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<figcaption class="figure-caption figtext" style="text-align:center; padding-top: 3%;padding-left:3%;padding-right:3%"> Table 1. The enzymes modeled, which templates were used and quality assessment by means of GMQE and QMEAN. GMQE ranges between 0 and 1, where one is good and zero is bad. As for QMEAN the higher the score, the better(1).</figcaption> | <figcaption class="figure-caption figtext" style="text-align:center; padding-top: 3%;padding-left:3%;padding-right:3%"> Table 1. The enzymes modeled, which templates were used and quality assessment by means of GMQE and QMEAN. GMQE ranges between 0 and 1, where one is good and zero is bad. As for QMEAN the higher the score, the better(1).</figcaption> | ||
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Revision as of 21:09, 1 November 2017
Abstract
The three enzymes in our crocin pathway are relatively newly discovered and thus poorly characterized, with no structures available. In addition, we were only able to find enzymatic parameters concerning one of the enzymes, UGTCs2 (1). Via homology modeling we could draw the conclusion that UGTCs2 and CaCCD2 are monomers while CsADH2946 is a tetramer. We could also ensure that the N-terminal was facing outward from the protein and could safely put a His-tag there for purification. Furthermore, the extensive 100 ns MD simulation of our models verified that the models were stable in solvent and that we could further work with the models to estimate the binding affinity between enzyme and substrate. Steered molecular dynamics simulations showed that CsADH2946 is specific to its substrate crocetin dialdehyde and that it has an affinity in the µM range to the substrate. The estimation of KM from the experimental activity measurements also showed that CsADH2946 has a high affinity towards the substrate crocetin dialdehyde, in agreement with Steered Molecular Dynamics results.
Homology Modeling of the Uncharacterized Enzymes
One of the first things we noticed when looking at our selected enzymes was that no three-dimensional structures were available and the enzymes were poorly characterized in general. To be able to get structural information we turned to homology modeling.
The idea of homology modeling is to construct a 3D-structure by mapping the amino acid sequence onto a template – i.e. a known structure of a related, homologous protein through sequence alignment. For this to work you need a template with a solved 3D-structure. The quality of the model is determined by the alignment with, and, the structure of the template. Thus, ideally, you would like a high-resolution structure with high sequence identity.
The tool we used to generate our homology models was SwissDock /2/, a fully automated protein structure homology-modeling server (2, 3, 4). We plugged in the sequences of our chosen enzymes ((CaCCD2), (CsADH2946) and (UGTCs2)) and started modeling. The templates were chosen based upon quality parameters such as Global Mean Quality Estimation, QMEAN, resolution of the crystal structure and sequence identity (5). After choosing the best templates we obtained the models detailed in figure 1 and the models along with the quality scoring are summarized in table 1. We could make two immediate observations. The CsADH2946 model seemed the most promising one, quality-wise with GMQE close to 1 and higher QMEAN being better. In addition, looking at the N-terminals (the blue ends in figure 1) we could see that they are stretched out, poking outwards from the protein. This was a good indication that we could put a His-tag at this end, with no complications. Another discovery we made was that the second step enzyme CsADH2946 is most likely a tetramer. This information was helpful when purifying the enzyme and going forth with molecular dynamics.
Molecular Dynamics in GROMACS
– The Art of Putting Digital Molecules in Digital Boxes of Water
To assess the models and prepare them for further characterization we used GROMACS /1/ to simulate our enzymes in saline water for a total of 100 ns. This lets us assess their stability and obtain new models that are closer to their native conformation which would be the most probable state of the enzymes during the activity measurements in our wet lab.
How We Simulated Our Enzymes
The MD simulations were performed based on previously defined protocols, which were nicely summarized by Justin Lemkul in a tutorial (6). All the steps until the production MD can be done on practically any system while the production MD will require a supercomputer to reduce time. Next follows a short description of the main steps in the protocols as well as some tips and general comments.
Define Box and Solvate
The protein has to be put in a box containing solvent where the simulation will take place. We chose a cubic box with at least 1 nm between the protein and the box. The simulation is run with periodic boundary conditions, meaning that if the molecule touches the boundary it will appear on the other side of the box.
Add Ions
We neutralized our enzymes and added ions to a concentration of 0.15 M to get closer to physiological conditions (7).
Energy Minimization
In this step the energy of the system is minimized using a steepest descent algorithm. This is done to remove any conformations that are unfavourable in terms of energy.
Equilibration
Equilibration is done to relax the system into an equilibrated state. It starts of by doing a simulation with constant volume, temperature (310 K) and number of particles. Once the first one is finsihed, another simulation with constant temperature (310 K), pressure (1 bar) and a constant amount of particles is run. The system is also equilibrated in the beginning of the production simulation, but by performing a more refined equilibration protocol in advance, time is saved.
Production Molecular Dynamics
Once the system was equilibrated production MD was carried out with constant pressure (1 bar), temperature (310 K) and number of particles. The simulations were run at 100 ns on a supercomputer with 24 parallel processors. The time it takes for the simulation to complete is dependant on the amount of particles in the system, therefore the simulation for CsADH2946 took more time as it is a tetramer (it took approximately one month to run the simulation for CsADH2946).
The Resulting Stable Enzyme Models
The result we got from the 100 ns stability simulations in GROMACS show a trajectory of each enzyme wiggling around trying to equilibrate into a low energy state. We created movies of these simulations that can be viewed in figure 2.
Figure 2. These videos are the result of simulating CaCCD2 (leftmost), CsADH2946 (middle) and UGTCs2 (rightmost) for 100 ns in saline water.
The movies all confirmed that our homology models are good in the sense that they are not melting. Along with the movies we received RMSD plots. The RMSD plot describes the distances between the atoms of the initial conformation going into the simulation and the atoms of the different conformational states the enzyme develops over the 100 ns. As can be seen in figure 3, The RMSD curve for each enzyme model converge towards one low, stable value. This shows that the models equilibrate to a stable state with low energy in the solvent and indicates that our homology models are in fact good models to represent our enzymes.
Steered Molecular Dynamics (Pulling) with CsADH2946 and Crocetin Dialdehyde
Since CsADH2946 had great advancements in the lab, has the best homology model score of our enzymes and also has the RMSD which converges fastest at the lowest value showing that it is a stable structure, we decided to focus the rest of our computer power to do Steered Molecular Dynamics (pulling simulations) with this enzyme. A pulling simulation between the protein and a substrate allows us to estimate the dissociation constant Kd which can be compared to KM. This is very useful to compare to the experimentally estimated KM for CsADH2946 in order to validate both the simulation and experiments.
Docking
To be able to execute pulling simulations we had to pick the ligands that were going to be pulled in the simulations. The obvious ligand of choice was crocetin dialdehyde, which is converted to crocetin by CsADH2946. To be able to verify that CsADH2946 specifically binds crocetin dialdehyde, another ligand, the common acetaldehyde was chosen to be able to compare the enzyme's specificity. Acetaldehyde was run in a separate simulation to crocetin dialdehyde.
Before being able to start the pulling simulations it is required to select an initial position which is done by docking the ligands. That position should be the active site of the enzyme. The location of the active site was found by looking at the template molecule (PDB entry 4fqf) (8). In that article the active site was on a loop containing three cysteines (C301, C302 and C303). In our homology model that corresponded to C337, C338 and C339. Because of (8) we also decided to focus on one of the subunits. The docking itself was done using SwissDock (9, 10). For the docking mol2 files for both of the ligands were generated and found through the ligand database SwissDock provided. The pdb file for CsADH2946 was the last frame of 100 ns MD simulation. As for parameters, in SwissDock you can provide room coordinates for centering and the size of a box where the server should try to dock the ligand. When the docking was complete one of the seeds was chosen based on the distance to the active site and the ligand coordinates were used for the pulling simulations.
Pulling
Steered molecular dynamics (pulling) is a way of estimating the binding affinity between a protein and a ligand. We based our simulations on a previously defined protocol by Justin Lemkul (11). Before starting the simulation we needed to select a trajectory in which the ligands were to be pulled. The choice of trajectory was based on a path that was not obstructed by any residues. After being equilibrated for 200 ps, the pulling simulation was run for 8000 picoseconds pulling the ligands at a velocity of 0.25 nm/ns. The results from the simulation can be seen in the movies below (figure 4) and in figure 5.
Figure 4. Results of the pulling simulations of one subunit of CsADH2946 with crocetin dialdehyde (leftmost) and acetaldehyde (rightmost). The molecules were pulled with a velocity of 0.25 nm/ns.
These indicated that more force is required to be able to pull out crocetin dialdehyde than acetaldehyde from the active site of CsADH2946 as the peaks in figure 5 can be interpreted as energy barriers being crossed. This can also be seen in the movies where crocetin dialdehyde gets stuck in two positions. Thus, the CsADH2946 model demonstrates specificity towards crocetin dialdehyde.
Using the Pulling Simulation to Estimate the Dissociation Constant of Crocetin Dialdehyde
The resulting maximum force applied to crocetin dialdehyde could then be used to roughly calculate the dissociation constant. To do this the following equation was used where 𝜟G is Gibbs free energy, R is the gas constant, T the temperature and Kd the dissociation constant:
\Delta G = -RTln(K_{d})
What we need is 𝜟G to be able to calculate the dissociation constant. To get 𝜟G the maximum force (284.2160 kJ/(mol*nm)) was first converted into pN. The resulting force was 471.9628 pN. 𝜟G was then calculated by extrapolating data from a study where they plotted the maximum force against their experimental 𝜟G values (12). Calculation of Kd using the equation above yielded a value of 4.9321 µM.
Thus we are able to compare the dissociation constant from our molecular dynamics simulations to the value of KM (~20.7842 µM) we estimated in our Bayesian inference model using our experimental data. Under the equilibrium approximation where substrate and enzyme complex are in an instantaneous equilibrium KM and Kd are equal. From our experiments and simulations we indeed see that the estimated KM and Kd are similar considering the fact that the dissociation constant has been calculated from an energy. This further shows that the molecular dynamics simulation is accurate, validating the result that CsADH2946 is specific to crocetin dialdehyde.
Experimental Estimation of KM for CsADH2946
Since the kinetic parameters for CsADH2946 have never been determined, we wanted to characterize the Michaelis-Menten kinetics of the reaction and estimate KM of our CsADH2946 using the activity measurement results. The substrate crocetin dialdehyde has low water solubility and will therefore partially precipitate when coming in contact with water. Quantitative kinetic characterization of such a system is especially complicated since the substrate concentration at the beginning of the experiment, S0, is not known. We have therefore developed a probabilistic method that is capable of estimating Michaelis-Menten model parameters as well as the error associated with them for such systems and we demonstrate its use on our enzyme CsADH2946. The MATLAB-script we created can be downloaded here.
Enzymatic reactions are often modeled with Michaelis-Menten kinetics. In this model, the reaction rate is described by the differential equation:
(1)
where [C] and [S] are the concentrations of product and substrate, respectively. Vmax is the maximum production rate of the system at saturated substrate concentration and KM is the substrate concentration when the reaction rate is half of Vmax. Reaction rate is not directly measured in the assay, so we used the experimental product concentrations Ĉ(t) to estimate the Michaelis-Menten parameters. This was done by integrating equation 1 numerically and fitting the integrated C(KM,Vmax,S0,t) to the experimentally measured product concentrations, Ĉ(t).
The product concentrations, Ĉ(t), were estimated at every timepoint from the experimentally measured absorbance spectra. Fitting was then performed by minimizing the sum of the squared differences (SSD) between the model prediction, C (from integration) and the experimentally measured progress curve, Ĉ(t). These fitting methods are good at finding the parameters that describe the data best but give no information about the uncertainty in the parameters described by the data. Use of methods minimizing the SSD is further complicated when the substrate concentration at the beginning of the experiment, S0, is not known, introducing further uncertainty in the data and demonstrating the need for good error estimation of the model parameters.
We developed a probabilistic method for estimating the kinetic parameters and the uncertainty in them. The method computes and integrates the probability density P(KM,Vmax,S0) as a function of all model parameters. In this method we used Bayesian statistical inference to estimate the parameters from the experimental data. In short that means calculating P(θ|Ĉ); the probability of the model parameters, θ, given the experimental data. We estimated this distribution from the experimental data and the mean and variance of each parameter could be calculated as:
(2)
The posterior probability P(θ|Ĉ) was calculated using Bayes theorem:
(3)
where the probability of the data P(Ĉ) is a normalization constant, the prior P(θ) describes your expectations of the model parameters before observing any data and the likelihood P(Ĉ|θ) is the probability of the data given the parameters.
The likelihood is a function of the product concentration C(KM,Vmax,S0,t) calculated from the Michaelis-Menten model. We modelled the deviation between the experimentally measured concentrations and model product concentration C as independent and identically normally distributed at every time-point. This gave us the likelihood
(4)
where σ is the standard deviation of the normal distribution describing the deviation between the data and the model. With a flat prior (a uniform prior where all model parameters are equally likely before observing any data) the posterior P(θ|Ĉ) can simply be written as
(5)
(6)
where Z is a normalization constant.
To estimate the mean and variance of our four model parameters we calculated the integrals in equation 2 and 3, i.e., numerically integrating the likelihood L(θ) over the four dimensions of the parameters. It is a problem that is very numerically complex if L(θ) is to be evaluated for all values of θ. Therefore, we implemented a version of importance sampling, where we only evaluate L(θ) were it is large enough to contribute to the integral. We start at the maximum likelihood set of parameter θmax (found by SSD fitting) where L(θ) is maximized and take discrete steps in θ until L(θ) is essentially 0. Therefore we do not have to compute L(θ) for all values of θ, but only at the values that actually contribute to the integral. A visual of this is displayed in figure 6. We saved the values of L(θ) of all these points in four dimensional parameter space and the marginalized distribution for the individual parameters could then be calculated. For example for KM
(7)
The mean and error estimate of KM and the other parameters was then obtained by calculating the mean and standard deviation of the marginalized distribution. A plot of the marginalized distribution for each parameter can be seen in Figure 7.
The Resulting Estimated Kinetic Parameters
So, the kinetic parameters for CsADH2946 were estimated using this probabilistic method where the experimental data was fitted to the model. As you can see in Figure 8, we could compute a curve (blue) with the estimated parameters that fit the experimental data. This means that our parameters are good approximations that can be used to describe the actual data.
To evaluate our estimated parameters, we first compared the values obtained by our algorithm with values of the parameters calculated with maximum likelihood. These were similar, which shows that our values are reasonable. To further analyse and validate our algorithm, we ran our algorithm on a simulated a progress curve based on the estimated parameters but with added normally distributed noise. The fitting of the simulated noisy data using our algorithm should return similar parameter values as the initial experimental data generated. As can be seen in figure 9, the parameters from the fitting of the simulated noisy data did return similar parameter values. We also tried to compare our results with parameters estimated from fitting the experimental data in DynaFit. However, DynaFit was unable to return a good model fit, possibly because of our unknown substrate concentration in the beginning of the experiment.
The KM estimated for CsADH2946 is low, which indicates a high affinity towards the substrate crocin dialdehyde. This is also agrees with the pulling simulation, where the enzyme showed specificity towards this substrate. We compared the results with the binding of acetaldehyde and validated that CsADH2946 has specificity against crocetin dialdehyde since a higher force was required to pull this substrate from the active site. These results greatly support our choice in selecting CsADH2946 as an enzyme candidate in our crocin crafting pathway.
References
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(6) Vt.edu [homepage on the Internet]. Virginia: Department of Biochemistry; 2015 [cited 1 October 2017]. Available from: http://www.bevanlab.biochem.vt.edu/Pages/Personal/justin/gmx-tutorials/lysozyme/
(7) Search BioNumbers - The Database of Useful Biological Numbers. online: http://bionumbers.hms.harvard.edu/search.aspx?log=y&task=searchbytrmorg&trm=Salt&org=. Accessed October 30, 2017.
(8) Lang BS, Gorren ACF, Oberdorfer G, Wenzl MV, Furdui CM, Poole LB, et al. Vascular Bioactivation of Nitroglycerin by Aldehyde Dehydrogenase-2. J Biol Chem. 2012 Nov 2;287(45):38124–34.
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Further Reading
