update to figure 2 (#136)

Author: cwehmeyer

manuscript/figures/figure_2.pdf

@@ -282,8 +282,8 @@ \subsection{Feature selection}
 \includegraphics{figure_2}
 \caption{Example analysis of the conformational dynamics of a pentapeptide backbone: (a)~The Trp-Leu-Ala-Leu-Leu pentapeptide in licorice representation~\cite{vmd}.
 (b)~The VAMP-2 score indicates which of the tested featurizations contains the highest kinetic variance.
-(c)~The sample density projected onto the first two time-lagged independent components (ICs) at lag time $\tau=0.5$~ns shows multiple density maxima and
-(d)~the time series of the first two ICs of the first trajectory.}
+(c)~The sample free energy projected onto the first two time-lagged independent components (ICs) at lag time $\tau=0.5$~ns shows multiple minima and
+(d)~the time series of the first two ICs of the first trajectory show rare jumps.}
 \label{fig:io-to-tica}
 \end{figure}
 
@@ -299,7 +299,7 @@ \subsection{Feature selection}
 \label{fig:its-and-ck}
 \end{figure}
 
-In Markov state modeling our objective is to model the slow dynamics of a molecular process.
+In Markov state modeling, our objective is to model the slow dynamics of a molecular process.
 In order to approximate the slow dynamics in a statistically efficient manner,
 a lower dimensional representation of our simulation data is necessary.
 However, the features (e.g. torsion angles, distances or contacts) which best represent the slow dynamical modes of a given molecular system are unknown a priori~\cite{NoeClementiReview}.
@@ -330,8 +330,8 @@ \subsection{Dimensionality reduction}
 TICA is a special case of the variational principle~\cite{noe-vac,nueske-vamk} and is designed to find a projection preserving the long-timescale dynamics in the dataset.
 Here, performing TICA on the backbone torsions at lag time~$0.5$~ns yields a four dimensional subspace using a~$95\%$ kinetic variance cutoff
 (note that we perform a $\cos/\sin$-transformation of the torsions before TICA in order to preserve their periodicity).
-The sample density projected onto the first two independent components (ICs) exhibits several maxima (Fig.~\ref{fig:io-to-tica}c).
-Discrete jumps between the maxima can be observed by visualizing the transformation of the first trajectory into these ICs (Fig.~\ref{fig:io-to-tica}d).
+The sample free energy projected onto the first two independent components (ICs) exhibits several minima (Fig.~\ref{fig:io-to-tica}c).
+Discrete jumps between the minima can be observed by visualizing the transformation of the first trajectory into these ICs (Fig.~\ref{fig:io-to-tica}d).
 We thus assume that our TICA-transformed backbone torsion features describe one or more metastable processes.
 
 \subsection{Discretization}

manuscript/manuscript.tex

@@ -1396,47 +1396,37 @@
     "ax_mol.set_axis_off()\n",
     "ax_mol.imshow(plt.imread('static/pentapeptide-structure.png'))\n",
     "\n",
-    "ax_feat_label = fig.add_subplot(gs[2000:3150, 180:1800])\n",
-    "ax_feat_upper = fig.add_subplot(gs[2000:2720, 400:1800])\n",
-    "ax_feat_lower = fig.add_subplot(gs[2790:3150, 400:1800])\n",
-    "for ax in (ax_feat_upper, ax_feat_lower):\n",
-    "    ax.bar(\n",
-    "        vamp_bars_plot['labels'],\n",
-    "        vamp_bars_plot['scores'],\n",
-    "        yerr=vamp_bars_plot['errors'],\n",
-    "        color=['C0', 'C1', 'C2'])\n",
-    "for key in ('top', 'bottom', 'left', 'right'):\n",
-    "    ax_feat_label.spines[key].set_visible(False)\n",
-    "ax_feat_label.set_ylabel('VAMP2 score')\n",
-    "ax_feat_label.set_xticks([])\n",
-    "ax_feat_label.set_yticks([])\n",
-    "ax_feat_upper.set_title(r'lag time $\\tau$ = {:.1f} ns'.format(vamp_bars_plot['lag'] * 0.1))\n",
-    "ax_feat_upper.spines['bottom'].set_visible(False)\n",
-    "ax_feat_upper.set_xticks([])\n",
-    "ax_feat_upper.set_ylim(2.85, 3.65)\n",
-    "ax_feat_lower.spines['top'].set_visible(False)\n",
-    "ax_feat_lower.tick_params(axis='x', labelrotation=20)\n",
-    "ax_feat_lower.set_ylim(0.0, 0.4)\n",
-    "\n",
-    "ax_density = fig.add_subplot(gs[2000:3150, 2200:3350])\n",
-    "_, _, misc = pyemma.plots.plot_density(\n",
+    "ax_feat = fig.add_subplot(gs[2000:3150, 400:1800])\n",
+    "ax_feat.bar(\n",
+    "    vamp_bars_plot['labels'],\n",
+    "    vamp_bars_plot['scores'],\n",
+    "    yerr=vamp_bars_plot['errors'],\n",
+    "    color=['C0', 'C1', 'C2'])\n",
+    "ax_feat.set_ylabel('VAMP2 score')\n",
+    "ax_feat.set_title(r'lag time $\\tau$ = {:.1f} ns'.format(vamp_bars_plot['lag'] * 0.1))\n",
+    "ax_feat.set_ylim(2.75, 3.65)\n",
+    "ax_feat.tick_params(axis='x', labelrotation=20)\n",
+    "\n",
+    "ax_sample_free_energy = fig.add_subplot(gs[2000:3150, 2200:3350])\n",
+    "_, _, misc = pyemma.plots.plot_free_energy(\n",
     "    *tica_concatenated.T[:2],\n",
-    "    ax=ax_density,\n",
+    "    ax=ax_sample_free_energy,\n",
     "    cax=fig.add_subplot(gs[1900:1950, 2200:3350]),\n",
     "    cbar_orientation='horizontal',\n",
-    "    logscale=True)\n",
-    "misc['cbar'].set_ticks(LogLocator(base=10.0))\n",
+    "    legacy=False)\n",
+    "misc['cbar'].set_label('sample free energy / kT')\n",
+    "misc['cbar'].set_ticks(np.arange(9))\n",
     "misc['cbar'].ax.xaxis.set_ticks_position('top')\n",
     "misc['cbar'].ax.xaxis.set_label_position('top')\n",
-    "ax_density.set_xlabel('IC 1')\n",
-    "ax_density.set_ylabel('IC 2')\n",
+    "ax_sample_free_energy.set_xlabel('IC 1')\n",
+    "ax_sample_free_energy.set_ylabel('IC 2')\n",
     "\n",
     "x = 0.1 * np.arange(tica_output[0].shape[0])\n",
     "ax_tic1 = fig.add_subplot(gs[3650:4000, 400:3350])\n",
     "ax_tic2 = fig.add_subplot(gs[4000:4350, 400:3350])\n",
     "\n",
-    "ax_tic1.plot(x, tica_output[0][:, 0])\n",
-    "ax_tic2.plot(x, tica_output[0][:, 1])\n",
+    "ax_tic1.plot(x, tica_output[0][:, 0], linewidth=0.25)\n",
+    "ax_tic2.plot(x, tica_output[0][:, 1], linewidth=0.25)\n",
     "ax_tic1.set_ylabel('IC 1')\n",
     "ax_tic2.set_ylabel('IC 2')\n",
     "ax_tic2.set_xlabel('time / ns')\n",