Nonreceptor tyrosine kinases of the Src family are large multidomain allosteric proteins that are crucial to cellular signaling pathways. In a previous study, we generated a Markov state model (MSM) to simulate the activation of c-Src catalytic domain, used as a prototypical tyrosine kinase. The long-time kinetics of transition predicted by the MSM was in agreement with experimental observations. In the present study, we apply the framework of transition path theory (TPT) to the previously constructed MSM to characterize the main features of the activation pathway. The analysis indicates that the activating transition, in which the activation loop first opens up followed by an inward rotation of the αC-helix, takes place via a dense set of intermediate microstates distributed within a fairly broad "transition tube" in a multidimensional conformational subspace connecting the two end-point conformations. Multiple microstates with negligible equilibrium probabilities carry a large transition flux associated with the activating transition, which explains why extensive conformational sampling is necessary to accurately determine the kinetics of activation. Our results suggest that the combination of MSM with TPT provides an effective framework to represent conformational transitions in complex biomolecular systems.
Markov state models; conformational transition; transition path theory.
Conflict of interest statement
The authors declare no conflict of interest.
A) Cartoon representation of the conformational transition in c-Src catalytic domain. The inactive conformation is colored in blue, and the active conformation is colored in yellow. The main structural changes include the rotation of the αC-helix and the movement of the activation (A-) loop. E310 (chicken c-Src numbering) in the αC-helix is explicitly shown to illustrate the movement of the αC-helix in the transition. E310 is pointing outward in the inactive conformation, whereas it is pointing inward in the active-like conformation so that a catalytically important salt bridge can be formed (36). The A-loop is partially folded in the inactive kinase, but it becomes fully extended in the active conformation. ( B) Atoms that define the space of CVs. The Cartesian coordinates of the selected atoms are used as CVs. A total of 50 atoms are selected. The carbon atoms are colored in orange, and the nitrogen atoms are colored in blue. ( C) Network representation of the conformational transition. Each node represents a microstate from MSM, and edges represent nonzero elements of the transition probability matrix. The size of each node is proportional to the Boltzmann weight of the corresponding microstate. The largest node size is set to be 150, whereas the smallest node size is 10. Microstates are colored by their committor probability values. The program Gephi (37) was used to generate this network representation.
A) Free energy of MSM microstates as a function of state index. ( B) Committor probability of microstates as a function of state index. Microstates in both plots are colored by their committor probability values.
A) Two-dimensional PMF from replica-exchange molecular dynamics/umbrella sampling calculation. The inactive conformation of kinase domain occupies the lowest free energy region, which is located at the lower left corner. The active conformation occupies the upper right corner. A free energy basin which associates with an intermediate state can be seen at the lower right corner. d 1 is the distance between E310 Cδ atom and R409 Cζ atom. d 2 is the distance between E310 Cδ atom and K295 Nζ atom. d 3 is the average of distances between O-Asp413 and N-Thr417, O-Asn414 and N-Ala418, and O-Glu415 and N-Arg419. The 2D-PMF reflects the free energy landscape projected onto the αC-helix and the A-loop motions. ( B) Projection of MSM microstates onto 2D-PMF coordinates. MSM microstates are colored by their committor probability values. Although the microstates were obtained from unbiased MD simulations, projection of the microstates onto 2D-PMF still helps understand features of the conformational changes and the energy landscape.
TPT analysis of all MSM microstates. (
A) Free energy profile as a function of the committor probability. ( B) The heat map of F +( q i, d i). The heat map is plotted on a log10 scale of the net effective flux. Regions having F + to be zero are assigned a value of 10 −7 when taking the logarithm. ( C) Two-dimensional histogram of (π i, ). It is zoomed-in so that nonzero counts are highlighted. F i +
A) Distance from a microstate to the geometric center as a function of the committor probability. The size of each circle is proportional to the Boltzmann weight (equilibrium probability of a microstate, π i). According to our selection of the reactant and the product, there is only one microstate for each, so that the reactant and the product are not included in generating A. Furthermore, only two microstates were found to fall into the bin centered at q = 0.9. Hence, only one distance value (one point in this figure) of 2.4 Å could be obtained. ( B) Distance from a microstate to the geometric center as a function of the committor probability. The size of each circle is proportional to the equilibrium probability of the reactive trajectory ( ). π i R
Analysis of string
S 0. ( A) Projection of string S 0 onto 2D-PMF coordinates. ( Inset) The committor probability as a function of the index of string images. ( B) Scatter plot of the net flux of a microstate vs. its distance to S 0 in the CV space. The size of each circle is proportional to the equilibrium probability of the microstate. Microstates are colored by their committor probability values. The reactant state is excluded when making this plot because of its large Boltzmann weight and net flux.
A) Analysis of microstates around S 0. ( B) Histogram of the distance from a microstate to S 0. A statistical test of the normality is performed on the distribution of values, using the null hypothesis ( d i → S 0 H 0) that the probability density is Gaussian. The P value yielded from the Shapiro–Wilk test is smaller than 0.01. The values are hence not normally distributed, although the shape of the histogram resembles a Gaussian. d i → S 0
Two-dimensional histogram of the distance to
S 0 and the net effective flux.
Histogram of the reactive fluxes among those 200 pathways. An estimated kernel density is also displayed as a solid line.
A) Projection of microstates onto 2D-PMF coordinates. ( B) Distance from a microstate to the geometric center as a function of the committor probability. In both plots, the microstates are collected from the 200 pathways. Microstates are colored by their committor probability values. The spatial distribution of microstates from 200 pathways resembles that from using all microstates.
Comparison of the distance between an image to the starting point of the string and the length of the string up to that image, along each transition pathway for the 200 pathways.
Free energy profiles along strings. (
A) Free energy profile along S 1 from Markovian milestoning simulations. ( B) Free energy profile along S 0 from the MSM microstates.
Analysis of the markovian milestoning simulations. (
A) Average drift along principal components as a function of image index. For the sake of clarity, only the drifts along the first three principal components are displayed. ( B) Histogram of distances from MSM microstates to strings S 1 and S 2.
All figures (13)
Src kinase conformational activation: thermodynamics, pathways, and mechanisms.
PLoS Comput Biol. 2008 Mar 28;4(3):e1000047. doi: 10.1371/journal.pcbi.1000047.
PLoS Comput Biol. 2008.
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Tyrosine Kinase Activation and Conformational Flexibility: Lessons from Src-Family Tyrosine Kinases.
Acc Chem Res. 2017 May 16;50(5):1193-1201. doi: 10.1021/acs.accounts.7b00012. Epub 2017 Apr 20.
Acc Chem Res. 2017.
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The Activation of c-Src Tyrosine Kinase: Conformational Transition Pathway and Free Energy Landscape.
J Phys Chem B. 2017 Apr 20;121(15):3352-3363. doi: 10.1021/acs.jpcb.6b08409. Epub 2016 Oct 28.
J Phys Chem B. 2017.
27715044 Free PMC article.
Src protein-tyrosine kinase structure and regulation.
Biochem Biophys Res Commun. 2004 Nov 26;324(4):1155-64. doi: 10.1016/j.bbrc.2004.09.171.
Biochem Biophys Res Commun. 2004.
Markov state models provide insights into dynamic modulation of protein function.
Acc Chem Res. 2015 Feb 17;48(2):414-22. doi: 10.1021/ar5002999. Epub 2015 Jan 3.
Acc Chem Res. 2015.
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On the activation and deactivation pathways of the Lck kinase domain: a computational study.
J Comput Aided Mol Des. 2019 Jun;33(6):597-603. doi: 10.1007/s10822-019-00204-0. Epub 2019 May 10.
J Comput Aided Mol Des. 2019.
Tuning the "violin" of protein kinases: The role of dynamics-based allostery.
IUBMB Life. 2019 Jun;71(6):685-696. doi: 10.1002/iub.2057. Epub 2019 May 7.
IUBMB Life. 2019.
31063633 Free PMC article.
Efficient Sampling of Knotting-Unknotting Pathways for Semiflexible Gaussian Chains.
Polymers (Basel). 2017 May 29;9(6):196. doi: 10.3390/polym9060196.
Polymers (Basel). 2017.
30970873 Free PMC article.
Multiscale Methods in Drug Design Bridge Chemical and Biological Complexity in the Search for Cures.
Nat Rev Chem. 2018 Apr;2(4):0148. doi: 10.1038/s41570-018-0148. Epub 2018 Apr 11.
Nat Rev Chem. 2018.
30949587 Free PMC article.
SAXS-guided Enhanced Unbiased Sampling for Structure Determination of Proteins and Complexes.
Sci Rep. 2018 Dec 10;8(1):17748. doi: 10.1038/s41598-018-36090-z.
Sci Rep. 2018.
30531946 Free PMC article.
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CSK Tyrosine-Protein Kinase
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