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Thermal-induced folding and unfolding of a transmembrane protein (CorA)
Accepted Manuscript Thermal-induced folding and unfolding of a transmembrane protein (CorA) Sunan Kitjaruwankul, Panisak Boonamnaj, Sunita Subedi Paudel, Warin Jetsadawisut, Pornthep Sompornpisut, R.B. Pandey
PII: DOI: Reference:
S0378-4371(18)30550-8 https://doi.org/10.1016/j.physa.2018.05.014 PHYSA 19554
To appear in:
Physica A
Received date : 18 September 2017 Revised date : 12 February 2018 Please cite this article as: S. Kitjaruwankul, P. Boonamnaj, S.S. Paudel, W. Jetsadawisut, P. Sompornpisut, R.B. Pandey, Thermal-induced folding and unfolding of a transmembrane protein (CorA), Physica A (2018), https://doi.org/10.1016/j.physa.2018.05.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Highlights (for review)
Highlights:
Protein CorA is critical in transport of Mg2+ across the ion channels. Inner segment of protein contracts on raising the temperature in native phase. Outer segment of protein is less organized in its native phase. Inner segment is globular and outer segment is random coil. Conformations of both segments in native phase differ from that in denatured phase.
*Manuscript Click here to view linked References
Thermal-induced folding and unfolding of a transmembrane protein (CorA) Sunan Kitjaruwankul1, Panisak Boonamnaj2, Sunita Subedi Paudel3, Warin Jetsadawisut2, Pornthep Sompornpisut2, R.B. Pandey3 1
Faculty of Science at Sriracha, Kasetsart University Sriracha Campus, Chonburi 20230, Thailand 2 Department of Chemistry, Chulalongkorn University, Bangkok 10330, Thailand 3 Department of Physics and Astronomy, University of Southern Mississippi, Hattiesburg, MS 39406, USA Abstract: Thermal response of the inner (iCorA) and outer (oCorA) segments of a transmembrane protein CorA is investigated by a large-scale coarse-grained Monte Carlo simulation in native phase. We find that the conformation of iCorA contracts on raising the temperature, in contrast to its thermal response in denatured phase. The conformational response of the oCorA in its native phase appears to be less organized but differs considerably from that in its denatured phase where an abrupt increase of its radius of gyration occurs in a narrow temperature range. The inner segment (iCorA) retains its globular conformation in native phase while oCorA resorts to random-coil configurations with some coagulations on raising the temperature. PACS numbers: 87.15.A-, 87.15.ak, 87.15.hp How a protein folds is very important in its versatile yet specific functions. Protein folding has been a subject of intense investigations for decades with a range of models [1-5]; list of citations is overwhelmingly too large to cite. Despite enormous insight gained over the time, folding and unfolding of many proteins in its native and denatured phase remains to be explored. Of a diverse range of proteins with prolific response properties (unique to universal), we focus on a transmembrane protein here. Ion channel transmembrane proteins play a critical role in selective transport of ions across the membrane. A transmembrane protein such as CorA for the magnesium channel spans across the membrane with well-defined functions of its inner (iCorA) and outer (oCorA) membrane segments [6-20]. Functional structure of CorA across the membrane is known to exist as a homo-pentamer [16]. Enormous efforts have been made to understand the selective transport of Mg2+ across the ion channels by examining the binding of Mg2+ and identifying the role of special metal binding motifs such as Gly-Met-Asn. Understanding the basic mechanism of ion transport, however, remains speculative. The transport of ions depend on the ion-permeation pathways which depends, at least in part, on the conformation of the protein. Because of the underlying matrix (a crowded cellular environment) with different internal (hydrophobic within the membrane) and external (hydrophilic) solvent and solute environments, structures of inner and outer components of the protein differ considerably. It is important to point out that extensive efforts have been recently made to understand the structural dynamics of CorA embedded in a realistic membrane model with solvent by all-atom MD simulations [16]; such investigations are very useful in probing the small scale structural responses. Despite a large-scale simulations (order of months of cpu), the dynamical changes appear too small to probe large-scale structural responses; some degree of coarse-graining [20] is almost impossible 1
to avoid in such large-scale investigations. In order to probe how the proteins and underlying matrix assemble due to interplay between cooperative and competing interactions, one has to probe some basic issues on a large-time scale, at least comparable to the relaxation time of its constitutive elements. Even with an efficient coarse-grained approach (as the one used here), simulations become compute-intense to generate quality data. We plan to incorporate the complexity of crowded membrane components systematically in our on-going efforts in a longterm and identify the effect of the underlying media on the structural response of CorA. It is important to understand the structure and dynamics of individual protein and its inner and outer segments first (figure 1) in absence of environmental complexity, for example, as a function of temperature, before incorporating the external components and parameters systematically. Generally one would expect that the conformation of a protein (e.g. CorA) would expand on heating as we have recently observed [20] which can be intuitively understood when the thermal energy dominates over the residue interactions. What will happen when the residue interactions dominate over the thermal noise as in the native state of the protein? Native structure of the protein plays a critical role in its specific functions, therefore, it is critical to examine the thermal response of the structure of the protein where the residue interactions are more relevant than the thermal noise as planned in this study. We find that the thermal response of CorA segments in native phase, not only differs dramatically from that of its denatured phase (see below) but also contracts on heating. This finding can provide unique insights into the fundamental understanding of the protein folding pathways in context to transport of Mg2+ across the ion channel.
Figure 1: Representation of inner (iCorA, left) and outer (oCorA, right) segments of CorA.
2
We use a coarse-grained model to describe the protein as a chain of residues on a lattice with ample degrees of freedom: the outer membrane segment (oCorA) is a chain of 290 nodes (residues) while the inner transmembrane segment (iCorA) consists of 61 residues. Consecutive nodes along the backbone of the protein chain are connected by a flexible peptide bond with its length varying between 2 and (10) in unit of lattice constant (a); a node (residue) occupies [21] a cube of size (2a)3. There are ample degrees of freedom for each node to move and bond-length to fluctuate with the strictly implemented excluded volume constraint. Coarse-graining of the simulation box and the residues representation make it one of the efficient computational method for modeling such systems as protein while retaining the potential for fine-graining [22] to further enhance the degrees of freedom. Each residue interacts with the neighboring residues within a range (rc) of interaction with a generalized Lennard-Jones potential, 6 12 , r ij U ij ij ij r rij ij
< rc
(1)
where rij is the distance between the residues at site i and j; rc=8 and = 1 in units of lattice constant. The potential strength, ij, is unique for each interaction pair with appropriate positive (repulsive) and negative (attractive) values selected from the knowledge-based contact interactions [23, 24]. We use a residue-residue contact matrix by Betancourt-Thirumalai (BT) [23], an improved version of classic Miyazawa-Jernigan (MJ) interaction [24]. It should be emphasized that the interaction potential (1) is phenomenological with 20 20 residue-residue contact elements [23] ij (1.34 (Cys-Cys), 0.68 (Cys-Gly), 0.83 (Lys-Cys), etc.) with 210 independent pair interactions. These knowledge-based residue-residue interactions [23, 24] are derived from the distribution of the amino acids in a growing ensemble of frozen protein structures in protein data bank (PDB); the underlying solvent environment is therefore taken into account implicitly. Various assumptions and approximations are further made in deriving these contact potentials which makes it somewhat difficult to calibrate the scales of the physical quantities in absolute units. The relative strength of residue-residue interactions is critical for protein to adopt its specific conformations. The residue-residue interaction energy competes with the temperature as the residues perform its stochastic moves via the Metropolis algorithm which is implemented as follows. We select a residue (node) at a site i randomly and attempt to move it to a randomly selected nearest neighbor site j. If the limits on the bond lengths constraints (excluded volume), then the residue is moved with the Boltzmann probability exp(-Eij/T), where Eij is the change in energy between its new (Ej) and old (Ei) configuration Eij = Ej – Ei and T is the temperature in reduced unit of the Boltzmann constant. Attempts to move each residue once defines a unit Monte Carlo step (MCS). We monitor a number of local and global physical quantities such as the energy of each residue, its mobility, mean square displacement of the center of mass of the protein, radius of gyration and its structure factor. All quantities are measured in arbitrary unit including the temperature T which is in reduced units of the Boltzmann constant. At each temperature, simulations are performed for a sufficiently long time (typically ten million time steps) with many independent samples (typically 150-500 samples) to estimate the average values of the physical quantities. Although most of our data are produced on a 1503 for iCorA and 3503 for oCorA, we have used different sample sizes to make sure that our qualitative findings are independent of the finite size.
3
Figure 2: Snapshots of iCorA at the end of 107 MCS time on a simulation box of size 1503 at T=0.010, 0.13, 0.018 and 0.020. Instead of considering the whole protein chain (i.e. CorA with 351 residues), we will focus primarily on its outer (oCorA with 291 residues) and inner (iCorA with 60 residues) segments primarily to differentiate their thermal response. Few snapshots of iCorA is presented in figure 2 at representative temperatures. Spreads of each protein structure appear to be comparable in size, though there is a tendency for residue consolidation with increasing temperature.
Figure 3: Radius of gyration (Rg) of iCorA in low temperature (native phase, lower X-axis (T), left Y-axis (Rg)) and high temperature (denature phase, upper X-axis, right Y-axis (Rg)) [20]. Simulations are performed on a box of size 1503 with 500 independent samples at each temperature. Based on a crude calibration of Rg from a CGMC data with that from an all-atom molecular dynamics (MD) simulation [25] for a different membrane protein, the range of reduced temperature (T=0.010 0.020) seem to span over the room temperature (order of magnitude) in native phase and continue to increase in denatured phase. Dependence of the protein’s size on the temperature can be quantified by analyzing the variation of its radius of gyration (Rg) as shown in figure 3. We see that the radius of gyration decreases on increasing the temperature, a negative response, in low temperature regime (T = 0.010 0.020) which is opposite to common perception that the thermal agitation generally enhances the spread. For comparison, the variation of the radius of gyration (Rg) in higher temperature regime (T = 0.018 0.042) is also included. It is clear that Rg increases continuously with the temperature in high T regime [20] as one would expect. The decay of radius of gyration 4
in low temperature regime shows that the size of protein contracts despite the reduction in the configurational entropy on increasing the temperature. Residue-residue interactions play a more dominant role over the thermal energy in low temperature regime; thermal agitations however help in achieving the more compact stable structures in native phase. It is worth pointing out that the unusual negative thermal response in native phase is also observed in thermal response of another membrane protein [25]. We speculate that such unusual structural response may be due to specificity (sequence and size) of the protein. It may however be difficult to generalize it to membrane proteins based on computer simulation data for few proteins. The stability of a conformation depends on the competing and cooperative effects of the residue-residue interaction and the thermal agitation. We plan to continue exploring the structural response of different proteins particularly in its native phase towards search for some kind of quasi-universality. Snapshots of oCorA at representative temperatures are presented in figure 4. It is a bit difficult to identify the change in spread of the protein due to relatively large size (291 residues) of oCorA. Figure 5 shows the variation of the radius of gyration of oCorA with the temperature. Trend in the thermal response of Rg in low temperature regime (native phase) is a bit difficult to assess due to large error bars, although there is a slight decreasing pattern with the temperature. The positive thermal response in the high temperature (T = 0.028 0.042) regime (denatured phase) included for comparison, is rather clear in a narrow temperature region (T = 0.030 0.032) reported before. It is important to note, however, that the thermal response of oCorA in native phase is different (muted) from that in the denature phase (abrupt).
Figure 4: Snapshots of oCorA at the end of 107 MCS time on a simulation box of size 3503 at T=0.010, 0.13, 0.018 and 0.020.
5
Figure 5: Radius of gyration (Rg) of oCorA in low temperature (native phase, lower X-axis (T), left Y-axis (Rg)) and high temperature (denature phase, upper X-axis, right Y-axis (Rg)) [20]. Simulations are performed on a box of size 3503 with 150 independent samples at each temperature. These findings on the structural variability are critical in understanding the conformational response of the inner and the outer segments of the protein in its native phase in context to selective transport of ions across the membrane. Note that there are dramatic differences in thermal response in native phase from that in denatured phase. In contrast to increase in size of the inner (iCorA) and outer (oCorA) segments with the temperature in denatured phase [20], these segments contract on raising the temperature in their native phase. The inner segments consolidate more than the outer segment in the native phase. Conformational responses in native phase provide the fundamental basis in modulating the pathways for the flow of ions in and out of the membrane. As in our previous studies [20, 22], the structure factor S(q) of both iCorA and oCorA is also analyzed in detail to assess the global distribution of residues over the length scales comparable to radius of gyration. Variation of the structure factor S(q) with wave factor q = 2/ in native phase of both segments at two temperatures (T = 0.013, 0.018) are presented in figure 6; the wavelength is the linear length scale over which the mass (residues) of the protein is distributed. From scaling of the structure factor with the wave length (), i.e., S(q) D, one can estimate the exponent D which is the effective dimension of the protein. Inner segment of the protein shows globular structure D 3 at both temperatures (figure 6) while the outer transmembrane segment appears to be random-coil (D 2) at T = 0.013 and becomes consolidated with a higher density (D 2.5) at T = 0.018.
6
Figure 6: Structure factor S(q) versus the wavelength for iCorA and oCorA at temperature T=0.013 and T=0.018. Slopes are the estimated for the fitted data points appropriate for the size (Rg) of the protein. Simulations are performed on 1503 and 3503 lattices for 107 MCS time with 150-500 independent samples at each temperature. The range of X and Y coordinates are pointed out on the axes labels for the clarity. In conclusion, we find that the conformational response of the inner and outer segments show a negative thermal response., i.e., the size (measured by Rg) of the protein contracts on raising the temperature in contrast to that in denatured phase where it expands in specific temperature range. The thermal response of iCorA however differs from that of oCorA in the native phase. The self-organizing inner segments consolidate its mass (induced by the thermal agitations) more than the outer segment in the native phase; the thermal response of the oCorA appears to be less organized. The conformational response of these segments in native phase is critical in modulating the gating mechanism for the transport of magnesium ions across the cellular membrane. Our findings provide a fundamental basis to understanding of the underlying pathways for the transport through ion channels. ACKNOWLEDGMENTS: This research has been supported by the Ratchadaphiseksomphot Endowment Fund, Chulalongkorn University to PS, the 100th Anniversary Chulalongkorn University Fund for Doctoral Scholarship to PB. Support from the Chulalongkorn University for a visiting professorship is gratefully acknowledged by RBP along with the warm hospitality by the Department of Chemistry. This work is devoted to the remembrance of His Majesty King Bhumibol Adulyadej (1927–2016) for his life-time dedication to Thailand. References: 1. J.N. Onuchic, Z. Luthey-Schulten, P.G. Wolynes, Annu. Rev. Phys. Chem. 48 (1997) 545-600. 2. K.A. Dill, J.L. MacCallum, Science 338 (2012) 1042-1046. 7
3. 4. 5. 6.
P.G. Wolynes, W.A. Eaton, A.R. Fersht, 109 (2012) 17770-17771. H. Abe, H. Wako, Physica A 388 (2009) 3442-3454. D. Mallamace et al. Physica A 412 (2014) 39-44.1 S. P. Hmiel, M. D. Snavely, J. B. Florer, M. E. Maguire, and C. G. Miller, J. Bacteriol. 171 (1989) 4742-4751. 7. M. E. Maguire, J Bioenerg Biomembr 24 (1992) 319-328. 8. D. G. Kehres, C. H. Lawyer, and M. E. Maguire, Microb Comp Genomics 3 (1998) 151169. 9. S. Eshaghi, D. Niegowski, A. Kohl, D. Martinez Molina, S. A. Lesley, and P. Nordlund, Science 313 (2006) 354-357. 10. V. V. Lunin et al. Nature 440 (2006) 833-837. 11. J. Payandeh, C. Li, M. Ramjeesingh, E. Poduch, C. E. Bear, and E. F. Pai, J Biol Chem 283 (2008) 11721-11733. 12. J. Payandeh, and E. F. Pai, EMBO J 25 (2006) 3762-3773. 13. O. Dalmas et al. Structure 18 (2010) 868-878. 14. O. Dalmas, P. Sompornpisut, F. Bezanilla, E. Perozo, Nat Commun 5 (2014) 3590. 15. C. Neale, N. Chakrabarti, P. Pomorski, E. F. Pai, R. Pomes, PLoS Comput Biol 11 (2015) e1004303. 16. S. Kitjaruwankul, P. Wapeesittipan, P. Boonamnaj, P. Sompornpisut, J Phys Chem B 120 (2016) 406-417. 17. D. Matthies et al. Cell 164 (2016) 747-756. 18. N. Chakrabarti, C. Neale, J. Payandeh, E. F. Pai, R. Pomes, Biophys J 98 (2010) 784-792. 19. N. Nordin et al. Biochem J 451 (2013) 365-374. 20. S. Kitjaruwankul, Channarong Khrutto, Pornthep Sompornpisut, B.L. Farmer, R.B. Pandey, J Chem Phys 145 (2016) 135101. 21. Monte Carlo and Molecular Dynamics Simulations in Polymer Science’ Ed. K. Binder, (Oxford University Press, 1995). 22. R. B. Pandey, B. L. Farmer, J Chem Phys 141 (2014) 175103. 23. M. R. Betancourt, and D. Thirumalai, Protein Sci 8 (1999) 361-369. 24. S. Miyazawa, and R. L. Jernigan, Macromolecules 18 (1985) 534-552. 25. Sunita Subedi Paudel, ‘Conformation of Transmembrane Segments of a Protein by a Coarse Grain Model’ MS Thesis (2017), University of Southern Mississippi (https://aquila.usm.edu/masters_theses/312/)
8
PII: DOI: Reference:
S0378-4371(18)30550-8 https://doi.org/10.1016/j.physa.2018.05.014 PHYSA 19554
To appear in:
Physica A
Received date : 18 September 2017 Revised date : 12 February 2018 Please cite this article as: S. Kitjaruwankul, P. Boonamnaj, S.S. Paudel, W. Jetsadawisut, P. Sompornpisut, R.B. Pandey, Thermal-induced folding and unfolding of a transmembrane protein (CorA), Physica A (2018), https://doi.org/10.1016/j.physa.2018.05.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Highlights (for review)
Highlights:
Protein CorA is critical in transport of Mg2+ across the ion channels. Inner segment of protein contracts on raising the temperature in native phase. Outer segment of protein is less organized in its native phase. Inner segment is globular and outer segment is random coil. Conformations of both segments in native phase differ from that in denatured phase.
*Manuscript Click here to view linked References
Thermal-induced folding and unfolding of a transmembrane protein (CorA) Sunan Kitjaruwankul1, Panisak Boonamnaj2, Sunita Subedi Paudel3, Warin Jetsadawisut2, Pornthep Sompornpisut2, R.B. Pandey3 1
Faculty of Science at Sriracha, Kasetsart University Sriracha Campus, Chonburi 20230, Thailand 2 Department of Chemistry, Chulalongkorn University, Bangkok 10330, Thailand 3 Department of Physics and Astronomy, University of Southern Mississippi, Hattiesburg, MS 39406, USA Abstract: Thermal response of the inner (iCorA) and outer (oCorA) segments of a transmembrane protein CorA is investigated by a large-scale coarse-grained Monte Carlo simulation in native phase. We find that the conformation of iCorA contracts on raising the temperature, in contrast to its thermal response in denatured phase. The conformational response of the oCorA in its native phase appears to be less organized but differs considerably from that in its denatured phase where an abrupt increase of its radius of gyration occurs in a narrow temperature range. The inner segment (iCorA) retains its globular conformation in native phase while oCorA resorts to random-coil configurations with some coagulations on raising the temperature. PACS numbers: 87.15.A-, 87.15.ak, 87.15.hp How a protein folds is very important in its versatile yet specific functions. Protein folding has been a subject of intense investigations for decades with a range of models [1-5]; list of citations is overwhelmingly too large to cite. Despite enormous insight gained over the time, folding and unfolding of many proteins in its native and denatured phase remains to be explored. Of a diverse range of proteins with prolific response properties (unique to universal), we focus on a transmembrane protein here. Ion channel transmembrane proteins play a critical role in selective transport of ions across the membrane. A transmembrane protein such as CorA for the magnesium channel spans across the membrane with well-defined functions of its inner (iCorA) and outer (oCorA) membrane segments [6-20]. Functional structure of CorA across the membrane is known to exist as a homo-pentamer [16]. Enormous efforts have been made to understand the selective transport of Mg2+ across the ion channels by examining the binding of Mg2+ and identifying the role of special metal binding motifs such as Gly-Met-Asn. Understanding the basic mechanism of ion transport, however, remains speculative. The transport of ions depend on the ion-permeation pathways which depends, at least in part, on the conformation of the protein. Because of the underlying matrix (a crowded cellular environment) with different internal (hydrophobic within the membrane) and external (hydrophilic) solvent and solute environments, structures of inner and outer components of the protein differ considerably. It is important to point out that extensive efforts have been recently made to understand the structural dynamics of CorA embedded in a realistic membrane model with solvent by all-atom MD simulations [16]; such investigations are very useful in probing the small scale structural responses. Despite a large-scale simulations (order of months of cpu), the dynamical changes appear too small to probe large-scale structural responses; some degree of coarse-graining [20] is almost impossible 1
to avoid in such large-scale investigations. In order to probe how the proteins and underlying matrix assemble due to interplay between cooperative and competing interactions, one has to probe some basic issues on a large-time scale, at least comparable to the relaxation time of its constitutive elements. Even with an efficient coarse-grained approach (as the one used here), simulations become compute-intense to generate quality data. We plan to incorporate the complexity of crowded membrane components systematically in our on-going efforts in a longterm and identify the effect of the underlying media on the structural response of CorA. It is important to understand the structure and dynamics of individual protein and its inner and outer segments first (figure 1) in absence of environmental complexity, for example, as a function of temperature, before incorporating the external components and parameters systematically. Generally one would expect that the conformation of a protein (e.g. CorA) would expand on heating as we have recently observed [20] which can be intuitively understood when the thermal energy dominates over the residue interactions. What will happen when the residue interactions dominate over the thermal noise as in the native state of the protein? Native structure of the protein plays a critical role in its specific functions, therefore, it is critical to examine the thermal response of the structure of the protein where the residue interactions are more relevant than the thermal noise as planned in this study. We find that the thermal response of CorA segments in native phase, not only differs dramatically from that of its denatured phase (see below) but also contracts on heating. This finding can provide unique insights into the fundamental understanding of the protein folding pathways in context to transport of Mg2+ across the ion channel.
Figure 1: Representation of inner (iCorA, left) and outer (oCorA, right) segments of CorA.
2
We use a coarse-grained model to describe the protein as a chain of residues on a lattice with ample degrees of freedom: the outer membrane segment (oCorA) is a chain of 290 nodes (residues) while the inner transmembrane segment (iCorA) consists of 61 residues. Consecutive nodes along the backbone of the protein chain are connected by a flexible peptide bond with its length varying between 2 and (10) in unit of lattice constant (a); a node (residue) occupies [21] a cube of size (2a)3. There are ample degrees of freedom for each node to move and bond-length to fluctuate with the strictly implemented excluded volume constraint. Coarse-graining of the simulation box and the residues representation make it one of the efficient computational method for modeling such systems as protein while retaining the potential for fine-graining [22] to further enhance the degrees of freedom. Each residue interacts with the neighboring residues within a range (rc) of interaction with a generalized Lennard-Jones potential, 6 12 , r ij U ij ij ij r rij ij
< rc
(1)
where rij is the distance between the residues at site i and j; rc=8 and = 1 in units of lattice constant. The potential strength, ij, is unique for each interaction pair with appropriate positive (repulsive) and negative (attractive) values selected from the knowledge-based contact interactions [23, 24]. We use a residue-residue contact matrix by Betancourt-Thirumalai (BT) [23], an improved version of classic Miyazawa-Jernigan (MJ) interaction [24]. It should be emphasized that the interaction potential (1) is phenomenological with 20 20 residue-residue contact elements [23] ij (1.34 (Cys-Cys), 0.68 (Cys-Gly), 0.83 (Lys-Cys), etc.) with 210 independent pair interactions. These knowledge-based residue-residue interactions [23, 24] are derived from the distribution of the amino acids in a growing ensemble of frozen protein structures in protein data bank (PDB); the underlying solvent environment is therefore taken into account implicitly. Various assumptions and approximations are further made in deriving these contact potentials which makes it somewhat difficult to calibrate the scales of the physical quantities in absolute units. The relative strength of residue-residue interactions is critical for protein to adopt its specific conformations. The residue-residue interaction energy competes with the temperature as the residues perform its stochastic moves via the Metropolis algorithm which is implemented as follows. We select a residue (node) at a site i randomly and attempt to move it to a randomly selected nearest neighbor site j. If the limits on the bond lengths constraints (excluded volume), then the residue is moved with the Boltzmann probability exp(-Eij/T), where Eij is the change in energy between its new (Ej) and old (Ei) configuration Eij = Ej – Ei and T is the temperature in reduced unit of the Boltzmann constant. Attempts to move each residue once defines a unit Monte Carlo step (MCS). We monitor a number of local and global physical quantities such as the energy of each residue, its mobility, mean square displacement of the center of mass of the protein, radius of gyration and its structure factor. All quantities are measured in arbitrary unit including the temperature T which is in reduced units of the Boltzmann constant. At each temperature, simulations are performed for a sufficiently long time (typically ten million time steps) with many independent samples (typically 150-500 samples) to estimate the average values of the physical quantities. Although most of our data are produced on a 1503 for iCorA and 3503 for oCorA, we have used different sample sizes to make sure that our qualitative findings are independent of the finite size.
3
Figure 2: Snapshots of iCorA at the end of 107 MCS time on a simulation box of size 1503 at T=0.010, 0.13, 0.018 and 0.020. Instead of considering the whole protein chain (i.e. CorA with 351 residues), we will focus primarily on its outer (oCorA with 291 residues) and inner (iCorA with 60 residues) segments primarily to differentiate their thermal response. Few snapshots of iCorA is presented in figure 2 at representative temperatures. Spreads of each protein structure appear to be comparable in size, though there is a tendency for residue consolidation with increasing temperature.
Figure 3: Radius of gyration (Rg) of iCorA in low temperature (native phase, lower X-axis (T), left Y-axis (Rg)) and high temperature (denature phase, upper X-axis, right Y-axis (Rg)) [20]. Simulations are performed on a box of size 1503 with 500 independent samples at each temperature. Based on a crude calibration of Rg from a CGMC data with that from an all-atom molecular dynamics (MD) simulation [25] for a different membrane protein, the range of reduced temperature (T=0.010 0.020) seem to span over the room temperature (order of magnitude) in native phase and continue to increase in denatured phase. Dependence of the protein’s size on the temperature can be quantified by analyzing the variation of its radius of gyration (Rg) as shown in figure 3. We see that the radius of gyration decreases on increasing the temperature, a negative response, in low temperature regime (T = 0.010 0.020) which is opposite to common perception that the thermal agitation generally enhances the spread. For comparison, the variation of the radius of gyration (Rg) in higher temperature regime (T = 0.018 0.042) is also included. It is clear that Rg increases continuously with the temperature in high T regime [20] as one would expect. The decay of radius of gyration 4
in low temperature regime shows that the size of protein contracts despite the reduction in the configurational entropy on increasing the temperature. Residue-residue interactions play a more dominant role over the thermal energy in low temperature regime; thermal agitations however help in achieving the more compact stable structures in native phase. It is worth pointing out that the unusual negative thermal response in native phase is also observed in thermal response of another membrane protein [25]. We speculate that such unusual structural response may be due to specificity (sequence and size) of the protein. It may however be difficult to generalize it to membrane proteins based on computer simulation data for few proteins. The stability of a conformation depends on the competing and cooperative effects of the residue-residue interaction and the thermal agitation. We plan to continue exploring the structural response of different proteins particularly in its native phase towards search for some kind of quasi-universality. Snapshots of oCorA at representative temperatures are presented in figure 4. It is a bit difficult to identify the change in spread of the protein due to relatively large size (291 residues) of oCorA. Figure 5 shows the variation of the radius of gyration of oCorA with the temperature. Trend in the thermal response of Rg in low temperature regime (native phase) is a bit difficult to assess due to large error bars, although there is a slight decreasing pattern with the temperature. The positive thermal response in the high temperature (T = 0.028 0.042) regime (denatured phase) included for comparison, is rather clear in a narrow temperature region (T = 0.030 0.032) reported before. It is important to note, however, that the thermal response of oCorA in native phase is different (muted) from that in the denature phase (abrupt).
Figure 4: Snapshots of oCorA at the end of 107 MCS time on a simulation box of size 3503 at T=0.010, 0.13, 0.018 and 0.020.
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Figure 5: Radius of gyration (Rg) of oCorA in low temperature (native phase, lower X-axis (T), left Y-axis (Rg)) and high temperature (denature phase, upper X-axis, right Y-axis (Rg)) [20]. Simulations are performed on a box of size 3503 with 150 independent samples at each temperature. These findings on the structural variability are critical in understanding the conformational response of the inner and the outer segments of the protein in its native phase in context to selective transport of ions across the membrane. Note that there are dramatic differences in thermal response in native phase from that in denatured phase. In contrast to increase in size of the inner (iCorA) and outer (oCorA) segments with the temperature in denatured phase [20], these segments contract on raising the temperature in their native phase. The inner segments consolidate more than the outer segment in the native phase. Conformational responses in native phase provide the fundamental basis in modulating the pathways for the flow of ions in and out of the membrane. As in our previous studies [20, 22], the structure factor S(q) of both iCorA and oCorA is also analyzed in detail to assess the global distribution of residues over the length scales comparable to radius of gyration. Variation of the structure factor S(q) with wave factor q = 2/ in native phase of both segments at two temperatures (T = 0.013, 0.018) are presented in figure 6; the wavelength is the linear length scale over which the mass (residues) of the protein is distributed. From scaling of the structure factor with the wave length (), i.e., S(q) D, one can estimate the exponent D which is the effective dimension of the protein. Inner segment of the protein shows globular structure D 3 at both temperatures (figure 6) while the outer transmembrane segment appears to be random-coil (D 2) at T = 0.013 and becomes consolidated with a higher density (D 2.5) at T = 0.018.
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Figure 6: Structure factor S(q) versus the wavelength for iCorA and oCorA at temperature T=0.013 and T=0.018. Slopes are the estimated for the fitted data points appropriate for the size (Rg) of the protein. Simulations are performed on 1503 and 3503 lattices for 107 MCS time with 150-500 independent samples at each temperature. The range of X and Y coordinates are pointed out on the axes labels for the clarity. In conclusion, we find that the conformational response of the inner and outer segments show a negative thermal response., i.e., the size (measured by Rg) of the protein contracts on raising the temperature in contrast to that in denatured phase where it expands in specific temperature range. The thermal response of iCorA however differs from that of oCorA in the native phase. The self-organizing inner segments consolidate its mass (induced by the thermal agitations) more than the outer segment in the native phase; the thermal response of the oCorA appears to be less organized. The conformational response of these segments in native phase is critical in modulating the gating mechanism for the transport of magnesium ions across the cellular membrane. Our findings provide a fundamental basis to understanding of the underlying pathways for the transport through ion channels. ACKNOWLEDGMENTS: This research has been supported by the Ratchadaphiseksomphot Endowment Fund, Chulalongkorn University to PS, the 100th Anniversary Chulalongkorn University Fund for Doctoral Scholarship to PB. Support from the Chulalongkorn University for a visiting professorship is gratefully acknowledged by RBP along with the warm hospitality by the Department of Chemistry. This work is devoted to the remembrance of His Majesty King Bhumibol Adulyadej (1927–2016) for his life-time dedication to Thailand. References: 1. J.N. Onuchic, Z. Luthey-Schulten, P.G. Wolynes, Annu. Rev. Phys. Chem. 48 (1997) 545-600. 2. K.A. Dill, J.L. MacCallum, Science 338 (2012) 1042-1046. 7
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