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Fix stray unicode character
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paper/basic_training.tex

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@@ -307,8 +307,8 @@ \subsubsection{Key concepts}
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A fundamental equilibrium concept that can only be sketched here is the representation of systems of enormous complexity (many thousands, even millions of atoms) in terms of just a small number of coordinates or states.
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The conformational free energy of a state, e.g., $F_A$ or $F_B$ is a way of expressing the average or summed behavior of all the Boltzmann factors contained in a state: the definition requires that the probability (or population) $\peq$ of a state in equilibrium be proportional to the Boltzmann factor of its conformational free energy: $\peq_A \sim \exp(-F_A/k_BT)$.
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Because equilibrium behavior is caused by dynamics, there is a fundamental connection between rates and equilibrium, namely that $\peq_A k_AB = \peq_B k_BA$, which is a consequence of ``detailed balance''.
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There is a closely related connection for on- and off-rates with the binding equilibrium constant.
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For a \emph{continuous} coordinate (e.g., the distance between two residues in a protein), the probability-determining free energy is called the ``€œpotential of mean force''€ (PMF): the Boltzmann factor of the PMF gives the relative probability of a given coordinate.
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There is a closely related connection for on- and off-rates with the binding equilibrium constant.
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For a \emph{continuous} coordinate (e.g., the distance between two residues in a protein), the probability-determining free energy is called the ``potential of mean force'' (PMF); the Boltzmann factor of a PMF gives the relative probability of a given coordinate.
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Any kind of free energy implicitly includes \emph{entropic} effects; in terms of an energy landscape (Fig.\ \ref{landscapes}), the entropy quantifies the \emph{width} of a basin.
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These points are discussed in textbooks, as are the differences between free energies for different thermodynamic ensembles -- e.g.., $F$, the Helmholtz free energy, when $T$ is constant, and $G$ , the Gibbs free energy, when both $T$ and pressure are constant -- which are not essential to our introduction~\cite{DillBook, Zuckerman:2010:}.
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