The human prion protein (hPrP) is a membrane N-linked glycosylphosphatidylinositol-anchored glycoprotein that has 253 amino acids when it is newly synthesized. It is expressed in various tissues, but is particularly present in nervous system. Its primary structure includes an N-terminal 22-residue signal peptide, which mediates translocation into the endoplasmic reticulum [1] , and is cleaved during importation. Soon after importation event, core glycans are attached to N181 and N197, and also a glycosylphosphatidylinositol anchor is trans- ferred to S230 [2] [3] . Core glycans are subjected to further processing in the Golgi compartment [4] . hPrP also has oxidation-susceptible methionines at positions 129, 134, 154, 166, 205, 206, 231 [5] . Two cysteine residues at positions 179 and 214 are linked by a single disulfide bond [6] . The last C-terminal 22 amino acid residues comprise another signal sequence, which is also absent in the 209-residue mature form of the protein [1] .

Sequence PQGGGGWGQ is among important structural regions of hPrP, beginning at residue number 51, and followed by four repetitions of the octapeptide PHGG(G/S)WGQ which encompasses residues 60 to 91; such octapeptides are cofactor binding sites. It also has a palindromic sequence AGAAAAGAA that spans residues 113 to 120, as part of a downstream tightly packed hydrophobic core. Residues at positions 127 and 129 are polymorphic, as it could be either glycine or valine in the first case, and methionine or valine in the second one [7] .

In accordance with the protein-only hypothesis, a misfolding of human prion protein is the cause of prion diseases. Experimental evidence supports that this is the sole etiologic agent of a group of neurodegenerative diseases related to the conversion of the native isoform, an alpha-helix rich cellular protein (PrP^C), into a beta- strand rich misfolded conformer, named “Scrapie” prion protein (PrP^Sc) [8] . The PrP^Sc is thought to be infectious through nucleation of complete or partial PrP^Sc forming rod-like aggregates. Template assistance and nucleated polymerization models have been proposed to explain the mechanisms of conformational conversion and aggregation, but they are still poorly understood [5] . Thus, this work is aimed to provide insight into them by using a molecular dynamics approximation to the problems.

PrP^C has a flexibly disordered N-terminal tail and a structured C-terminal globular domain from amino acid 125 to 231. The C-terminal globular domain includes three alpha-helixes known as H1, H2 and H3 at 144 - 154, 173 - 194 and 200 - 228 positions, and a short antiparallel beta-strand region at 127 - 130 and 161 - 164 residues (S1 and S2). It also has three zones of structural irregularity at 167 - 171, 187 - 194 and 219 - 228 [9] . H1 and H2 are linked by a loop formed by 165 - 171 residues, better known as X-loop. The protein hydrophobic core comprises interactions between H2 and H3 and between H3 and the loop preceding H1 (S1-H1 loop), as well as contacts between the beta-strand with the rest of the globular domain [5] .

More than 30 different punctual mutations in the open reading frame of the human prion gene (PRNP) have been studied as they are linked to human prion inherited diseases, such as Gerstmann-Sträussler-Scheinker syndrome, fatal familial insomnia and familial Creutzfeldt-Jakob disease. All these diseases have variations in clinical, physiological and pathological characteristics, which are probably explained by the differences in the mechanism of destabilization of PrP^C, conversion into PrP^Sc, aggregation, and by the specific brain regions where all these processes occur. It is particularly remarkable that many missense point mutations are clustered within H2 and H3, and the loop between them. Mutations leading to disease have also been reported, although much less represented, at N-terminal domain, particularly at the octapeptide region and the disordered zone before S1 [10] - [14] .

Mutations may alter either the thermodynamic stability of PrP^C, change surface properties that in turn modify interactions, and vary the response to cellular pathways control processes, or a combination of these mechanisms. However, solution structures of hPrP mutants are conformationally similar to the wild-type protein, and only molecular simulation techniques have been capable of elucidate differences between them [15] - [18] .

Table 1 summarizes different mutations associated with the development of human prion inherited diseases.

Extensive all-atom molecular dynamics simulations at 37˚C and different pH values were made to study the structure of wild-type human prion protein, first in the vacuum, and then using water as solvent. We used spatial coordinates of human prion protein structured region (amino acid residues 125 - 228) as in 1QLZ code of Protein Data Bank.

In order to relax the protein in vacuum, MD was applied at minimum energy conditions and under the influence of GROMOS96 force field at GROMACS 4.0.7 suite of programs [19] . Consecutively, periodic frontier conditions were incorporated by using a rhombic dodecahedral water box which volume was 283 nm³. This process was repeated using 7778 water molecules as solvent with Simple Point Charge (SPC) model.

The system protein-water was neutralized by addition of sodium and chloride ions, and the potential energy was defined as the sum of two types of non-bonded interactions (electrostatic and van der Waals) and three types of bonded interactions (chemical, angles and twisting).

The equilibration process was started with a set of velocities taken from a Maxwell-Boltzmann distribution until it reached 305 K in about 350 ps using the Berendsen thermostat for both systems (protein and solvent). The production process was implemented with the same thermostat and the Parrinello-Rahman barostat; the total simulation length was 80 ns. The performance of computer system was 5.0 ns per day.

The measure of the deviation between the position of particle and some reference position was calculated with the Root Mean Square Fluctuation (RMSF).

where is the time over one wants to calculate the average, is the position of the particle on the time and is the reference position of the particle. In order to obtain the relative vibrational motion of different regions of the protein we use the B-factor

where is the mean square displacement and is related with the self-diffusion coefficient via the Einstein relation

where is the initial position of the particle.

Also we used the -component pressure tensor to estimate the shear viscosity which evaluates the rates of possible changes in the protein conformation, both variables are related by

Here, is the volume, the temperature, the initial time and the Boltzmann constant [21] [22] .

The solvated protein was stabilized with an initial temperature of 310 K, and then the temperature of the solvent was modified in order to stimulate the protein and identify the regions with higher vibrational states. Figure 1 shows that such regions correspond to residues 144 - 149, 178 - 181, 193 - 197 and 221 - 223. The RMSF was calculated with (1).

In order to identify the relative vibrational motion of different parts of the protein, we calculated de B-factor for the same solvent temperatures, as can be observed in Figure 2.

It is well known that calculation of viscosity with (4) converges very slowly [21] ; however we were interested in analyzing its evolution in early times because its variations stimulate conformational changes on the protein. Figure 3 shows that viscosity has partially uniform oscillations around 1.5 cP when the solvent has the lowest temperature, in other words, viscosity varies more uniformly at the lowest temperature than at other temperatures, maintaining values predominantly below 2 cP.

The regions of high susceptibility to conformational changes are close to mutation sites experimentally tested and reported. According to Figure 1, the regions with higher vibrational states correspond to residues 144 - 149, 178 - 181, 193 - 197 and 221 - 223. The simulation showed important oscillations in nanosecond time scale order. These oscillations are not due to viscosity fluctuations, but due to temperature changes in solvent. The oscillations observed in three different properties indicate that the van der Waals term of the force field employed is very rigid, so we need to prove a more flexible potential with more realistic repulsion and attraction contributions, although it increases the computational time required for simulations.

The authors wish to thank Universidad Autónoma del Estado de México for financial support through project ID 3697/2014/CID.