BIBECHANA Vol. 22, No. 1, April 2025, 63-72 ISSN 2091-0762 (Print), 2382-5340 (Online) Journal homepage: http://nepjol.info/index.php/BIBECHANA Publisher:Dept. of Phys., Mahendra Morang A. M. Campus (Tribhuvan University)Biratnagar Thermal properties and non-bonded interactions in human PMP2 variants: A molecular dynamics study Prabin Aryal, Jhulan Powrel Department of Physics, Butwal Multiple Campus, Tribhuvan University ∗Corresponding author. Email: prabinaryal.0d@gmail.com(PA) jhulan.sumi@gmail.com(JP) Abstract Charcot-Marie-Tooth disease, a genetic disorder linked to mutations in the peripheral myelin protein 2, currently lacks an effective cure. In this study, we have used molecular dynamics simulations, focusing on non-bonded interactions and thermal properties, to ex- plore the effects of M114T mutation on PMP2 at the temperatures of 305K, 310K and 315K. Our findings indicate that the mutation slightly destabilizes PMP2, reducing its structural integrity by decreasing hydrogen bonds and altering few salt bridges, although the differences are minimal. Additionally, the mutant exhibits slightly increased thermal diffusivity. A non- linear change in Cv with temperature was also observed in both protein systems. This work further extends to verify the Maxwell-Boltzmann distribution law and demonstrate the Gaus- sian nature of the temperature fluctuations in the protein systems. Keywords Charcot-Marie-Tooth 1A, Comparative analysis, M114T mutant, NAnoscale Molecular Dynamics. Article information Manuscript received: September 24, 2024; Revised: January 13, 2025; Accepted: January 15, 2025 DOI https://doi.org/10.3126/bibechana.v22i1.70049 This work is licensed under the Creative Commons CC BY-NC License. https://creativecommons. org/licenses/by-nc/4.0/ 1 Introduction Neurons are a type of specialized cells in the ner- vous system through which electrical impulses, also known as action potential, propagate to different cells in the rest of the body [1]. For efficient trans- mission of electrical impulses, the axons in the neu- rons are insulated by concentric layers of plasma membranes called a myelin sheath [2]. In the cen- tral nervous system, the Oligodendrocyte cells make and maintain myelin sheath, whereas in the periph- eral nervous system this is done by the Schwann cells [3]. A single schwann cell forms one myelin sheath. High level of saturated long chain fatty acids is present in myelin along with Fatty acid binding proteins like Myelin Basic Protein (MBP) and Peripheral Myelin Protein 2 (PMP2) which play a crucial role in inter-molecular cohesion with the lipids which stack the myelin layers together to form myelin sheath [4,5]. In particular, PMP2 is one of the most prevalent constituents in the myelin of the human PNS [6]. Mutations in PMP2 protein have been linked with various types of Charcot-Marie-Tooth (CMT) disease [7–10], a Hereditary Motor and Sensory Neuropathy (HMSN), which primarily targets the 63 http://nepjol.info/index.php/BIBECHANA prabinaryal.0d@gmail.com jhulan.sumi@gmail.com https://doi.org/10.3126/bibechana.v22i1.70049 https://creativecommons.org/licenses/by-nc/4.0/ https://creativecommons.org/licenses/by-nc/4.0/ Prabin Aryal and Jhulan Powrel/ BIBECHANA 22 (2025) 63-72 64 Peripheral Nervous System [11]. One such recently discovered mutation in this protein is M114T, which was associated with the CMT type 1A disease in German and Bulgarian families [10]. Many at- tempts, including using ascorbic acid [12], have failed to cure CMT disease, as no significant im- provement in nerve conduction velocity was ob- served. To date, no therapeutic cure exists. Research on the PMP2 protein has revealed its tetragonal crystal structure in the space group P 41 21 2. Its molecular weight is approximately 15 kDa, and has high solubility in aqueous buffer solu- tion. The structure of protein plays an important role in proper functioning. Destabilized structures can result in the loss of function which can lead to aggregation of protein and formation of toxic species. In the case of this protein, there are ten anti-parallel β strands and two α helices [13]. There is a fatty acid, Palmitate, inside the barrel shape of the protein. From the atomistic molecular dy- namics simulation study of wild-type PMP2, it was found that the absence of this fatty acid increased the dynamics in the 2α helix [14]. Non-bonded interactions within protein structures dictate their integrity and function, with alterations leading to misfolding and aggregates linked to diseases like Alzheimer’s and Parkinson’s.. The mutant protein has a similar tetragonal crystal structure, but with increased fatty acid binding ability. Also, using the CD spectroscopy, the melting temperature for wild- type protein was found to be +61.6°C whereas that for M114T mutant was +49.2°C [15]. Figures 1 and 2 show the chemical structures of Methionine (left) and Threonine (right) at the mutation site, and the normal PMP2 protein with Methionine and Threonine at position 114, respec- tively. CMT disease has a low mortality rate, with chil- dren being at relatively higher risk than adults [16]. However, there is a greater risk on the mental health of patients as they are psychologically more vul- nerable. Issues like depression, anger, guilt, and frustration due to lack of independence could dis- turb their mental peace and well-being [17]. While previous research has explored the structural and functional roles of PMP2, there has been limited focus on the effects of this specific mutations on in- teraction dynamics and thermal behavior. So, this research work got attention towards the compara- tive study of non-bonded interactions and thermal properties in normal and M114T mutant human PMP2 protein. Also, no such study has yet been done at temperatures of 305 K, 310 K, and 315 K – the normal and extreme core body temperatures in humans [18, 19]. As there are many enzymatic activities essential for cellular processes, studying the changes in the thermal properties and their im- pact on them is crucial to understanding the effects of the mutation on the body, which can aid in the development of proper therapeutic drugs. We have presented the details regarding the methods and methodology in section 2, computa- tional details in section 3, and the results and dis- cussions in section 4. Finally, the conclusions and concluding remarks are presented in the section 5. Figure 1: Chemical structure of Methionine (left) and Threonine (right) in the amino acid chain of PMP2 near mutation cite. Figure 2: Normal PMP2 protein with Methionine at 114th position (left), and mutant PMP2 protein with Threonine at the 114th position (right). 2 Methods and Methodology In Molecular Dynamics, different properties such as RMSD, H-bonding, Salt Bridge formation, etc can be estimated using the information of the tra- jectories of the particles in 6N-dimensional phase space. For this, at first the particles are assigned a position. Then, the subsequent positions during simulation are generated by solving the equation of motion given by, mi ∂2ri(t) ∂t2 = Fi {ri(t)} − γi dri(t) dt + Ri(t) (1) where mi ∂2ri(t) ∂t2 , Fi {ri(t)} and γi dri(t) dt are the net force on the ith atom, total force on the ith atom due to the neighbouring atoms, and damping force, respectively at time t. And Ri(t) accounts for the random force that acts on the atoms [20]. Both the bonded (VB) and non-bonded (VNB) potentials act on the system. If the ith and jth atom at distance rij have partial charges Qi and Qj, then the total potential (VT) is obtained as, V T = V B + V NB (2) Prabin Aryal and Jhulan Powrel/ BIBECHANA 22 (2025) 63-72 65 where VB = Vbond + Vangle + Vimproper + Vproper , and VNB = VLJ + Vcoulomb The Lennard-Jones potential VLJ, between a pair of atoms is given by the equation [21], VLJ = 4ε [(σ r )12 − (σ r )6] (3) And the Coulomb electrostatic interaction po- tential Vcoulomb is given by the equation, Vcoulomb = Qi ·Qj 4πϵmrij (4) 2.1 Root Mean Square Deviation (RMSD) The RMSD at an instant is the standard deviation of the position of the atom from mean position at that instance. It tells about the stability of the protein over time and can be used to compare the structure and conformation of two proteins. Higher value of RMSD means reduced stability. The equa- tion that gives the RMSD of a system [22] is, RMSD (ti) = √√√√(∑Nα α=1 ( −→rα (ti) − ⟨−→rα⟩) 2 Nt ) (5) With, ⟨−→rα⟩ = 1 Nt Nt∑ i=1 ⟨−→rα (ti)⟩ Here, Nα and Nt respectively represent the num- ber of atoms and number of time steps over which atomic positions are being compared, −→rα (ti) repre- sents the position of atom α at time ti and ⟨−→rα (ti)⟩ represents the corresponding average value [23]. 2.2 Hydrogen Bonds Hydrogen bond is a non-bonded interaction, so the bonds are not stable over time. As such, the stability and strength can be understood only by analysing the average frequency of formation of H- bonds. It contributes to the elastic stiffness of the protein and its structural stability. For moderate strength H-bonding, which is mainly electrostatic, the donor-acceptor distance is 2.5 Å - 3.2 Å [24]. In this research, cutoff distance and angle for H-bonds is taken as 3.2 Å and 30◦, respectively. However, due to this approximation, the weak H-bondings will not be taken into account, which might bring some error in the observed results. 2.3 Salt Bridges Salt bridge is a type of non-bonded interaction that exists between acidic and basic residues. If such residues are within the cutoff distance than they are counted as salt bridges. Here, the oxygen-nitrogen cutoff distance for the salt bridges is taken as 3.2 Å. Salt bridges prevent the diffusion of solution [25]. 2.4 Gaussian Distribution Gaussian distribution is one of the widely observed distribution identified by the probability distribu- tion function [26], P (x) = 1√ 2πσx exp ( − (x− ⟨x⟩)2 2σ2 x ) −∞ ≤ x ≤ +∞ (6) where x is the random variable, whose expecta- tion is ⟨x⟩ and standard deviation is σx. The temperature fluctuation of the system in the NVE ensemble is expected to follow the Gaus- sian distribution [22]. 2.5 Maxwell-Boltzmann Distribution Law According to Maxwell and Boltzmann [27, 28], the distribution of molecular velocity (v) of an ideal gas of molecular mass m at absolute temperature T is described by the function, f(v) = √ 2 π v2e− v2 2a2 a3 , v ≥ 0 (7) With parameter a = √ KBT m , where KB is Boltzmann constant. Using the expression for Kinetic energy, Ek = 1 2 mv2 = 3 2 KBT and with proper normalization, we get the prob- ability distribution function for the kinetic energy [22] as, f (Ek) = 2√ π 1 (KBT ) 2 3 √ Ek exp ( − Ek KBT ) (8) 2.6 Thermal Diffusivity The three-dimensional heat equation is, ∂T (−→r , t) ∂t = D · ∇2T (−→r , t) (9) The time dependence of the average tempera- ture in the water-sphere system considered here is given by the equation [22], ⟨T ⟩ (t) = Tbath +6·Tinitial − Tbath π2 ∞∑ n=1 1 n2 exp [ − (nπ R )2 Dt ] (10) where Tbath and Tinitial are the temperatures of outer shell of sphere and the initial temperature of the interior of sphere, respectively. R (= 25 Å) is Prabin Aryal and Jhulan Powrel/ BIBECHANA 22 (2025) 63-72 66 radius of sphere excluding the outer shell of thick- ness 5 Å. To fit a curve with the obtained data, we have approximated to the first 11 terms only, and the other terms are neglected. So, the expression con- sidered here is, ⟨T ⟩ (t) = 200 + 66.87 · [ ∞∑ i=1 1 i2 · e−i2·0.0158·D·t ] (11) 2.7 Specific Heat Capacity at constant vol- ume (Cv) Molar specific heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one Kelvin. In NAMD, the specific heat capacity at constant volume can be obtained from a single NVT production simulation using the equation [29,30], Cv = 〈 E2 〉 − ⟨E⟩2 KBT 2 (12) where ⟨E⟩ is the average of the total energy and〈 E2 〉 is the average of the square of the total en- ergy. 3 Computational details This research is based on the theoretical and com- putational techniques of molecular dynamics. For this, the structure of the wild-type and M114T mu- tant PMP2 proteins were obtained from RCSB.org. The PDB ID of the chosen wild-type protein is 2WUT and of the chosen mutant is 7NRW. Then, the simulation is performed using the NAMD (NAno scale Molecular Dynamics) and VMD (Vi- sual Molecular Dynamics) softwares. However, in molecular simulations using these softwares, there are some approximations like fixed force fields and cutoff distances which might not fully capture the long-range interactions. At first, steps for the energy minimization are performed, followed by system equilibration. Fi- nally, production simulation is run to obtain the final data. The RMSD is calculated from the equi- libration output to check for the system stability before starting the production run, whereas rest of the analysis is done from the output of production run. For this, six systems are designed: two pro- teins, each kept at temperatures of 305 K, 310 K, and 315 K. The system's pH is set to 7.4, with a 12 Å cutoff distance, 16 Å pairlist distance, and an initial pressure of 1 bar. This limited cutoff for pairlist distance could lead to the interactions at the boundaries not being accounted, which might lead to inaccuracies in energy calculations; however, with a 2 fs timestep, these inaccuracies are expected to be minimal.. Also, for the study of non-bonded interactions, some K+ and Cl- are added to set the system to a 0.15 M/Litre concentration; however, for the study of thermal diffusivity, no ions are placed. The proteins are solvated with TIP3 wa- ter using modified charmm force field (CHARMM 36m). Equilibration and production both are done in the NVT ensemble. The details of the setup are as follows: For the study of non-bonded interactions, the wild-type PMP2 (2WUT) with 2,154 atoms is placed in a cubical water box of side length 67 Å. The study is done at the three temperatures with minute difference in the total number of atoms: 28,027 atoms at 305 K, 27,972 atoms at 310 K, and 28,009 atoms at 315 K. However, in mutant protein (7NRW) with 2,151 atoms, the cubical box is of side length 65 Å. The number of atoms for mutant at 305 K is 25,711, at 310 K is 25,741, and at 315 K is 25,720. The parameters, as mentioned above, are the same at all temperatures. Furthermore, for the study of thermal diffusiv- ity, both the proteins are kept inside a water sphere of radius 30 Å, with wild-type protein containing 11,551 atoms and mutant containing 11,563 atoms, at temperature of 310 K. Temperature coupling fea- ture of NAMD is used to set the interior tempera- ture to 300 K and that of outer shell (of thickness 5 Å) to 200 K. At last, for the verification of Maxwell- Boltzmann law, the systems are equilibrated for 100 ps in NVT ensemble at 310 K by removing the con- straints — the atoms are set free to move and none of the bonds are kept rigid. The distribution is stud- ied from the last time frame of the simulation. In addition to this, for the study of temperature fluc- tuation, a 1 ns production simulation is performed in NVE ensemble by turning off the thermostat and barostat. This approach overlooks quantum effects, cru- cial in biological systems, making the results purely classical. Additionally, short simulation timescales limit insights into slower or large-scale dynamics. 4 Results and Discussions In this section, we have presented the results of the various analyses performed on the two proteins in both graphical as well as tabular form. The posi- tions of atoms at different instances were calculated using equation (1), the vdW and electrostatic in- teraction energies were calculated using equations (3) and (4), respectively. Equations (5), (11) and (12) were used to calculate RMSD, thermal diffu- sivity and specific heat capacity at constant vol- ume, respectively. For the verification of Maxwell- Boltzmann law of distribution of kinetic energy, Prabin Aryal and Jhulan Powrel/ BIBECHANA 22 (2025) 63-72 67 equation (8) was used, whereas to study tempera- ture fluctuation in NVE ensemble and to fit a curve, equation (6) was considered. The RMSD of both proteins and corresponding distribution at 305 K, 310 K and 315 K are shown in Figure (3), (4) and (5), respectively. For wild- type protein, RMSD values at 305 K, 310 K and 315 K were 0.27 Å, 0.27 Å and 0.28 Å, respectively. For mutant, RMSD values at all temperatures were approximately the same at 0.28 Å. The standard de- viation in the observed RMSD of both proteins at all temperatures was approximately the same with value of 0.01. The range of fluctuation of RMSD was between 0.05 Å and 0.07 Å, with 0.07 Å be- ing for both proteins at 315 K. Increasing trend of RMSD with increase in temperature was observed. Figure 3: RMSD graph of P2WT and M114T at 305 K (left), and corresponding distribution (right) Figure 4: RRMSD graph of P2WT and M114T at 310 K (left), and corresponding distribution (right). Figure 5: RMSD graph of P2WT and M114T at 315 K (left), and corresponding distribution (right). The Number of H-bonds formed in both proteins and corresponding distribution at 305 K, 310 K and 315 K are shown in Figure (6), (7) and (8), respec- tively. The average number of H-bonds formed was as follows: at 305 K, 81.46 with standard deviation of 4.78 for P2WT and 79.14 with standard deviation of 4.66 for M114T; at 310 K, 80.19 with standard deviation of 4.98 for P2WT and 79.29 with standard deviation of 5.03 for M114T; at 315 K, 79.91 with standard deviation of 4.83 for P2WT and 77.28 with standard deviation of 4.97 for M114T. The fluctua- tion in the number of H-bonds formed was between 29 to 35. Gradual reduction in the formation of H- bonds with increase in temperature was observed. Table 1 shows the average RMSD and number of H-bonds formed in both proteins at all three tem- peratures. Figure 6: Graph of number of H-bonds formation over time in both proteins at 305 K (left), and cor- responding distribution (right). Figure 7: Graph of number of H-bonds formation over time in both proteins at 310 K (left), and cor- responding distribution (right). Figure 8: Graph of number of H-bonds formation over time in both proteins at 315 K (left), and cor- responding distribution (right). Prabin Aryal and Jhulan Powrel/ BIBECHANA 22 (2025) 63-72 68 Table 1: For wild-type and mutant PMP2 protein at various temperatures. Protein Temperature (K) Avg. RMSD (Å) Avg. Num of H-bonds P2WT (2WUT) 305 0.269 81.458 310 0.267 80.193 315 0.275 79.913 M114T (7NRW) 305 0.282 79.136 310 0.279 79.288 315 0.280 77.277 Figure (9), (10) and (11) show the bar-plot of average occupancy of salt bridges (in Å) in P2WT and M114T at 305 K, 310 K, and 315 K, respec- tively. Salt bridges between few residue pairs were absent, shown by vacancy in the plot; taller plots in- dicate weaker salt-bridges. The most noticeable dif- ference is observed in the residue pair ASP18-LYS22 and ASP19-LYS22 at 315 K. Decreasing strength of salt-bridges with increase in temperature was ob- served. Figure 9: Average salt-bridge occupancy in both proteins at 305 K. Figure 10: Average salt-bridge occupancy in both proteins at 310 K. Figure 11: Average salt-bridge occupancy in both proteins at 315 K. The particles of both systems were found to fol- low the Maxwell-Boltzmann law of distribution of kinetic energy. The degree of agreement of the ob- served data with the theoretical distribution can be seen in Figure (12). In both systems, the parameter of the observed data was about 0.61 and of the fit- ted curve was about 0.63. Furthermore, the graph of temperature fluctuation over time in both pro- teins at 310 K is shown in Figure (13) with the cor- responding distribution shown in Figure (14). The observed average temperature of the system with P2WT was 308.98 K with standard deviation of 1.47, while that with M114T was 308.83 K with standard deviation of 1.53. As expected, the distri- bution of temperature in NVE ensemble was found to be Gaussian in nature. Prabin Aryal and Jhulan Powrel/ BIBECHANA 22 (2025) 63-72 69 Figure 12: Maxwell-Boltzmann energy distribution at 310 K for P2WT (left), and for M114T (right). Figure 13: Graph of Temperature vs Simulation time in both proteins at 310 K. Figure 14: Temperature distribution at 310 K in P2WT (left), and for M114T (right). Figure (15) shows the change in temperature during the course of simulation in both proteins. From the simulation, the thermal diffusivity of the P2WT was found to be 4.03× 10−7 m2s−1 while that for the M114T was 4.06 × 10−7 m2s−1, as show in Table 2. Prabin Aryal and Jhulan Powrel/ BIBECHANA 22 (2025) 63-72 70 Figure 15: Graph of Temperature vs simulation time for heat diffusion in both proteins. Table 2: For wild-type and mutant PMP2 protein at 310 K temperature. Protein Thermal Diffusivity (m2 s-1) P2WT (2WUT) 4.033× 10−8 M114T (7NRW) 4.063× 10−8 The graph of fluctuation of total energy over time in both proteins at temperature of 305 K, 310 K and 315 K are shown in Figure (16), (17) and (18), respectively. The observed specific heat capacity at constant volume for both proteins at various temperatures are shown in Table 3. At 305 K, P2WT was found to have specific heat ca- pacity of 155.02 kcal/mol·K, which decreased to 146.45 kcal/mol·K at 310 K and increased again to 173.89 kcal/mol·K at 315 K. For M114T, at 305 K, the specific heat capacity was found to be 138.05 kcal/mol·K, which increased to 166.72 kcal/mol·K at 310 K and decreased back to 139.68 kcal/mol·K. Table 3 also shows the observed vdW and elec- trostatic interaction energies along with their sum in both protein systems. These energies were found to decrease with temperature, with the P2WT sys- tem having higher energies than that of the mutant system at all temperatures. Figure 16: Graph of total energy fluctuation over time in both proteins at 305 K. Figure 17: Graph of total energy fluctuation over time in both proteins at 310 K. Figure 18: Graph of total energy fluctuation over time in both proteins at 315 K. Prabin Aryal and Jhulan Powrel/ BIBECHANA 22 (2025) 63-72 71 Table 3: For system with wild-type and mutant PMP2 protein at different temperatures (in kcal/mol for energies and kcal/molK for Cv). Protein Temperature (K) vdW Electrostatic Sum Cv (kcal/molK) P2WT (2WUT) 305 8264.38 -100956.64 -92692.26 155.02 310 8139.54 -100146.00 -92006.46 146.45 315 8048.23 -99679.56 -91631.33 173.89 M114T (7NRW) 305 7589.58 -94075.41 -86485.83 138.05 310 7501.03 -93641.22 -86140.19 166.72 315 7397.91 -93043.12 -85645.21 139.68 5 Conclusion and Concluding Remarks In this study, the RMSD of both proteins was found to be within the valid range (< 4 Å). The RMSD of wild-type protein was in the range of 0.26 Å to 0.27 Å while that of mutant was between 0.27 Å to 0.28 Å. With the increase in temperature from 305 K to 315 K, the decrease in the average num- ber of H-bonds formation—in wild-type, from 81.46 to 79.91, whereas in mutant, from 79.14 to 77.28— suggests reduction in stability of the protein; this is due to increased thermal agitation; such a drug specimen is to be chosen that can form strong non- bonded interactions with the protein, and opti- mized accordingly to increase the efficiency of the treatment. A notable difference in the formation of salt-bridges were observed, especially in the residue pairs ASP18-LYS22 and ASP19-LYS22 at higher temperatures, suggesting a clear difference in diffu- sion of solution. The mutant showed slightly better thermal diffusivity, but compared to water, both proteins were slow at conducting heat; this is vital in understanding how heat dissipation through pro- tein takes place during drug-protein binding. The magnitude of sum of vdW and electrostatic inter- action energies is higher in the system with wild- type protein suggesting a stronger non-bonded pro- file compared to that with mutant; it decreases with increase in temperature in both proteins which is due to increase in mean free path of the atoms. Fi- nally, the Cv of both systems were found to have a non-linear (concave nature) change, with system of wild-type protein being generally higher; drugs should be designed accordingly to prevent protein denaturation caused by heat generated during drug- protein binding. This unusual variation of Cv in both systems is not well understood. We found the necessity to study the variation of Cv of both proteins at smaller temperature incre- ments. 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