# Modelling of substrate access and substrate binding to cephalosporin acylases | Scientific Reports

### Structures

The 3D crystal structure of cephalosporin acylase from Pseudomonas sp. N176 was retrieved from the Protein Data Bank ( PDB introduction 4HSR ) 15, 51. This 2.13 Å resolution structure carries a single point mutant ( M31βF ) and it is referred as godforsaken type ( WT ). The structure besides contains the covalently bound ligand 5,5-dihydroxy-L-norvaline, which was removed. Mutant M31βF/F58βN/H70βS/I176βT 20, referred here as M6, was constructed by the mutagenesis tool of PyMOL ( The PyMOL Molecular Graphics System, Version 2.0 Schrödinger, LLC ). The structure of CPC was taken from the Protein Data Bank ( PDB submission 2VAV, ligand code CSC ) 52 .

### Force fields, protonation states and system settings

molecular dynamics ( MD ) simulations were performed using the software GROMACS interpretation 5 53 at constant pressure of 1 bar and at ceaseless temperature of 310.15 K ( NPT ensemble ). The v-rescale and Berendsen algorithm were used for temperature and pressure match, respectively 54, 55. electrostatic interactions were calculated by the smooth particle-mesh Ewald summation 56. Water was simulated as SPC/E model 57, while the CPC force battlefield was derived by a RESP fit approach 58. The RESP calculations were performed on the R.E.D. Server ( RESP ESP commission Derive Server ) where the software Firefly version 8 was used 59, 60. fond charges were derived for the cephalosporin C core ( Fig. S6 ) considering different possible conformations : all the low energy accessible conformations were computed using the software Confab setting 1 Å and 50 kcal/mol as geomorphologic and energy cut-offs 61. The concluding CPC topology was obtained by using the tool MKTOP 62 with standard OPLS atoms and using the partial derivative charges coming from the RESP match calculation together with those of the standard alanine OPLS definition ( Fig. S6, CPC forcefield in supporting data ). such build block operation was implemented to reuse the alanine OPLS definition. Since experimental activeness measurements were performed at ph 8.0 15, 16, 17, 19, 20, the same was considered for defining the protonation express of the model systems. The two acidic moieties of CPC were considered as negatively charged, while the amino group was considered as positively charged, therefore resulting in an overall CPC tear of −1. Protein power field definitions were obtained using the tool pdb2gmx of GROMACS 5. The pdb2pqr waiter was used to calculate the protonation country of each enzyme variant at ph 8.0 63. For the two enzymes, the side chains of D/E and K/R were considered to be negatively and positively charged, respectively. end residues were considered charged, except for the β1 serine which was defined as neutral, in agreement with the proposed catalytic mechanism ( Fig. S1 ) 15. The protonation states of the histidine residues are reported in Table S1 .

### Simulation of the enzyme-substrate complex

Each modeled enzyme was simulated with a single CPC atom manually placed into the binding pocket, with the substrate amide shackle oriented to fit the stabilizing network in the catalytic mechanism ( Fig. S1 ). The CPC orientation was adjusted to avoid steric clashes with the enzyme. The initial CPC orientation course was identical for all the model systems. interestingly, was not possible to obtain dock substrate poses in agreement with the catalytic mechanism by applying automated docking algorithm. Each enzyme-substrate complex system was then placed in the center of a cubic box of 1000 nm3. Each organization was solvated using denotative SPC/E body of water 57, 64 and neutralized by adding the appropriate total of ions ( Na+ or Cl− ). Each system resulted in about 100000 atoms. For each enzyme-substrate complex considered, a series of five autonomous model runs was performed. Each system was minimized for 10000 steps, using a exorbitant lineage algorithm and subsequently equilibrated for 10 ns. During the 10 north equilibration, position restraints was applied to the protein heavy atoms and the CPC atoms ( force constant 1000 kJ·mol−1·nm−2 ). The position restraints on CPC were gradually reduced during the equilibration ( 1000 kJ·mol−1·nm−2 for 4 ns, 500 kJ·mol−1·nm−2 for 3 ns, 300 kJ·mol−1·nm−2 for 3 normality ). subsequently, all the restraints were removed and each system was promote equilibrated for 200 ns. After equilibration, each arrangement was simulated for 1.8 µs. therefore, each enzyme random variable in complex with CPC was simulated for a sum time of 9 µs ( 5 independent runs of 1.8 µs each ). Frames were saved every phosphorus .

### Simulation of substrate access

Each modeled enzyme was simulated in a cubic corner of 4096 nm3 and at four different CPC concentrations by adding a unlike total of substrate molecules ( 11, 20, 50, or 100 CPC molecules were randomly added using the GROMACS tool gmx insert-molecules ). Each system was solvated using explicit SPC/E water 57, 64 and neutralized by adding the appropriate number of ions ( Na+ or Cl− ). Each system resulted in about 500000 atoms. Systems were minimized for 10000 steps using the steepest descent algorithm. For each CPC concentration, 5 freelancer simulations were performed. Each system was first gear equilibrated for 10 ns with position restraints applied to the protein clayey atoms and to the CPC molecules ( force out changeless 1000 kJ·mol−1·nm−2 ). subsequently, the restraints were removed, and the systems were promote equilibrated for 50 ns. After the equilibration phase, each system was simulated and subsequently analyzed for 200 ns. Each enzyme form in building complex with CPC was simulated for a sum time of 1 µs for each CPC assiduity ( 5 independent runs of 200 normality each ). Frames were saved every postscript.

### NAC distance

According to the proposed catalytic mechanism, the substrate has to bind in a productive tie put in its footing state. The latter closely resembles the transition state prior to the nucleophilic attack by the β1 serine side chain. This about Attack Conformation ( NAC ) 25, 26, 27 is characterized by four catalytically relevant distances ( Fig. 9 ) : between the hydroxyl oxygen of the catalytic β1 serine and the carbonyl carbon paper of the substrate ( d 1 ) and between the oxyanion hole residues and carbonyl oxygen of the substrate ( d 2, d 3, d 4 ) .Figure 9 conventional representation of the first step of the proposed catalytic mechanism. The substrate is assumed to bind in a reason state shape which is closely related to the transition submit of the chemical reaction : the Near Attack Conformation ( NAC ). The four distances used for calculating dNAC are indicated in loss and labeled. Full size prototype A distance d NAC was calculated as the beginning hateful square of d 1, d 2, and the minimum of d 3 and d 4 :

$${d}_{NAC}=\sqrt{\frac{{d}_{1}^{2}+{d}_{2}^{2}+{d}_{{\rm{\min }}(3,4)}^{2}}{3}}$$

( 2 ) d NAC constitutes a reaction coordinate and was calculated at every postscript and for every substrate atom give in the simulation. In most simulations of the enzyme-substrate complex, d NAC deviated from its initial rate of 2.2 Å and varied in a image of 2.2 to 13 Å. A few simulations were discarded, because the value of d NAC did not deviate from its initial rate indicating kinetic trap of CPC in its initial conformation .

### Free energy profile of CPC

The detached energy profile of CPC was calculated as the logarithm of the proportion between the watch frequency of d NAC in the presence of the enzyme and the forecast frequency at a given CPC concentration in the absence of the enzyme. d NAC frequencies were summed up for all replicates and analyzed in bins of 1 Å. The probability p(i) of having CPC atom at bin i was obtained by dividing the number of substrate molecules found at bank identification number i during the model by the sum number of conformers analyzed :

$$p{(i)}_{enzyme}=\frac{{N}_{i}}{\#\,conformers}$$

( 3 ) where N i represents the number of substrate molecules within a given bin ( bins of 1 Å in d NAC ) and # conformers indicates the sum number of sample conformers. In a substrate solution at assiduity c ( in the absence of any enzyme ), the number of substrate molecules N i in a layer of thickness of δb = 1 Å at a distance a i from the plaza is :

$$N{(i)}_{withoutenzyme}=\frac{4}{3}\pi ({({a}_{i}+\delta b)}^{3}-{{a}_{i}}^{3})\cdot c\cdot {N}_{0}$$

( 4 ) with Avogadro constant NA = 6.022·1023 mol−1. By considering the fake system in a thermal balance at temperature T, assuming a Boltzmann distribution, the probability of finding the arrangement in a given state of matter is related to its free energy 28, 29. frankincense, the impression of the enzyme can be expressed as a unblock energy difference ΔG for each bin, and the loose energy profile of CPC as a function of d NAC is calculated as :

$$\frac{{\rm{\Delta }}{\rm{G}}}{kT}=-ln\,\frac{p{(i)}_{enzyme}}{N{(i)}_{withoutenzyme}}$$

( 5 ) At large distances ( d NAC > 60 Å ), the enzyme does not interact with the substrate, and the free energy profile of CPC approaches 0. therefore, the bulge concentrations c of the molecular systems after equilibration were obtained by fitting p(i) enzyme and N(i) without enzyme at d NAC > 60 Å ( Fig. S3 ) .

### Conformational sampling

Conformational sampling of substrate poses was performed by isolating all the CPC molecules within a given d NAC range. Therefore, all molecules except for the protein and the selected CPC molecules were discarded. The Cα atoms of the protein were used for superimposition of the selected conformers. last, the CPC molecules were clustered based on their RMSD using the gmx cluster of the GROMACS package and considering all the CPC atoms .

### Electrostatic properties

The electrostatic electric potential at the protein airfoil of the wild type enzyme ( WT ) was analyzed by the PyMol plugin for the APBS creature ( adaptive Poisson-Boltzmann Solver ) 30. Results were visualized on the protein structures using a range from −1 ( red ) to + 1 ( blue ) .

### Binding affinity

A substrate atom ( CPC ) was defined as apprenticed to the protein open close to the entrance to the tie down pocket, if its plaza of aggregate was within 5 Å from any protein atom within 25 Å from the hydroxyl oxygen of β1 serine. The affinity of CPC for the enzyme was determined by fitting a Langmuir ski binding exemplary 65, assuming non-cooperative bind to a limited number of identical bind sites. The number of bound substrate molecules CPC b was determined by counting ( GROMACS tool gmx trjorder ) the issue of CPC molecules bound to the protein and by averaging over the pretense runs at the same substrate concentration. standard errors were calculated by considering standard deviations from each model run and by mistake propagation during the average procedure. ultimately, CPC b was fitted with the CPC bulk concentration c by a Langmuir model 31, 65 :

$$CP{C}_{b}=\frac{CP{C}_{b}^{MAX}\cdot c}{K+c}$$

( 6 ) where CPC b MAX represents impregnation ( the maximum number of substrate molecules bound to the enzyme ) and K the tie down changeless .

### Data deposition

The force sphere has been deposited as auxiliary substantial .