Edits from Zuckerman

Author: davidlmobley

paper/basic_training.tex

@@ -98,7 +98,8 @@ \section{Introduction}
 \label{sec:intro}
 
 Molecular simulation techniques play a very important role in our quest to understand and predict the properties, structure, and function of molecular systems, and are a key tool as we seek to enable predictive molecular design.
-Simulation methods are extremely useful for studying the structure and dynamics of complex systems that are too complicated for pen and paper theory and helping interpret experimental data in terms of molecular motions, as well as (increasingly) for quantitative prediction of properties of use in molecular design and other applications~\cite{Nussinov2014,Towns2014,Kirchmair2015,Sresht2017,Bottaro2018}.
+Simulation methods are extremely useful for studying the structure and dynamics of complex systems that are too complicated for pen and paper theory, helping interpret experimental data in terms of molecular motions.
+Additionally, they see increasing use for quantitative prediction of properties of use in molecular design and other applications~\cite{Nussinov2014,Towns2014,Kirchmair2015,Sresht2017,Bottaro2018}.
 
 The basic idea of any molecular simulation method is straightforward; a particle-based description of the system under investigation is constructed and then the system is propagated by either deterministic or probabilistic rules to generate a trajectory describing its evolution over the course of the simulation~\cite{Frenkel:2001:,LeachBook}.
 Relevant properties can be calculated for each ``snapshot'' (a stored configuration of the system, also called a ``frame'') and averaged over the the entire trajectory to compute estimates of desired properties.
@@ -287,21 +288,21 @@ \subsubsection{Key concepts}
 
 Once you have understood that MD behavior reflects system timescales, you must set this behavior in the context of an \emph{extremely} complex energy landscape consisting of almost innumerable minima and barriers, as schematized in Fig.\ \ref{landscapes}(b).  
 Each small basin represents something like a different rotameric state of a protein side chain or perhaps a tiny part of the Ramachandran spaces (backbone phi-psi angles) for one or a few residues.  
-Observing the large-scale function motion of a protein then would require an MD simulation longer than the sum of all the timescales for the necessary hops, bearing in mind that numerous stochastic reversals are likely during the simulation.  
-Because functional biomolecular timescales tend to be on $\mu$s - ms scales, it is challenging if not impossible to observe them in traditional MD simulations.  
+Observing the large-scale motion of a protein then would require an MD simulation longer than the sum of all the timescales for the necessary hops, bearing in mind that numerous stochastic reversals are likely during the simulation.  
+Because functional biomolecular timescales tend to be on $\mu$s - ms scales and beyond, it is challenging if not impossible to observe them in traditional MD simulations.  
 There are numerous enhanced sampling approaches~\cite{Zuckerman:2011:AnnuRevBiophys, Chong:2017:CurrentOpinioninStructuralBiology} but these are beyond the scope of this discussion and they have their own challenges which often are much harder to diagnose (see~\cite{Grossfield:2009:AnnuRepComputChem} and  \url{https://github.com/dmzuckerman/Sampling-Uncertainty}).
 
 What is the connection between MD simulation and equilibrium?  The most precise statement we can make is that an MD trajectory is a single sample of a process that is relaxing to equilibrium from the starting configuration~\cite{Zuckerman:2015:StatisticalBiophysicsBlog, Zuckerman:2010:}.  
 \emph{If} the trajectory is long enough, it should sample the equilibrium distribution -- where each configuration occurs with frequency proportional to its Boltzmann factor.  
 In such a very long trajectory (only), a time average thus will give the same result as a Boltzmann-factor-weighted, or ensemble, average.  
 We refer to such a system, where the time and ensemble averages are equivialent, as ``ergodic.''
-Note that the Boltzmann-factor distribution implies that every configuration has some probability, and so it is unlikely that a single conformation or even a single basin dominates an ensembles. 
+Note that the Boltzmann-factor distribution implies that every configuration has some probability, and so it is unlikely that a single conformation or even a single basin dominates an ensemble. 
 Beware that in a typical MD trajectory it is likely that only a small subset of basins will be sampled well -- those most quickly accessible to the initial configuration.  
 It is sometimes suggested that multiple MD trajectories starting structures can aid sampling, but unless the equilibrium distribution is known in advance, the bias from the set of starting structures is simply unknown and harder to diagnose.
 
 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.  
 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: $\peq_A \sim \exp(-F_A/k_BT)$.  
-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''.
+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''.
 There is a closely related connection for on- and off-rates with the binding equilibrium constant.   
 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.  
 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.  
@@ -354,7 +355,7 @@ \subsubsection{Key concepts}
 This means atoms or molecules separated by considerable distances can still have quite strong electrostatic interactions, though this also depends on the degree of shielding of the intervening medium (or its relative permittivity or dielectric constant).
 
 %\item Polarizability, dielectric constants
-The static dielectric constant of a medium, or relative permittivity $\epsilon_r$ (relative to that of vacuum), affects the prefactor for the decay of these long range interactions, with interactions falling off as $\frac{1}{\epsilon_r}$. 
+The static dielectric constant of a medium, or relative permittivity $\epsilon_r$ (relative to that of vacuum), affects the prefactor for the decay of these long range interactions, with interactions reduced by $\frac{1}{\epsilon_r}$. 
 Water has a relatively high relative permittivity or dielectric constant close to 80, whereas non-polar compounds such as n-hexane may have relative permittivities near 2 or even lower. 
 This means that interactions in non-polar media such as non-polar solvents, or potentially even within the relatively non-polar core of a larger molecule such as a protein, are effectively much longer-range even than those in water. 
 The dielectric constant of a medium also relates to the degree of its electrostatic response to the presence of a charge; larger dielectric constants correspond to larger responses to the presence of a nearby charge.
@@ -703,7 +704,7 @@ \subsubsection{Background and How They Work}
 
 The temperature of a molecular dynamics simulation is typically measured using kinetic energies as defined using the equipartition theorem: $\frac{3}{2} N k_{\text{B}} T = \left<\sum_{i=1}^{N} \frac{1}{2} m_i v_i^2\right>$.
 The angled brackets indicate that the temperature is defined as a time-averaged quantity.
-If we use the equipartition theorem to calculate the temperature for a single snapshot in time of a molecular dynamics simulation instead of time-averaging, this quantity is referred to as the instantaneous temperature.
+If we use the equipartition theorem to calculate the temperature for a single snapshot in time of a molecular dynamics simulation~\cite{Zuckerman:2010:, LeachBook} instead of time-averaging, this quantity is referred to as the instantaneous temperature.
 The instantaneous temperature will not always be equal to the target temperature; in fact, in the canonical ensemble, the instantaneous temperature should undergo fluctuations around the target temperature.
 
 Thermostat algorithms work by altering the Newtonian equations of motion that are inherently microcanonical (constant energy).
@@ -1235,6 +1236,7 @@ \section{Should you run MD?}
 A critical question \emph{before} preparing an MD simulation of your system is whether you even \emph{should} use MD for your system in view of the resources you have and what information you hope to obtain.
 MD is a tool, but it may not be the right tool for your problem.
 Before beginning any study, it is critical to sort out what questions you want to answer, what resources (computational and otherwise) you have at your disposal, and whether you have any information about your system(s) of interest that indicate you can realistically expect to answer those questions given a set of MD simulations.
+Try to understand basic concepts of statistical uncertainty (\cite{Grossfield:2009:AnnuRepComputChem} and \url{https://github.com/dmzuckerman/Sampling-Uncertainty}) and use these to make an educated guess regarding your chances of extracting pertinent and reliable information from your simulation.
 
 As noted above, the frequency of the fastest vibrational motions in a system of interest sets a fundamental limit on the timestep which, given fixed computational resources, sets a limit on how much simulation time can be covered with any reasonable amount of computer time.
 Thus, as noted in Section~\ref{sec:intro}, the longest all-atom MD simulations are on the microsecond to millisecond timescale.