ATP is famously the fuel of the cell, but to understand this quantitatively - or even in a qualitatively accurate way - we need to use the free energy and chemical potential concepts developed here. Berkowitz, T. Darden, H. Lee, L.G. GTP}} Lett. \newcommand{\nr}{N_R} Brenner, H.A. The key point is that, in general, the chemical potential depends on everything about the system. 36, 381 (2004), Article  \! 77, 977 (2005), M. Sbragaglia, S. Succi, Phys. Thus, for example, if the concentrations of C and D exceed their equilibrium values, then the free energy change is positive - take the log of Eq. Here we consider a somewhat more general reaction that will be useful for nucleotides, namely. Straatsma, J. Phys. Simul. Pedersen, J. Chem. The importance of chemical potential in the determination of water slip in nanochannels. Kollman, J. Comput. When the product (B) is "favored" (i.e., when $\conceq{B} > \conceq{A}$), then $\dgstd$ is negative, but when reactant A is favored then $\dgstd$ is positive. Rev. 112, 119 (1999), B. Hess, C. Kutzner, D. van der Spoel, E. Lindahl, J. Chem. \newcommand{\conceq}[1]{[\mathrm{#1}]^{\mathrm{eq}}} Acad. Diffusion basics: Single-particle tracking etc. \newcommand{\dmu}{\Delta \mu} % Rate notation: o = 1; w = two; r = three; f = four \newcommand{\kkeq}{K^{\mathrm{eq}}} \newcommand{\rstarx}{R^* \! \cdot \!, DOI:, Over 10 million scientific documents at your fingertips, Not logged in Chem. ADS  \! \newcommand{\dgtp}{\mathrm{D \! Phys 135, 204704 (2011), Institute of Computational Physics, University of Vienna, Sensengasse 8/9, 1090, Vienna, Austria, Department of Physics and INFN, University of “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy, Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, 00185, Rome, Italy, You can also search for this author in Rev. Signalling 554, 25 (2006), MATH  The chemical potential $\mu$, which is simply the free energy per molecule, is probably the most useful thermodynamic quantity for describing and thinking about chemical systems. E 84, 1 (2011), M. Chinappi, Applications of All-Atom Molecular Dynamics to Nanofluidics (InTech, Rijeka, Croatia, 2012) Chapt. \newcommand{\minus}[1]{\mbox{#1}^{-}} with $\dgstd = -7.3$ kcal/mol (which refers to the forward/hydrolysis direction) according to Berg's textbook. \newcommand{\kd}{K_{\mathrm{d}}} Learn more about Institutional subscriptions, H. Lamb, Hydrodynamics, 6th edition (Dover, New York, 1945), H. Stone, A. Stroock, A. Ajdari, Annu. 19, L. Bocquet, E. Charlaix, Chem. Mark, W.R.P. Barrat, Phys. The immediate energy source for synthesis of ATP - addition of phosphate to ADP - is a proton electrochemical gradient in most cells. Papavassilioua, L.L. We investigate the slip properties of water confined in graphite-like nanochannels by non-equilibrium molecular dynamics simulations, with the aim of identifying and analyze separately the influence of different physical quantities on the slip length. The European Physical Journal E The chemical potential, by design, is the perfect tool for analyzing chemical behavior. Netz, L. Bocquet, Phys. Cookie Policy, Answer added by ahmad qahran, عامل انتاج , شركة المصانع السعودية اللبنانية للشوكولاته والسكاكر, Chemical Potential: Change in Gibbs free energy at const T & P, Fugacity: How much chemical potential of a phase differ from its standard state and its equal to partial pressure in case of ideal gas. \newcommand{\nc}{N_{C}} The 2002 edition is. \newcommand{\kftot}{k_f^{\mathrm{tot}}} Subscription will auto renew annually. From the detailed-balance condition of equilibrium, we know that the ratio of rate constants also yield the equilibrium ratio of concentrations. GDP}} MEANINGS Any response to the question, ‘‘What is the meaning of the chemical potential?,’’ is necessarily subjective. \newcommand{\kwo}{\ku} % {\ku(21)} Chem. Berkowitz, J. Chem. Nanofluid. We have now seen the full set of equilibrium connections among the chemical potential, standard free energy difference, and reaction rates. Sega, M., Sbragaglia, M., Biferale, L. et al. \newcommand{\conc}[1]{[\mathrm{#1}]} $, $ \newcommand{\avg}[1]{\langle #1 \rangle} \newcommand{\conc}[1]{[\mathrm{#1}]} \newcommand{\conceq}[1]{[\mathrm{#1}]^{\mathrm{eq}}} \newcommand{\dgstd}{\Delta G^{\circ'}} %\newcommand{\dgstd}{\Delta G^{\circ}'} %\newcommand{\dgstd}{xx} \newcommand{\idl}[1]{{#1}^{\mathrm{idl}}} \newcommand{\kcat}{k_{\mathrm{cat}}} \newcommand{\kdt}{k_{\mathrm{dt}}} \newcommand{\kdtsol}{k^{\mathrm{sol}}_{\mathrm{dt}}} \newcommand{\kkeq}{K'_{\mathrm{eq}}} \newcommand{\kmmon}{\kon^{\mathrm{ES}}} \newcommand{\kmmoff}{\koff^{\mathrm{ES}}} \newcommand{\kconf}{k_{\mathrm{conf}}} \newcommand{\koff}{k_{\mathrm{off}}} \newcommand{\kon}{k_{\mathrm{on}}} \newcommand{\ktd}{k_{\mathrm{td}}} \newcommand{\ktdsol}{k^{\mathrm{sol}}_{\mathrm{td}}} \newcommand{\mustd}{\mu^{\circ}} \newcommand{\mustdp}{\mu^{\circ'}} \newcommand{\rall}{\mathbf{r}^N} \newcommand{\rl}{\rightleftharpoons} \newcommand{\ss}{\mathrm{SS}} $, Free Energy is the Energy Available for Work, Thermodynamic Connection Between Free Energy and Work, Underpinnings of Mass Action: The Ideal Gas, The Ideal Gas in a Field: Transmembrane Ionic Gradients, Advanced Diffusion and the Fokker-Planck Picture, Discrete-state kinetics and Markov models, Binding: Allostery (in a transport cycle), Simple Concentration Gradient Across a Bilayer, Ionic Concentration Gradient Across a Bilayer, Advanced diffusion and the Smoluchowski/Fokker-Planck picture, Recycling of ATP and Coupling to Cellular Processes, Antiporters (Exchanger or Counter-transporter), The Membrane, Ions, and "Electrostatic Health". \newcommand{\awo}{\alpha_{u}} \newcommand{\rstarc}{R^* \! \newcommand{\kr}{k_r} Ministry of Defence -Medical Services Directorate. Building on our statistical mechanics discussion of the ideal gas, we can derive an equation for the chemical potential of a system of molecules, under the assumption they do not interact with one another.