Projecting the structural network onto the 2d free energy surface.

<p>The 2d free energy surface <i>W</i>(<i>Q</i>_i,<i>Q</i>_a) was generated from a total of 200 µsec simulation data present in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#pcbi-1000047-g003" target="_blank">Figure 3 (bottom)</a>. The structural network was taken from the <i>T</i>(5) and the color code for each cluster is the same as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#pcbi-1000047-g006" target="_blank">Figure 6</a>. Each cluster falls nicely on top of the 2d free energy surface. Two representative reactive paths (as shown later in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#pcbi-1000047-g008" target="_blank">Figure 8</a>) are also shown in green (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#pcbi-1000047-g008" target="_blank">Figure 8B</a>) and magenta (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#pcbi-1000047-g008" target="_blank">Figure 8D</a>), respectively.</p

Semi-validation of the multi-state switching model.

<p>Comparison of thermal fluctuation between experiments, atomic simulations, and multi-state model (MSM) simulations. Shown are the data for the inactive (A) and active (B) states, respectively (top row). Experimental B-factors are taken from the full-length Hck and c-Src, respectively. For the active form, the Hck model structure was built from homology modeling of c-Src (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#s3" target="_blank">Materials and Methods</a>). The RMS fluctuations (RMSf) (bottom row) were computed from the last 4 ns atomic simulations for the full-length Hck, and 10⁹-step MSM simulations with β = 1, respectively. Results show that the multi-state model correctly captures overall features of thermal fluctuation presented in both experiments and atomic simulations. For clarity, secondary structural elements of α-helices are indicated by black boxes.</p

The characteristic time of the transition probability matrix <i>T</i>(<i>t</i>) Relaxation times (−<i>t</i>/ln λ) as functions of lag times <i>t</i> for <i>N</i> = 25.

<p>Shown are the second and third eigenvalues of the transition matrix <i>T</i>. The relaxation time approaches a constant around a lag time of <i>t</i> = 100 with a relaxation time of <i>t^*</i>∼450. In the regime where <i>t</i>≪100, the system behaves as non-Markovian.</p

A switching mechanism observed from the simplified model for the αC helix, the A-loop, and the N-terminus.

<p>(Top) Two-dimensional PMF as functions of Δ<i>Q</i>_αC and Δ<i>Q</i>_A-loop indicates that the A-loop first opens up while the αC helix remain in the inactive conformation. This process is then followed by the αC helix rotation to adopt its active conformation. Residues I411 to P425 are used to define the flexible region of the A-loop. (Bottom) Two-dimensional PMF as functions of Δ<i>Q</i>_Nterm and Δ<i>Q</i>_αC suggests that the N-terminus is less restricted when the αC helix is in its active-like orientation. is defined as the contact difference between the inactive and active states. and are the number of contacts made between any residue in the αC helix and any other residues for the inactive (I) and active (A) state, respectively. Similar definitions for Δ<i>Q</i>_A-loop and Δ<i>Q</i>_Nterm are used for the A-loop and the N-terminus, respectively. Residues P253 to L273 are used to define the N-terminus. The color bar in these contour plots represents the relative free energy in <i>k</i>_B<i>T</i>.</p

Structural features for Src catalytic domain activation.

<p>Ensembles of structures corresponding to selected clusters along transition pathways were used to illustrate the transitions. The inactive state is shown as a reference state in light blue. The activation loop is highlighted in yellow and the αC helix in green. The partially unfolding occurs in the β strands at the N-terminal region.</p

Thermodynamics from the Markov analysis.

<p>The equilibrium (or steady-state) population of all clusters (<i>N</i> = 25). Shown is the comparison between the cluster population from brute-force simulations and that from <i>T</i>(5) and <i>T</i>(20). The equilibrium distribution derived from the transition matrix <i>T</i> is equal to the true distribution from simulations. This is guaranteed by the construction of <i>T</i>(<i>t</i>).</p

The switching of a network of representative interactions from simulations.

<p>Switching mechanism for the Src activation among the A-loop (residues 403–429), the αC helix (residues 304–314), and the β5 strand (residues 335–338) in the N-lobe. This can be represented by three highly conserved residues, Glu310, Thr338 and Arg409, where Glu310 exchanges interaction parters from Arg409 to Thr338 during the activation process from the inactive (A) to active (B) state. (C) One representative reactive path shows the interaction switch in the two-distance space (Glu310-Arg409, and Glu310-Thr338). The blue and red dots represent the inactive and active states, respectively.</p

Experimental structures of the Src catalytic domain and cartoon representation for the multi-state model using switching by exponential averaging.

<p>(A) Crystallographic structures are taken from the inactive Hck (left, PDB ID: 1QCF) and the partially active c-Src (right, PDB ID: 1Y57), respectively <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#pcbi.1000047-Schindler1" target="_blank">[12]</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#pcbi.1000047-CowanJacob1" target="_blank">[15]</a>. The primary conformational changes occur in a central activation loop (with Tyr416), as well as the relative orientation between the upper and lower portion (N-lobe and C-lobe), and the αC helix in the back. The color code in the active state (right) shows that the RMS-deviation from the inactive state for each residue. (B) A multi-state model: Switching by exponential averaging. Two reference structures supplied by the inactive and active Src are described by their own energy functions and (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#s3" target="_blank">Materials and Methods</a>). Then these two potentials are combined in a way such that they preserve the shape of energy surface near the energy minima while transitions are allowed between two minima, using an exponential averaging <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#pcbi.1000047-Hummer1" target="_blank">[33]</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#pcbi.1000047-Best1" target="_blank">[35]</a>. The resulting energy function (Equations 1 and 5) encodes two experimental structures. The topological entropy of each reference structure is reflected by the width of the potential well. The adjustable parameter of β is used in simulations to tune the energetic barrier height to achieve a reasonable transition rate between two minima.</p

The structural network of Src catalytic domain conformational changes.

<p>Shown are the 2d force-directed layout of the networks of <i>T</i>(2), <i>T</i>(5), <i>T</i>(20), and <i>T</i>(100). The (forward) committor functions <i>q_i</i> (Equation 6) (from inactive to active) for each cluster are shown by the color bar. Node 18 is the inactive cluster and node 2 is the active. <i>q</i>₁₈ and <i>q</i>₂ were set to be 0 and 1, respectively. The size of each node represents the cluster population as shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#pcbi-1000047-g013" target="_blank">Figure 13</a>. For clarity, a cutoff of <i>L_ij</i>>0.007 was used for the plot. The network of interconnecting clusters may be displayed as a 2d force-directed layout. Within this system, pairs of clusters (<i>i</i> and <i>j</i>, <i>i</i>≠<i>j</i>) are linked by elastic springs with spring constant , where <i>p_i</i> is the stationary distribution of any cluster <i>i</i> and {<i>p_i</i>} is the eigenvector with unit eigenvalue of <i>T</i>. To achieve the 2d graphic layout, practically, we used a Monte Carlo search to find a local favorite combination, which resembles one state of the connectivity of these <i>N</i> interacting clusters (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000047#s3" target="_blank">Materials and Methods</a>).</p

Free energy surfaces of Src conformational changes in the Src activation.

<p>Two-dimensional potentials of mean force <i>W</i>(<i>Q</i>_i,<i>Q</i>_a) are shown as functions of <i>Q</i>_i (the number of contacts made using the inactive state as a reference state) and <i>Q</i>_a (the number of contacts made using the active state as a reference). Each <i>W</i>(<i>Q</i>_i,<i>Q</i>_a) was computed from 100 µsec Langevin simulations with the multi-state model at 315 K. At a higher barrier (β = 1), the experimental structures are stable in their own minima (top row); at a lower barrier (β = 0.05), transitions occur between two minima (bottom row). The simulations were started with initial conformations in the inactive (left) and active (right), respectively.</p