Basic Principles Underlying Cellular Processes

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$ \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 } $
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Notation

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.

 

splitscreen view

Notation

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.