Protein Dynamics: Relaxation Rates, Rotation Correlations, and Molecular Motion of Phenylalanine₂, Alanine₅, Leucine₇, Alanine₈,and Alanine₁₀

Abstract:

Protein dynamics, which include relaxation rates, rotation correlations, and molecular motion, was studied for five residues, phenylalanine₂,alanine₅,leucine₇,alanine_8, and alanine₁₀ (F_2,A_5,L_7,A8, & A10), of the polypeptide, GF₂SKA₅EL₇A₈KA₁₀RAAKRGGY using NMR testing. This study found that relaxation rates of these carbon residues vary depending on sequence position. The external carbons, who may have more freedom of movement than the internal carbons, decreased in relaxation rate as temperature decreased while the internal carbons failed to follow the expected pattern. This may be due to the interactions between the internal carbons as the a-helix is being formed at lower temperatures. The internal carbons may play a role in the actual formation of the a-helix, causing them to relax slower as they find their positions in the helix. The values of t_o increased as temperature decreased possibly due to varying internal rotation correlations (t_i) of the five residues. The general trend of t_i showed that the t_i increased, then finally decreased as temperature decreased at 278K, possibly commencing the formation of the a-helix.

Introduction:

This study of protein dynamics focused on relaxation rates, rotation correlations, and molecular motion of specific residues in GF₂SKA₅EL₇A₈KA₁₀RAAKRGGY [appendix I]. The polypeptide GF₂SKA₅EL₇A₈KA₁₀RAAKRGGY forms an a-helical structure at 278K (5°C), or at low temperatures. The residues F_2,A_8, and A_5,L₇ were analyzed using NMR to determine the relaxation rates of different portions of the polypeptide. These series of residues were chosen because of their distance from each other and their structural position in the polypeptide. Residue F₂ is toward the end of the polypeptide, outside of the a-helix and shows a large section of the peptide when analyzed with residue A₈. The portions of the polypeptide from A₅ to L₇ shows a smaller section of the polypeptide that is in the a-helix. Rotation correlations were also studied, involving the residues F_2, A_5, L_7, and A_10. The residues in the polypeptide were synthesized with carbon-13, rather than carbon-12, to enable NMR testing. This study of relaxation rates, rotation correlations, and molecular motion may help determine if the peptide is able to model dynamics in naturally occurring proteins.

Hypothesis:

As temperature increases, the expectation is that t_o will increase, t_i will increase, and s² will decrease. Higher temperatures cause more motion, thus overall rotation (t_o) and internal rotation (t_i ) increase. The order parameter of motion, s² , decreases with increased temperature because the molecules of the peptide are becoming less ordered. Also, as temperature decreases, the relaxation rate should increase, due to the energy states of the molecules.

Background:

The folding of peptides depends on three major factors: 1) the temperature of the peptide, 2) the rotational correlation of the peptide, which is how the peptide rotates as well as its basic internal and overall motion, and 3) the size of the peptide.
Peptides can fold into three different structures. As seen in appendix II, a peptide can establish a spiral-like a-helical structure, a pleated sheet b-configuration, or a sketchy random structure.¹

There is a direct relationship between a peptide’s folding structure and temperature. Small peptides form a-helical structures at low temperatures while large peptides show a-helical structures at higher temperatures. Overall, the a-helical structure is the most organized of the three different structures.²

The relaxation rate (1/s), the rate at which a peptide moves from its excited state back to its ground (resting) state, is the most important factor in studying protein dynamics. Relaxation rate shows an indirect relationship with temperature. High temperatures result in low (slow) relaxation rates, which in turn affect the rotation of the peptide. This occurs because as temperature increases, the molecules move faster and rapidly, so the molecules take longer to return to their original ground state.³ At higher temperatures, the carbons of the peptide become very excited and, thus take a longer time to relax and return to their original ground state.

Rotation, how the peptide rotates, is comprised of three parameters that directly or indirectly affect the relaxation rates. First is correlation time of the overall rotation of the molecules in the peptides, defined as t_o. The second parameter, which focuses on the internal rotation of the peptide, is t_i. This parameter is called the internal correlation and is a result of the individual internal rotation of the carbons in the residue. The last of the three parameters, s², is the order parameter of motion of the molecule, which shows the degree of isotropic motion. When s² is 1 (isotropic), there is absolutely no internal rotation. When s² is 0 (unisotropic), there is totally random motion. The most common state of peptide motion for s² is about 0.7, resulting in a “flip-flop” motion of the peptide. These three parameters (t_o, t_i, and s²) are measured as functions of temperature [see appendix II]. When temperature increases, the expectation is that t_o will increase, t_i will increase, and s² will decrease, as seen in Figure A. Higher temperatures cause more motion, thus overall rotation (t_o) and internal rotation (t_i ) increase. The order parameter of motion, s² , decreases with increased temperature because the molecules of the peptide are becoming less ordered.

Protein dynamics, such as relaxation rates and rotation, can be studied using nuclear magnetic resonance (NMR) testing. The residues, F_2,A_5,L_7, and A₈, were synthetically constructed using amino acids enriched with carbon-13. Carbon-13 plays a large role in NMR. The carbon-13 isotopes in the synthesized residues of F_2,A_5,L_7, and A₈ have what are called spin properties. One property involves the magnetic behavior of the carbon-13 nuclei, which is due to the varying peptide orientations. NMR, acting as an external magnetic field, flips the nuclei of the carbon-13 from one energy state to another.⁴ Carbon-12 is found in naturally occurring proteins. It, however, does not have the spin properties of carbon-13. This is the reason why F_2,A_5,L_7, and A₈ were synthesized using carbon-13 rather than carbon-12. The NMR can only identify the nuclei with magnetic properties (carbon-13). The NMR, activated by carbon-13, uses variables such as temperature and frequencies, to further test aspects of protein dynamics.⁵ By measuring the nuclei’s energy movements, relaxation rates can be calculated.

Materials and Methods:

Part I: Preparing the GF₂SKA₅EL₇A₈KA₁₀RAAKRGGY Peptide Solution

10 mg of carbon-13 enriched GF₂SKA₅EL₇A₈KA₁₀RAAKRGGY were weighed. The measured amount was placed into a storage tube. Next, 600 mL of deuterium oxide (D₂O) were added to the peptide powder in the tube. The prepared mixture was placed in a centrifuge and mixed for about 20 seconds, or until completely dissolved. The mixture was titrated with Blue Buffer Solution to adjust the pH 6 (+ .3). After transferring the mixture into a clean NMR tube, it was refrigerated and ready for NMR testing.

Part II: Nuclear Magnetic Resonance Testing

The prepared, refrigerated peptide was taken to a NMR testing station. The samples were tested at five different temperatures (278K, 283K, 288K, 293K, and 298K). Then, the peptide was tested using two different frequencies: 500 mH and 600 mH.

Part III: Data and Graphical Analysis

As seen in Table I, the sequence in which the residues were analyzed by NMR testing was determined by ordering the carbons as they appear on the parts per million scale. For example, for leucine₇ and alanine₅, the zeros of the individual scales were aligned and the carbons were then matched up from left to the right. The sequence in which leucine₇ and alanine₅ were measured by NMR is: L₇ a, A₅ a, L₇ b, L₇ g, L₇ d, L₇ d, and A₅ b.
After the NMR testing was completed, the data was processed and transferred to data analysis sheets. The height of each peptide peak in the NMR spectra was measured and plotted versus temperature to find the slope (relaxation rate). The relaxation rates were then graphed versus inverse temperature (1000/T).

Results

Relaxation Rates (Figures 1-4):

As seen in Figure 1, F₂ e, and A₈ b, being the 1st and 6th carbons in the sequence, followed the expected pattern of relaxation rates, such that their relaxation rates both increased as temperature decreased. F₂ z, the second carbon in the sequence, follows this same pattern. The remaining three carbons show an initial increase and then final decrease in relaxation rate over decreasing temperature.
As seen in Figure 2, the relaxation rates of carbons F₂ a and A₈ a, which are the two middle carbons of the sequence, decreased, increased, then finally decreased as temperature decreased. The relaxation rate of carbons F₂ e and F₂ b, the 1st and 5th carbons, increased then decreased as temperature decreased. The 2nd and 6th carbons display opposite results. The relaxation rate of carbon F₂ g (2) increased, decreased, increased, and decreased as while the relaxation rate of carbon A₈ b (6) decreased, increased, decreased, and finally increased, as temperature decreased.
As seen in Figure 3, the relaxation rates of carbons L₇ d (5), L₇ d (6), and A₅ b (7) all increased respectively as temperature decreased. The relaxation rates of carbons L₇ a, L₇ b, and L₇ g, the 1st, 3rd, and 4th carbons in the sequence, increased and then decreased as temperature decreased while the relaxation rate of carbon A₅ a increased, decreased, and increased once again.

As seen in Figure 4, the relaxation rates resulted in five different patterns. The relaxation rates of the 1st and 2nd carbons’ relaxation rates, L₇ a and A₅ a, both decreased, increased, and decreased as temperature decreased. The relaxation rates of both carbons L₇ b and L₇ d , the 3rd and 6th carbons, increased. The relaxation rate of carbon L₇ g increased then decreased while the relaxation rate of carbon L₇ d decreased then increased as temperature decreased. Finally, the relaxation rate of carbon A₅ b increased, decreased, then increased with decreased temperature.

Rotation Correlations (Minimization and Average Minimization Results, Figures 5-6):

As seen in Figure 5, the general trend of the carbons is such that t_o increased as temperature decreased. The t_o of the carbons of F₂, however, decreased and finally increased as temperature decreased. The results of t_i varied. The t_i of carbons L₇ and F₂ decreased and finally increased in as temperature decreased. The t_i of the carbons A₅ and A₈ both increased then decreased as temperature decreased. Lastly, the t_i of carbon of A₁₀ decreased, increased, and finally decreased in t_i as temperature decreased. Carbons of L_7, F₂, and A₁₀ increased, decreased, then increased in s² as temperature decreased. The carbons of A₈ increased then decreased in s² as temperature decreased. Carbons of A₁₀ decreased, increased, and finally decreased in s² as temperature decreased.
As seen in Figure 6, t_o increased respectively as temperature decreased. Every carbon increased then finally decreased in t_i as temperature decreased. The general trend of s² decreased as temperature decreased while the carbons of residue F₂ increased in t_i as temperature decreased.

Conclusions:

Folding Patterns:

The peptide under observation was a short-chained peptide itself. As mentioned earlier, a short-chained peptide at 278K results in an organized a-helix. Due to the size of the peptide, the temperature of the peptide, and the rotational correlations of the peptide the final structure at 278K resulted in an a-helix. [see appendix IV]

Relaxation Rates (Figures 1-4):

The results of the relaxation rate data show the hypothesized pattern for certain carbons. The hypothesis that was established was that as temperature increases, the relaxation rate should decrease, because an increase in temperature results in an increase in molecular motion which further increases the time it takes to go from the excited state back to the ground (resting) state. The longer portion of the peptide (F₂ to A₈) shows that some carbon atoms of the residues display the expected patterns of the relaxations rates; the first and last carbons (F₂ e and A₈ b) show a general increase in relaxation rate as temperature decreases. The remaining carbons, however, failed to collectively follow the hypothesized relaxation rate trend. The same follows for the peptide A₅ to L₇. The 1st, 5th, 6th, and 7th carbons (L₇ a, L₇ d (5), L₇ d (6), and A₅ b) all increased in relaxation rate as temperature decreased. The carbons A₅ a, L₇ b and L₇ g, however, showed a decreased relaxation rate or failed to collectively represent simultaneous results as temperature decreased. In both peptide segments, the first and last carbons displayed the expected trend. In fact, the last three carbons of the shorter peptide (L₇ to A₅) showed the expected trend while the second carbon of F2,A8 [trial #1] did as well. The first and last (external) carbons, may have more freedom of movement than the internal carbons, thus their relaxation rate decreased as temperature decreased. This outcome shows that the internal carbons of both partial peptides, fail to follow the hypothesis. This may be due to the interactions between the internal carbons as the a-helix is being formed at lower temperatures. The internal carbons may play a role in the actual formation of the a-helix, causing them to relax slower as they find their positions in the helix.

Rotation Correlations (Minimization and Average Minimization Results, Figures 5-6):

Since t_o , was fixed to t_o in Figure 6, all residues increase accordingly. The t_o of Figure 5, however, was not set to t_o. The values of t_o as seen in Figure 5 increased as temperature decreased. The t_o, however, was expected to decrease as temperature decreased. This unexpected result may be due to varying internal rotation correlations (t_i) of the five residues. If the values of t_i are not consistent and ordered, it is possible that the t_o is affected through its overall rotation. The general trend of t_i shows that the t_i increased, then finally decreased as temperature decreased. This pattern supports the expected results and may be due to folding of the peptide. At 278K, the t_i decreased, possibly commencing the formation of the a-helix.

The most efficient way to explain the behavior of the order parameter (s²) in an a-helix is to take into account rotational correlations. Theory would predict that as temperature increases, order of parameter decreases. As seen in Figures 5 and 6, only the F₂ residue shows predicted behavior, while all other residues in the peptide show unexpected behavior. It is possible that s² in a-helixes are more important than t_i because t_i must increase with increased temperatures. Rotational correlations may also play a primary role in interactions between residues in a-helixes. If the data is applied to the s² formula developed by Dr.Vladimir Daragon: s²= 1- k₁(amplitude of rotation²),⁶ the data cannot be explained. As the temperature increases, the amplitude of rotation must increase, which would cause s² to decrease. In the case of all residues in the a-helix, as the temperature increases, s² decreases. In the case of the F₂ residue, which is not in the a-helix of the peptide, the residue displayed expected behavior. The factor that plays a large role in the dynamics of the peptides in the a-helix is probably internal correlation.

With these results and conclusions in mind, the advancement of protein dynamics is possible to its fullest scientific potential.

Figures:

Figure 1:Phenylalanine₂ and Alanine₈ Relaxation Rates vs 1000/T (Trial#1)

Figure 2: Phenylalanine₂ and Alanine₈ Relaxation Rates vs 1000/T (Trial#2)

Figure 3: Leucine₇ and Alanine₅ Relaxation Rates vs 1000/T (Trial#1)

Figure 4: Leucine₇ and Alanine₅ Relaxation Rates vs 1000/T (Trial#2)

Figure 5:Minimization Results of F_2,A_5,L_7,A_8, and A

Amino Acids are organic acids comprised of two main groups. The first is the carboxyl (-COOH) group. The second is the -NH₂, or amine group. They also have a R group, which is its hydrocarbon side chain. Nine amino acids are referred to as residues in this project. These amino acids are the subunits of proteins, the basis of this study. The bonds between the amino acids, also known as peptide bonds, result in polypeptide chains of residues.

Amino Acid 3-Letter Abbreviation 1-Letter Abbreviation
Alanine Ala A
Argine Arg R
Glutamic Acid Glu E
Glycine Gly G
Leucine Leu L
Lysine Lys K
Phenylalanine Phe F
Serine Ser S
Tyrosine Tyr Y

1-letter abbreviation: GF₂SKA₅EL₇A₈KARAAKRGGY
3-letter abbreviation: Gly-Phe-Ser-Lys-Ala-Glu-Leu-Ala-Lys-Ala-Arg-Ala-Ala-Lys-Arg-Gly-Gly-Tyr
Full Scientific Name: Glycine-Phenylalanine-Serine-Lysine-Alanine-Glutamic Acid-Leucine-Alanine-Lysine-Alanine-Arginine-Alanine-Alanine-Lysine-Arginine-Glycine-Glycine-Tyrosine

Appendix II: Normal S² vs Temperature⁸

Appendix IV: Folding Patterns






Alpha-Helical Structure (a-helical)







Beta Structure (b)






Random Structure

References

Daragon, Vladimir A. and Kevin H. Mayo. “Motional model analyses of protein and peptide dynamics using ¹³C and ¹⁵N NMR relaxation.” Progress in Nuclear Magnetic Resonance Spectroscopy: London: Elsevier, 1997.

Daragon, Vladimir A. and Kevin H. Mayo. “A Simple Approach to Analyzing Protein Side- Chain Dynamics from ¹³C NMR Relaxation Data.” Journal of Magnetic Resonance Article No. MN971310 (1998): 329-334.

Daragon, Vladimir. “Protein Dynamics.” Minneapolis. University of Minnesota, June 1998.

Fruen, Lois. The Real World of Chemistry. 3rd ed. Iowa: Kendall/Hunt Publishing Co, 1998.

Gould and Keeton. Biological Science. 6th ed. New York: Norton & Co, 1996.

Hardeman, Rachel. “A Study of the Relaxation Rates of Two Control Peptides Through Nuclear Magnetic Resonance.” Breck Science Research Paper. Minneapolis: Breck School, 1997.

Lehninger, Albert L. Short Course in Biochemistry.The Johns Hopkins University School of Medicine: Worth Publishers, Inc. 1973 page 65.

¹ Lehninger, Albert L.. Short Course in Biochemistry.The Johns Hopkins University School of Medicine: Worth Publishers, Inc. 1973 page 65

¹ Daragon, Vladimir. “Protein Dynamics.” Minneapolis. University of Minnesota, June 1998.

² Daragon, Vladimir. “Protein Dynamics.” Minneapolis. University of Minnesota, June 1998.

³ Hardeman, Rachel. “A Study of the Relaxation Rates of Two Control Peptides Through Nuclear Magnetic Resonance.” Breck Science Research Paper. Minneapolis. Breck School. 1997

⁴ Daragon, Vladimir. “Protein Dynamics.” Minneapolis. University of Minnesota, June 1998.

⁵ Daragon, Vladimir. “Protein Dynamics.” Minneapolis. University of Minnesota, June 1998.

⁶ Gould and Keeton. Biological Science. 6th ed. New York: Norton & Co, 1996

⁷ Daragon, Vladimir. “Protein Dynamics.” Minneapolis. University of Minnesota, June 1998.

⁸ Lehninger 65