We next asked if the reduced apparent binding signal was caused by a direct impairment of the p15/PCNA binding site or by an affected structure or stability of PCNA. Therefore, we conducted alchemical free energy calculations. Alchemical free-energy calculations are a useful
in silico method for studying the effect of mutations, as they can provide remarkable prediction accuracy, if properly set up [
45,
46]. It is possible to estimate the differences in the free energy (∆G) between two defined sets of states, i.e. the unfolded and folded state of a protein or the bound and free state of a complex. The effect of mutations on this free energy difference can also be given as the relative change in ∆G, which is commonly referred to as the relative folding free energy (∆∆G
folding) or the relative binding free energy (∆∆G
affinity). In case of PCNA, this allows to study the effect of the C148S mutation on protein stability (∆∆G
folding) and PCNA-p15 affinity (∆∆G
affinity).
Alchemical free-energy methods work by gradually transforming one chemical state into another following an unphysical pathway. The alchemical pathway does not need not follow the physical folding or binding pathway and is therefore more accessible by molecular dynamics (MD) simulations. In our case we made use of a non-equilibrium approach based on the Jarzynski equality and the Crooks fluctuation theorem [
47,
48,
49]. In this approach two standard MD simulations are run, one for each state (WT and C148S) of the system. Snapshots from these equilibrium simulations are extracted and used to perform alchemical transition by driving the Hamiltonian
H of the system from one state to another using a parameter called λ. This parameter is gradually increased from 0 to 1 during the simulation.
To estimate both the ∆∆G
folding of PCNA and the ∆∆G
affinity between PCNA and p15 upon amino acid mutation, the wild-type amino acid was alchemically morphed from a cysteine at position 148, to a serine. To keep the systems to a reasonable size, we included only one PCNA monomer, instead of the homotrimer. This drastically reduced computational cost. The stability of monomeric PCNA during 100 ns of MD simulation was tested. No great conformational change, and a root mean square deviation (RMSD) below 3 Å for the protein was observed. We therefore concluded that it was viable to only use the monomer going onward. For the calculation of ∆∆G
folding the transition for the unbound state, in this case approximated by a Gly-Cys-Gly tripeptide, and the folded state were performed [
50]. For the calculation of ∆∆G
affinity the transitions were performed for free PCNA and the PCNA-p15 complex. The resulting ∆G values for each transition were used to calculate the ∆∆G values according to the thermodynamic cycle shown in Figure S4. We also performed calculations for two further mutations to construct a closed thermodynamic cycle with the respective ∆∆G values at its edges to confirm convergence of the simulations (
Figure 6). This cycle includes mutations for serine to alanine and alanine to cysteine, forming a cycle with three edges. Furthermore, the simulation length for the transitions were optimized by running these simulations with different transition times. This optimization was performed for the mutation involving the biggest perturbation, in this case A148C. ∆∆G
folding was monitored as a function of transition time and no significant change in ∆∆G
folding was observed when increasing the transition time beyond 100 ps (Figure S5). We therefore concluded that a transition time of 100 ps was sufficient for the mutations and the system under investigation. Following this optimized setup, cycle closure for the calculation of ∆∆G
folding and ∆∆G
affinity was achieved, with all the single legs of each cycle summing up to 0.1 kcal/mol and -0.19 kcal/mol. These values are within the expected range of error for alchemical free energy calculations [
45,
46], and within the uncertainty of our approach as seen by the standard deviation over three independent replicas. The estimated ∆∆G
folding value of 2.39 ± 0.47 kcal/mol for the mutation C148S suggest a destabilizing effect of the mutation. An increase in ∆∆G
folding is equivalent to a more positive folding free energy of PCNA
C148S. This leads to a decreased thermostability and/or chemical stability [
51]. It furthermore increases the probability of the protein to adapt intermediate folding states, which are normally poorly populated. These intermediate states often display large hydrophobic patches on their surface which can initiate aggregation [
52]. The calculated ∆∆G
affinity of 0.21 ± 0.22 kcal/mol for the C148S mutation, suggest no direct change in binding affinity of PCNA
C148S to p15 compared to PCNA
WT. One likely conclusion is, that the mutation leads to a less stable variant of PCNA, which might be more prone to aggregation or denaturation. When this protein is used as the titrator in a binding assay, less functional protein than expected might be present in solution. The measured affinity would therefore be apparently lower than it actually is. This might explain the apparently reduced binding of p15 to PCNA measured with the FRET assay, even if the binding free energy is not changed by the mutation. We therefore decided to experimentally test the thermal and chemical stability of PCNA
C148S, as well as its aggregation behavior.