This work has been supported by NSFC Grant #11775016 and #11635002. JY has been supported by the CMCF of UCI via NSF DMS 1763272 and the Simons Foundation grant #594598 and start-up fund from UCI. LTD has been supported by Natural Science Foundation of Shanghai #20ZR1425400 and #21JC1403100. We also acknowledge the computational support from the Beijing Computational Science Research Center (CSRC).

1. Construction of the Markov state model (MSM) from atomic MD simulations
<ol>
	<li>Spontaneous protein stepping pathway and initial structures collection
	<ol>
		<li>Use a previously obtained 10-&#181;s all-atom MD&#160;trajectory8 to extract 10000 frames evenly from a &#34;forward&#34; 1-bp stepping path (i.e., one frame for each nanosecond). The total number of frames needs to be sufficiently large to include all representative conformations.</li>
		<li>Prepare the transitio...

This work addresses how to conduct structure-based computational simulation and samplings to reveal a transcription factor or TF protein moving along DNA, not only at atomic detail of stepping, but also in the processive diffusion, which is essential for the facilitated diffusion of TF in the DNA target search. To do that, the Markov state model or MSM of a small TF domain protein WRKY stepping for 1-bp along homogeneous poly-A DNA was first constructed, so that an ensemble of protein conformations on the DNA along with ...

Transcription factors (TF) search for the target DNA to bind and regulate gene transcription and related activities1. Aside from the three-dimensional (3D) diffusion, the facilitated diffusion of TF has been suggested to be essential for target DNA search, in which the proteins can also slide or hop along one-dimensional (1D) DNA, or jump with intersegmental transfer on the DNA2,3,4,5,6,7.
In a recent study, we have conducted tens of microseconds (&#181;s) all-atom equilibrium molecular dynamics (MD) simulations on a plant TF - the WRKY domain protein on the DNA8. A complete 1-bp stepping of WRKY on poly-A DNA within microseconds has been captured. The movements of the protein along the DNA groove and hydrogen bonds (HBs) breaking-reforming dynamics have been observed. While such a trajectory represents one sampled path, an overall protein stepping landscape is still lack of. Here, we show how to expand computational samplings around the initially captured protein stepping path with the constructed Markov state model (MSM), which have been implemented widely for simulating a variety of biomolecular systems involving substantial conformational changes and time-scale separation9,10,11,12,13,14,15,16,17,18,19. The purpose is to reveal the conformational ensemble and meta-stable states of the TF protein diffusion along DNA for one cyclic step.
While the above MD simulation reveals atomic resolution of the protein movements for 1 bp on the DNA, the structural dynamics of long-time processive diffusion of the TF along DNA at the same high-resolution is hardly accessible. Conducting coarse-grained (CG) MD simulations at residue level is however technically approachable. The CG simulation time scale can be effectively extended to tens or hundreds of times longer than the atomic simulations20,21,22,23,24,25,26,27,28,29. Here, we show the CG simulations conducted by implementing the CafeMol software developed by Takada lab30.
In current protocol, we present the atomic simulations of the WRKY domain protein along poly-A DNA and the MSM construction first, which focus on sampling the protein stepping motions for only 1 bp along DNA. Then we present the CG modeling and simulations of the same protein-DNA system, which extend the computational sampling to the protein processive diffusion over tens of bps along DNA.
Here, we use GROMACS31,32,33 software to conduct MD simulations and MSMbuilder34 to construct the MSM for sampled conformational snapshots, as well as to use VMD35 to visualize the biomolecules. The protocol requires that the user to be able to install and implement the software above. The installation and implementation of the CafeMol30 software is then necessary for conducting the CG MD simulations. Further analyses of the trajectories and visualization are also conducted in VMD.

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>CafeMol</td>
			<td>Kyoto University</td>
			<td></td>
			<td>coarse-grained (CG) simulations</td>
		</tr>
		<tr>
			<td>GROMACS</td>
			<td>University of Groningen Royal Institute of Technology Uppsala University</td>
			<td></td>
			<td>molecular dynamics simulations software</td>
		</tr>
		<tr>
			<td>Matlab</td>
			<td>MathWorks</td>
			<td></td>
			<td>Numerical calculation software</td>
		</tr>
		<tr>
			<td>MSMbuilder</td>
			<td>Stanford University</td>
			<td></td>
			<td>build MSM</td>
		</tr>
		<tr>
			<td>VMD</td>
			<td>UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN</td>
			<td></td>
			<td>molecular visualization program</td>
		</tr>
	</tbody>
</table>

structure-based simulation and sampling of transcription factor protein movements along dna from atomic-scale stepping to coarse-grained diffusion

One-dimensional (1-D) sliding of transcription factor (TF) protein along DNA is essential for facilitated diffusion of the TF to locate target DNA site for genetic regulation. Detecting base-pair (bp) resolution of the TF sliding or stepping on the DNA is still experimentally challenging. We have recently performed all-atom molecular dynamics (MD) simulations capturing spontaneous 1-bp stepping of a small WRKY domain TF protein along DNA. Based on the 10 &#181;s WRKY stepping path obtained from such simulations, the protocol here shows how to conduct more extensive conformational samplings of the TF-DNA systems, by constructing the Markov state model (MSM) for the 1-bp protein stepping, with various numbers of micro- and macro-states tested for the MSM construction. In order to examine processive 1-D diffusional search of the TF protein along DNA with structural basis, the protocol further shows how to conduct coarse-grained (CG) MD simulations to sample long-time scale dynamics of the system. Such CG modeling and simulations are particularly useful to reveal the protein-DNA electrostatic impacts on the processive diffusional motions of the TF protein above tens of microseconds, in comparison with sub-microseconds to microseconds protein stepping motions revealed from the all-atom simulations.

Rotation-coupled sliding or 1 bp stepping of WRKY from the MSM construction 
All protein conformations on the DNA are mapped to the longitudinal movement X and rotation angle of the protein COM along DNA&#160;(see Figure 3A). The linear coupling of these two degrees indicates rotation-coupled stepping of the WRKY domain protein on the DNA. The conformations can be further clustered into 3 macrostates (S1, S2, and S3) in the MSM. The forward stepping of WRKY then follows...

Watch this Scientific Journal Video about Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion at JoVE.com

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

The goal of this protocol is to reveal structural dynamics of one-dimensional diffusion of protein along DNA, using a plant transcription factor WRKY domain protein as an exemplary system. To do this, both atomistic and coarse-grained molecular dynamics simulations along with extensive computational samplings have been implemented.

One-dimensional (1-D) sliding of transcription factor (TF) protein along DNA is essential for facilitated diffusion of the TF to locate target DNA site ...

The goal of this protocol is to reveal structural dynamics of one-dimensional diffusion of protein along DNA, using a plant transcription factor WRKY domain protein as an exemplary system. The atomic simulations under the Markov state model construction reveal 1-bp stepping motions of protein along DNA at atomic details. While the coarse-grained simulations focus on sampling of protein processive diffusions over 10 of bps along DNA.To begin, use a 10 microsecond all-atom MD trajectory to extract 10, 000 frames evenly forward, one base pair stepping path. Prepare the transition path with 10, 000 frames in VMD by clicking File and Save Coordinates. Then, type protein or nucleic in the Selected Atoms box.Choose Frames in the frames box, and click Save to get the frames needed. Align the long axis of the reference from the crystal structure of DNA to the x-axis, and set the initial center of mass of the full 34 base pairs DNA at the origin of the coordinate space by clicking Extensions and then selecting TkConsole in VMD. Afterward, type the command in the TkConsole command window.Then, calculate the root means square distance of the protein backbone by clicking VMD, then go to Extensions, click Analysis, and select the RMSD Trajectory Tool. In the atom selection box, type nucleic and residue 14 to 23, and 46 to 55. Click ALIGN and then RMSD box.To calculate the rotational degree of protein around DNA theta T, with the initial angular positioning defined as theta 0, on the XY plane in MATLAB, execute the command. Enter the instructions in MATLAB to use K-means methods, and classify the 10, 000 structures into 25 clusters. Once done, gather the structures of the 25 cluster centers for further MD simulation.To conduct the first round MD simulation, build an atomistic system for the 25 structures by using GROMACS, and the build system sh file. Conduct 60 nanoseconds MD simulations for the 25 systems under NPT ensemble with a time step of two femtosecond by processing the the command in shell. To cluster the first round MD trajectories, remove the first 10 nanoseconds of each simulation trajectory and collect confirmations from the 25 times 50 nanosecond trajectories.For the time independent component analysis, enter the script in GROMACS, followed by choosing distance pairs between protein and DNA as input parameters projection. From the index. ndx file, to a new text file index.dat.To get the pair information between these atoms, use the Python script. Calculate the 415 distance pairs from every trajectory in MSMBuilder command window. Next, conduct a time independent component analysis to reduce the dimension of data onto the first two time independent components or vectors by executing the command.With the processing of the instruction in MSMBuilder, cluster the projected data sets into 100 clusters using the case center method and select the center structure of each cluster. To conduct second round MD simulation, conduct 60 nanosecond MD simulations starting from the 100 initial structures. After imposing random initial velocities on all the atoms, add the random initial velocities by turning on the Velocity generation in MDP file.Remove the first 10 nanoseconds of each simulation as described previously. And collect 2, 500, 000 snapshots from the 100 times 50 nanosecond trajectories, evenly, to construct the MSM. To cluster second round MD trajectories, conduct the time independent component analysis for the second round trajectories in the MSMBuilder as shown.And calculate the implied time scale to validate parameters by executing the Python script. Then, vary the lag time tau and micro-states number by changing the parameters. Classify the confirmations into 500 clusters by executing the command.For MSM construction, lump the 500 micro-states into three to six macro-states. To find out the number of macro-states that suit best, according to the PCCAplus algorithm in MSMBuilder by using the Python script. Map the high dimensional confirmations to the X and rotational angle of the protein along the DNA for each micro-state.To calculate the mean first passage times, conduct five 10 millisecond Monte Carlo trajectories, based on the transition probability matrix of the 500 micro-state MSM with the lag time of 10 nanoseconds set as the time step of Monte Carlo. Calculate mean first passage times between each pair of macro-states within the Python script and the average of standard error of the mean first passage times using the Bash file. In the CafeMol 3.0 software, run the course-grained simulation by executing the command on the terminal.After specifying the blocks in the Input file, set the filenames block and the job_cntl block with the individual commands. Next, set the unit_and_state block, followed by setting the energy_function block and the md_information block. All protein confirmations on the DNA were mapped to the longitudinal movement X and rotation angle of the protein along DNA, which can be further clustered into three macro-states.The S1 state is less favorable as the hydrogen bonds are similar to the modeled structure, whereas S3 refers to a metastable state where all the hydrogen bonds shifted after one base-pair stepping and appeared stable with the highest population of 63%The intermediate state S2 connects S1 and S3 with a medium high population of 30%The transition of S2 to S3 allows collective breaking and reforming of the hydrogen bonds in approximately seven microseconds, while S1 to S2 transition can occur in approximately 0.06 microseconds. The contact numbers between protein and DNA were calculated and four states were identified. In states 1 and 3, the zinc finger region binds toward the Y direction.Whereas in states 2 and 3, the zinc finger region binds toward the Y direction. The stepping size for each conserved residue on different sequences of DNA was measured, which revealed that the stepping sizes of these residues are more synchronized on polyA DNA than on polyAT or random DNA sequences. The important steps in Markov state model construction are choosing distance pairs between protein and DNA data repairs into the 1-bp stepping motions, and the selection of a suitable number of micro-states and macro-states.

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Abstract