbol or TermDefinition
The electrostatic potential, which generally will vary in space and different cellular compartments. See Ion Gradients.
The concentration of species (or state) $\mathrm{X}$, generally equal to $N_X/V$. See States & Kinetics, Equilibrium.
Thermodynamic average of the quantity $A$ (under specified conditions). See Free Energy & Work.
Helmholtz free energy, $\langle E \rangle - TS$ . See Free Energy & Work.
Boltzmann's constant. $k_B \, T \sim R T$ is the natural scale of thermal energy at temperature $T$. See The Ideal Gas.
Rate constant for transitions from $i$ to $j$. Probability per unit time to transition from $i$ to $j$. See Mass-Action Kinetics, States & Kinetics, Catalysis, Equilibrium.
Rate constant for unbinding - i.e., for bi-molecular dissociation. Probability per $s$ for a bi-molecular complex to dissociate. See Mass-Action Kinetics, Activated Carriers.
Rate constant for binding - i.e., for bi-molecular association. Probability per $s$ for a single molecule to bind one molecule of another species, with the latter at the reference 1M concentration. See Mass-Action Kinetics, Activated Carriers.
Rate constant for a process "X", which might be a chemical reaction, isomerization, or (un)binding process - and should be determined by the context. See Mass-Action Kinetics, States & Kinetics, Catalysis, Synthesis.
Number of systems or molecules in state $i$. See States & Kinetics, Equilibrium.
Number of copies of species (e.g., molecule) $\mathrm{X}$. See States & Kinetics, Equilibrium.
Probability of state $i$, generally equal to $N_i/N$. See States & Kinetics, Equilibrium.
The gas constant. $k_B \, T = R T$ is the natural scale of thermal energy at temperature $T$. See The Ideal Gas.
The configuration of a system of $N$ atoms or molecules, it is short-hand for the full set of Cartesian coordinates: $ \mathbf{r}^N = \{ x_1, y_1, z_1, \, x_2, y_2, z_2, \, \ldots, \, x_N, y_N, z_N \}$. See The Ideal Gas, Free Energy Storage in a Concentration Gradient.
Absolute temperature, in degrees Kelvin. See Free Energy & Work, The Ideal Gas.
Volume of system. See The Ideal Gas, Free Energy Storage in a Concentration Gradient.