**3. The temperature and viscosity dependences for spin-labeled Barstar in solution**

Spin labeling, EPR and all the method described above, based on the temperature-viscosity dependence experiment, was used to study the protein-protein interaction between the enzyme barnase (Bn) and its inhibitor barstar (Bs) (Timofeev et al., 2008). A mutant of barstar (C40A), containing only one cysteine residue, C82 was selectively modified by spin label (SL) 4-(2-chloromercurophenyl)-2,2,5,5-tetramethyl-3-imidazoline- <sup>3</sup> *Δ* -1-oxyl (Shapiro et. al., 1979). We used spin label which ensured higher ability of his reporter group to access different protein microenvironments. To estimate the mobility of the spin labeled C82 side group and the whole globular protein quantitatively, the temperature-viscosity approach was used.

To extract unambiguous information from experimental EPR spectra of spin-labeled macromolecules, it is necessary to have maximum possible control over the degrees of freedom (DOFs) an EPR line shape depends on. This effectively reduces linehape 'degeneracy' with respect to the set of parameters used to interpret these spectra. Generally, for complex objects like mutually interacting proteins, unequivocal interpretation of EPR spectra is possible only when BOPs are present. For small molecules undergoing relatively rapid rotations narrowing the spectrum at ambient temperatures, decreasing the temperature and increasing solvent viscosity increase order parameters, as well as macromolecule tumbling correlation time. This leads to broad outer peaks (BOPs) of increasing amplitude to appear in low and high field regions of EPR spectra. By processing a series of EPR spectra of spin-labeled samples and measuring the separation between the BOPs, one can estimate the effective rotational correlation time *τ* of the protein molecule and the order parameter *S* of the spin label attached to the side chain. EPR spectra of Bs-SL in solution with changing viscosity are shown on Fig. 1 and Fig. 2. Viscosity was controlled by addition of sucrose.

As can be seen from Fig. 4 and Fig. 5, BOPs shifts considerably towards field range end points with increasing viscosity, and this is an effect one expects to be able of studying temperature-viscosity dependence. According to formulas (11) for parameter 2A*'* , this dependence is shown on Fig. 6.

**Figure 4.** EPR spectra of Bs-SL at 1º C, with viscosity altered by addition of (1) 0%, (2) 6%, (3) 16%, and (4) 19.5 % sucrose (w/w).

**Figure 5.** EPR spectra of Bs-SL at 1º C, with viscosity controlled by addition of (5) 27 %, (6) 33 %, (7) 40 % sucrose (w/w). The experimental spectrum is plotted with heavy line and the simulation - with fine line. The theoretical calculation of spectra shown is discussed in the text.

(4) 19.5 % sucrose (w/w).

**Figure 4.** EPR spectra of Bs-SL at 1º C, with viscosity altered by addition of (1) 0%, (2) 6%, (3) 16%, and

**Figure 5.** EPR spectra of Bs-SL at 1º C, with viscosity controlled by addition of (5) 27 %, (6) 33 %, (7) 40 % sucrose (w/w). The experimental spectrum is plotted with heavy line and the simulation - with fine

line. The theoretical calculation of spectra shown is discussed in the text.

**Figure 6.** Temperature-viscosity dependences of separations between BOPs ( 2A*'* ) in the EPR spectra of Bs-SL (line **2**), and complex Bs-SL with Bn (line **l**) at 1º C. The data were fitted using the linear least squares method. Line 1 crosses the ordinate axis yielding the extrapolated value 2*A* = 63.9 G, whereas line 2 yields 2*A* = 57.8 G. Units are T for K, and cP (centipoises) for *η* . The value of TVD parameter *β = /b=* 1 0.74 .

It is clearly observable from EPR spectra presented in Fig. 4 and Fig. 5, that at lower viscosity values (6%, 16%, and 19.5% w/w sucrose in solution) BOPs are considerably asymmetrical. In fact, there are two poorly resolved BOP pairs, what is clearly seen in spectra at higher viscosities (27%, 33%, and 40% w/w sucrose in solution). Therefore, it is clear that spectra are composed of two components, first broad, and second, narrower. The separations between BOPs from narrow component (three points) 2A*'* are shown on the Fig. 6 (line 2). The first spectrum on Fig. 4 lacks of low-field BOP, thus there is no point for 0% sucrose on the line 2 (Fig. 6). At higher viscosity values (27%, 33%, and 40% sucrose in solution) BOPs from broad and narrow spectrum components were separated. Hence we define the separations between BOPs near to the center of the spectrum as 2A*'* (narrow) and farther from the center of the spectrum as 2A*'* (broad). As for the three points to 2A*'* (broad) they are visible on the line 2 (Fig. 7). In Fig. 7 for clarity, a line 1 is repeated as line 1 in Fig. 6.

For these double-component spectra, two explanations are possible. This is either due to the Bs-Bs interaction of two macromolecules (Timofeev, et al., 2008), or a spin label SL have two dynamic states with strongly different order parameters. To clarify this alternative, an experiment on the binding of macromolecules Bs-SL with adsorbent has been undertaken.

**Figure 7.** Temperature and viscosity dependences for BOPs separation ( 2A*'* /G) in EPR spectra of spinlabeled Barstar in solution, and on adsorbent. Solution: 6 points for BOPs from narrower component (line **1**): (1) 6%, (2) 16%, (3) 19.5 %, (4) 27%, (5) 33%, and (6) 40 % sucrose (w/w), and 3 points for broad component BOPs (line **2**): (1) 27%, (2) 33%, and (3) 40 % sucrose (w/w), at 1ºC. With adsorbent: **1A** line at 1ºC and **1B** line at 20ºC for narrow component BOPs; **2A** line at 1ºC and **2B** line at 20ºC for broad component BOPs. The data were fitted using the linear least squares method. Line 1 crosses the ordinate axis yielding the extrapolated value 2Ā = 57.8 G, and line 2 yields 2Ā = 66.1 G. The value of *β = /b=* 1 0.74 .

### **4. The temperature and viscosity dependences for immobilized Barstar**

If macromolecule with spin label attached to it can be immobilized, rendering effective correlation time to be large enough to mimic ridgid-limit spectrum. In case with spin labeled Barstar we used QFF sepharose to achieve this goal. The sample was prepared by addition of SL to Barstar solution in HEPES buffer, then added 6 mg SL corresponding concentration to have molar excess of protein. Then 200 ml of QFF sepharose suspension was added and sample washed to remove unbound protein by spinning on microcentrifuge. Spin-labeled protein-charged sepharose was used for recording of EPR spectra. Temperature dependence of these spectra (1, 10, 20, 30, 40C) without sucrose is shown on Fig. 8.

It is clear that all five EPR spectra display "quasi-powder" pattern (broad due to strong immobilization) as spin-labeled macromolecules are now attached to an adsorbent (cf. Fig.1). Over entire temperature range (1-40ºC) two components are clearly observable, with corresponding BOP separations of 2A*'* (narrow) and 2A*'* (broad).

Rotational Brownian motion of medium-sized macromolecules in solution is on the nanosecond range. Linking macromolecules to an adsorbent shifts it to the microsecond range, which, in fact, is not distinguishable from rigid-limit ("powder spectrum") at

**Figure 7.** Temperature and viscosity dependences for BOPs separation ( 2A*'* /G) in EPR spectra of spinlabeled Barstar in solution, and on adsorbent. Solution: 6 points for BOPs from narrower component (line **1**): (1) 6%, (2) 16%, (3) 19.5 %, (4) 27%, (5) 33%, and (6) 40 % sucrose (w/w), and 3 points for broad component BOPs (line **2**): (1) 27%, (2) 33%, and (3) 40 % sucrose (w/w), at 1ºC. With adsorbent: **1A** line at 1ºC and **1B** line at 20ºC for narrow component BOPs; **2A** line at 1ºC and **2B** line at 20ºC for broad component BOPs. The data were fitted using the linear least squares method. Line 1 crosses the ordinate axis yielding the extrapolated value 2Ā = 57.8 G, and line 2 yields 2Ā = 66.1 G. The value of *β = /b=* 1 0.74 .

**4. The temperature and viscosity dependences for immobilized Barstar** 

of these spectra (1, 10, 20, 30, 40C) without sucrose is shown on Fig. 8.

corresponding BOP separations of 2A*'* (narrow) and 2A*'* (broad).

If macromolecule with spin label attached to it can be immobilized, rendering effective correlation time to be large enough to mimic ridgid-limit spectrum. In case with spin labeled Barstar we used QFF sepharose to achieve this goal. The sample was prepared by addition of SL to Barstar solution in HEPES buffer, then added 6 mg SL corresponding concentration to have molar excess of protein. Then 200 ml of QFF sepharose suspension was added and sample washed to remove unbound protein by spinning on microcentrifuge. Spin-labeled protein-charged sepharose was used for recording of EPR spectra. Temperature dependence

It is clear that all five EPR spectra display "quasi-powder" pattern (broad due to strong immobilization) as spin-labeled macromolecules are now attached to an adsorbent (cf. Fig.1). Over entire temperature range (1-40ºC) two components are clearly observable, with

Rotational Brownian motion of medium-sized macromolecules in solution is on the nanosecond range. Linking macromolecules to an adsorbent shifts it to the microsecond range, which, in fact, is not distinguishable from rigid-limit ("powder spectrum") at

**Figure 8.** EPR spectra of the QFF-Bs-SL1 complex at 1ºC (1), 10ºC (2), 20ºC (3), 30ºC (4), and 40ºC (5). The spectral width is 100 G.

experimental conditions used. Therefore, the shape of "quasi-powder" EPR spectrum is exclusively determined by the fast reorientation of the spin label in a limited configuration/conformation space. This makes it easy to measure the order parameter of nitroxide (see expression (2)).

On the other hand, once the protein is adsorbed on the sepharose, the arising "quasipowder" EPR spectrum should not depend on oligomeric state of the protein, to an extent local structure of the protein close to labeling site is disturbed by weak inter-macromolecule interactions. Strong Barstar interaction with an heavily charged adsorbent is expected to significantly impair its ability to form dimer, and is expected to shift equilibrium to monomeric form. Therefore, we conclude that the order parameter *S* in the dimeric form of the protein (if any) and its monomeric form should be the same. Consequently, there are two conformational states of the spin label attached to the thiol group of the protein, corresponding to two spectral components with BOP separations of 2A*'* (narrow) , and 2A*'* (broad).

In further experiments EPR spectra of Bs-SL on the adsorbent at different viscosities have been recorded, for the full temperature-viscosity dependence to be obtained. Corresponding spectra, for different temperatures, are shown on Figure 9 (A, B). Two components found (two BOP pairs) were processed independently to get order parameters for both spin label conformational states. Fig. 7 displays TVD for sepharose-bound Barstar overlaid on these for free protein in solution at 1ºC (lines 1A and 2A) and 20ºC (lines 1B and 2B). As seen in Fig. 7, four lines (1A, 1B, 2A, 2B) are parallel to the x-axis. This behavior is expected, as both types of BOPs (from narrow and broad spectrum components) do not shift with increasing viscosity of the medium in the "quasi-powder" EPR spectra, given the value of *τ* for protein

is virtually infinite. Consequently, the separations between BOPs not change and, thus, in the case with adsorbent: 2A*'* (narrow) = 2*A* (narrow) and 2A*'* (broad) = 2*A* (broad). It also means that the second term in equation (1), for both spectrum components is zero.

**Figure 9.** EPR spectra of spin labeled Barstar immobilized on QFF sepharose (QFF•Bs-SL system) at 1ºC (A) and 20ºC (B) with viscosity altered by addition of (1) 0%, (2) 15%, (3) 30%, (4) 37%, (5) 48%, and (6) 56% sucrose (w/w).

It is now straightforward, knowing ZZ 2A and 0 2a , to calculate order parameters *S*1 (for narrow component) and *S*2 (for broad component) according to the formula (2) for both states of the spin label. Dependences of the order parameters *S*1 and *S*2 on the temperature are shown in Fig. 7, in this case *S*2 > *S*1.

300 Nitroxides – Theory, Experiment and Applications

56% sucrose (w/w).

is virtually infinite. Consequently, the separations between BOPs not change and, thus, in the case with adsorbent: 2A*'* (narrow) = 2*A* (narrow) and 2A*'* (broad) = 2*A* (broad). It also

**Figure 9.** EPR spectra of spin labeled Barstar immobilized on QFF sepharose (QFF•Bs-SL system) at 1ºC (A) and 20ºC (B) with viscosity altered by addition of (1) 0%, (2) 15%, (3) 30%, (4) 37%, (5) 48%, and (6)

means that the second term in equation (1), for both spectrum components is zero.

Thus the ensemble of spin-labeled molecules barstar Bs-SL is divided into two subensembles. In one sub-ensemble spin label is found in 1st state with corresponding order parameter *S*1, and another – in 2nd state with order parameter *S*2.

**Figure 10.** Values of the order parameters S2 (to 2nd state of SL, farther BOPs) – line 1; and S1 (to 1st state of SL, near BOPs) – line 2; in depend on the ambient temperatures.

Interestingly, the fast motion activation by temperature in each of the SL states in a local protein site (Cys82) is negligible. As seen in Fig. 7, parameters *S*1 or *S*2 drift only slightly over entire temperature range from 1 to 40ºC. This suggests that the rigid spin label samples almost the same amount of configuration space provided by rigid protein frame in this range of temperatures.

Addition of the Barnase (Bn) to Bs-SL solution results in a temperature-viscosity dependence, as shown in Fig. 3 by line 1. In this case, the spin label in the complex of BnBs-SL has a single state with a value of the order parameter (*S* = 0.86). Line 1 slope is two times less than that of line 2 (Fig. 3). Very strong affinity of Barstar to Barnase explains this, since the molecular weight of BnBs complex (22.7 kD) is about twice larger than the molecular weight of Barstar (10.3 kD).

When introduced to the system QFF•Bs-SL, Barnase had no significant effect on EPR spectrum (see Fig. 8). In case of stable Bn•Bs-SL complex formation, the EPR spectrum was expected to be substantially changed, which is the case in solution. The capacity of the QFF sepharose which is abundant in the sample mixture and its charge make Bn easier to bind to

**Figure 11.** The spectra EPR of QFF-Bs-SL (light line with sharp peaks of free SL) and the same at adding Bn in a bit large excess (dark line without sharp peaks) at 1ºC (1) and 20ºC (2).

the adsorbent, while bound Barstar may have its Bn binding interface unreachable. This leads to disruption of Bn•Bs-SL complex formation equilibrium. No change in EPR spectra at two temperatures, 1ºC and 20ºC indicate that there is apparently no significant amount of complex present. Smaller amount of free label (three narrow lines on Fig. 8) after Bn addition was due to centrifugation, and, therefore, better washing.

### **5. Spin-labeled Barstar EPR spectra simulation**

The procedure for simulating EPR spectra using the proposed model of the two motional nitroxide radical was described in section **2.3**. Here we want to give some examples of EPR spectra simulation, paying an attention to the similarity of theoretical spectra to experimental ones.

### **5.1. Barstar and formation of complex with Barnase**

On the Fig. 5 (A, B, C) fitted simulation EPR spectra superimposed onto experimental ones. As it appears, they can be described by two dynamical states of spin label rapid motion relative to Barstar molecule. If one assumed these states uncoupled, each of them corresponds to its own EPR spectrum, and experimental one corresponds to their weighted sum. On Figures 12 - 14 individual simulated spectra are shown for each state of spin label (1st and 2nd); their superposition results a final spectrum. Using Gaussian distribution on *α* averaging parameter helps to obtain better fit due to states dynamical coupling (exchange), and the spectra shown on these figures actually account for it this way (see legends).

We used following initial components of nitroxide magnetic tensors: *g*(X,Y,Z)= 2.00732; 2.0063; 2.0022; *A*(X,Y,Z)=6.55 G; 5.00 G; 35.40 G. In legends to figures, the rotational correlation times and linewidth, parameters used for calculation of partially averaged tensors components along with themselves, are given.

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**Figure 11.** The spectra EPR of QFF-Bs-SL (light line with sharp peaks of free SL) and the same at adding

the adsorbent, while bound Barstar may have its Bn binding interface unreachable. This leads to disruption of Bn•Bs-SL complex formation equilibrium. No change in EPR spectra at two temperatures, 1ºC and 20ºC indicate that there is apparently no significant amount of complex present. Smaller amount of free label (three narrow lines on Fig. 8) after Bn

The procedure for simulating EPR spectra using the proposed model of the two motional nitroxide radical was described in section **2.3**. Here we want to give some examples of EPR spectra simulation, paying an attention to the similarity of theoretical spectra to

On the Fig. 5 (A, B, C) fitted simulation EPR spectra superimposed onto experimental ones. As it appears, they can be described by two dynamical states of spin label rapid motion relative to Barstar molecule. If one assumed these states uncoupled, each of them corresponds to its own EPR spectrum, and experimental one corresponds to their weighted sum. On Figures 12 - 14 individual simulated spectra are shown for each state of spin label (1st and 2nd); their superposition results a final spectrum. Using Gaussian distribution on *α* averaging parameter helps to obtain better fit due to states dynamical coupling (exchange),

and the spectra shown on these figures actually account for it this way (see legends).

Bn in a bit large excess (dark line without sharp peaks) at 1ºC (1) and 20ºC (2).

addition was due to centrifugation, and, therefore, better washing.

**5. Spin-labeled Barstar EPR spectra simulation** 

**5.1. Barstar and formation of complex with Barnase** 

experimental ones.

**Figure 12.** Simulated EPR spectra (fine line) for of 1st state SL and 2nd state of SL in comparison with an experimental spectrum of Bs-SL at 1º C and 27 % sucrose in solution (heavy line).

Spectrum for of 1st state contains BOPs close to the center (narrow). It is described by three parameters which, according to section 2.3, determine partial averaging of tensors in 1st state by the values of *α* = 77(15)º, *θ* = 46º, *φ* = 5º. Each spectrum was calculated as the average by *α* with Gaussian distribution, as 77(15), where the value in brackets is the standard deviation. Magnetic tensors diagonal components: *g* (X,Y,Z) = 2.00696, 2.00562, 2.00323; *A* (X,Y,Z) = 6.66246 G, 11.9003 G, 28.3872 G. BOPs in simulated EPR spectrum (fine line) for 2nd state located farther from the center. This second state is described by parameters *α* = 30(44)º, *θ* =30º, *φ* =5º. Magnetic tensors diagonal components: *g* (X,Y,Z) = 2.00723, 2.00628, 2.0029; *A* (X,Y,Z) = 6.46487 G, 5.74586 G, 34.7363 G. Rotational correlation time for macromolecule was *τ* = 25 ns. Linewidth used was 1.7 G. The simulated spectra in both states were summed with the ratio of 28:72, which gives the resulting spectrum shown in Fig. 5(5).

All partial averaging parameters are the same as in the legend to Fig. 12. The protein rotational correlation time is *τ* = 38 ns. The simulated spectra in both states were summed with the ratio of 45:55, which gives the resulting spectrum shown in Fig. 5(6).

**Figure 14.** Simulated EPR spectra (fine line) for 1st and 2nd states of SL and 2 state SL in comparison to experimental one of Bs-SL at 1º C and 40 % sucrose in solution (heavy line).

All partial averaging parameters are the same as in the legend to Fig. 12. The protein rotational correlation time is *τ* = 60 ns. The simulated spectra in both states were summed with the ratio of 40:60, which gives the resulting spectrum shown on Fig. 5 (7).

304 Nitroxides – Theory, Experiment and Applications

**Figure 13.** Simulated EPR spectra (fine line) for 1st and 2nd states of SL and 2 state SL in comparison to

**Figure 14.** Simulated EPR spectra (fine line) for 1st and 2nd states of SL and 2 state SL in comparison to

experimental one of Bs-SL at 1º C and 40 % sucrose in solution (heavy line).

experimental one of Bs-SL at 1º C and 33 % sucrose in solution (heavy line).

**Figure 15.** EPR spectrum of QFF-sepharose-Bs-SL at 1º C and 0 % sucrose (heavy line) and the simulated spectrum of 1st or 2nd states (thin line). (A) The 1st state is described (see Fig. 9A) is described by three parameters which, according to section 2.3, determine partial averaging of tensors in 1st state by the values of *α* = 77(14)º, *θ* = 46º, *φ* = 5º. Components of averaged tensors: *g* (X,Y,Z) = 2.00696, 2.00562, 2.00323; *A* (X,Y,Z) = 6.66246 G, 11.9003 G, 28.3872 G. Each spectrum was calculated as the average by *α* with Gaussian distribution, as 77(15), where the value in brackets is the standard deviation. The rotational diffusion tensor components (expressed as correlation times) for macromolecule are *<sup>X</sup>τ* = 100 ns, *Yτ* = 1000 ns, *Zτ* = 1000 ns. Anisotropic linewidth components are *Xδ* = 1.3 G, *Yδ* = 1.5 G, *Zδ* = 1.5 G. (B) The 2nd state is described (see Fig. 9) by three parameter values of *α* = 27(32)º, *θ* = 27º, *φ* = 5º. Components of averaged tensors: *g* (X,Y,Z) = 2.00724, 2.00629, 2.00226; *A* (X,Y,Z) = 6.66246 G, 11.9003 G, 28.3872 G. The rotational diffusion tensor components (expressed as correlation times) for macromolecule are *<sup>X</sup>τ* = 100 ns, *Yτ* = 1000 ns, *Zτ* = 1000 ns. Anisotropic linewidth components are *Xδ* = 1.4 G, *Yδ* = 1.9 G, *<sup>Z</sup>δ* = 1.9 G.

(C) Spectrum of QFF-sepharose-Bs-SL at 1º C and 0 % sucrose in solution, (heavy line) and the simulated spectrum (fine line) obtained by summation of ones for 1st and 2nd states (Fig. 15 A, B), with ratio of 30:70.

The results obtained by fitting of simulated spectra to experimental ones for spin-labeled Bs-SL, are listed in legends to Figures 12, 13, 14. Thus, three points (27, 33 and 40% sucrose) on temperature-viscosity dependence (Fig. 6 line2; or Fig. 7 line1) correspond to simulated EPR spectra on Fig. 5 and Fig. 12, 13, 14. It is important to note that simulated EPR spectra differ solely in the rotational correlation time of macromolecule! This is highly consistent with proposed TVD advantage of separating BOPs shift contributions regarding to slow rotational dynamics of macromolecule, and rapid motion of spin label. The partial averaging of magnetic tensors conserve when temperature is held at constant level.

### **5.2. Sepharose-immobilized spin-labeled Barstar EPR spectra**

The EPR spectra of Bs-SL in solution in the presence of QFF sepharose on Fig. 8 and Fig. 9 are shown. This entire set of spectra can be simulated using the same principle described here. However, for an example we have selected only two experimental spectra to show procedure of simulation (see section **2.2.4**). We will discuss already shown simulated EPR spectra of Bs-SL in solution.

**Figure 16.** A. EPR spectrum of QFF-sepharose-Bs-SL at 1º C and 35% sucrose in solution (heavy line), and the simulated spectrum of 1st (fine line). Partial averaging parameters are the same as given in legend to Fig. 15A. The rotational diffusion tensor components (expressed as correlation times) for macromolecule are *Xτ* =200 ns, *Yτ* =1000 ns, *Zτ* =1000 ns. Anisotropic linewidth components are *Xδ* =1.5 G, *Yδ* =2.4 G, *Zδ* =2.4 G.

B. Spectrum of QFF-sepharose-Bs-SL at 1º C and 35% sucrose in solution (heavy line) and the simulated spectrum of 2nd state (fine line). Partial averaging parameters are the same as given in legend to Fig. 15A. The rotational diffusion tensor components (expressed as correlation times) for macromolecule are *<sup>X</sup>τ* = 200 ns, *Yτ* = 1000 ns, *Zτ* = 1000 ns. Anisotropic linewidth components are *Xδ* =2.0 G, *Yδ* =3.0 G, *Zδ* =2.0 G.

C. EPR spectrum of QFF-sepharose-Bs-SL at 1º C and 35 % sucrose in solution, (heavy line) and the simulated spectrum calculated as weighted sum of the above with ratio of 30:70.

On the Fig. 16, experimental spectra of QFF-sepharose-Bs-SL at 1º C and 35 % sucrose in solution, (heavy line), are shown along with simulated ones, demonstrating individual contributions from two SL states. The final spectrum (weighted sum of two states) is shown on Fig.15

### **5.3. Fast motion analysis by Molecular Dynamics**

306 Nitroxides – Theory, Experiment and Applications

spectra of Bs-SL in solution.

G, *Yδ* =2.4 G, *Zδ* =2.4 G.

=2.0 G.

solely in the rotational correlation time of macromolecule! This is highly consistent with proposed TVD advantage of separating BOPs shift contributions regarding to slow rotational dynamics of macromolecule, and rapid motion of spin label. The partial averaging

The EPR spectra of Bs-SL in solution in the presence of QFF sepharose on Fig. 8 and Fig. 9 are shown. This entire set of spectra can be simulated using the same principle described here. However, for an example we have selected only two experimental spectra to show procedure of simulation (see section **2.2.4**). We will discuss already shown simulated EPR

**Figure 16.** A. EPR spectrum of QFF-sepharose-Bs-SL at 1º C and 35% sucrose in solution (heavy line), and the simulated spectrum of 1st (fine line). Partial averaging parameters are the same as given in legend to Fig. 15A. The rotational diffusion tensor components (expressed as correlation times) for macromolecule are *Xτ* =200 ns, *Yτ* =1000 ns, *Zτ* =1000 ns. Anisotropic linewidth components are *Xδ* =1.5

B. Spectrum of QFF-sepharose-Bs-SL at 1º C and 35% sucrose in solution (heavy line) and the simulated spectrum of 2nd state (fine line). Partial averaging parameters are the same as given in legend to Fig. 15A. The rotational diffusion tensor components (expressed as correlation times) for macromolecule are *<sup>X</sup>τ* = 200 ns, *Yτ* = 1000 ns, *Zτ* = 1000 ns. Anisotropic linewidth components are *Xδ* =2.0 G, *Yδ* =3.0 G, *Zδ*

C. EPR spectrum of QFF-sepharose-Bs-SL at 1º C and 35 % sucrose in solution, (heavy line) and the

simulated spectrum calculated as weighted sum of the above with ratio of 30:70.

of magnetic tensors conserve when temperature is held at constant level.

**5.2. Sepharose-immobilized spin-labeled Barstar EPR spectra** 

Method of Molecular Dynamics (MD) has become a very powerful and versatile tool for research connected with protein dynamics. Significant growth of hardware computational capabilities recently makes it possible to incorporate MD simulations into many analysis workflows involving experimental data collected using modern physical methods. It is successfully used in conjunction with nuclear magnetic resonance (NMR) for elucidation of protein structure and dynamics. The spin labelling and EPR may provide similar type of information, in form of order parameters (although on different time scale). Conventional MD method itself is completely theoretical (that is, pure calculation with no use of experimental data regarding particular system), but it is attractive as it provides detailed information on the system (macromolecule) dynamics. As a result of MD run, one obtains a trajectory with the time course of all atomic coordinates of the system. Modern software and visualization hardware allows viewing the resulted trajectory, and one can see a visual representation of the molecular system in time, which makes this technique a powerful tool for analyzing the dynamic properties of macromolecules. The trajectory obtained from MD enables one to calculate virtually any property of the system. We suggest it is very attractive to join the MD method with EPR techniques, once the latter provide experimental data to be guidance for designing MD runs, and/or verifying its results. On the other side, MD calculations may help in interpretation of EPR spectra.

MD method was used here to study the internal structural and dynamical properties of spin-labeled Barstar and its complex with Barnase. It was already mentioned in section 2, that EPR spectrum gives 'digest' type of information about the system dynamics. Most efforts to bridge MD and EPR techniques are now focused on attempt to simulate EPR spectrum from MD trajectory. We adopt different approach, similar to one used in NMR, based on order parameters. As a quantitative estimate for comparing the results of the two methods we used parameter *S*, which characterizes the angular reorientations of the attached spin label and the spatial constraints of the immediate protein environment. This order parameter, easily and unambiguously determined from the temperature and viscosity dependencies, can be calculated from the MD trajectory. The order parameter was calculated in two ways from the MD trajectories: the McConnell's method (axially symmetrical case), and the method of Model Free approach.

The initial structure of barstar molecules with a resolution of 2.8 A (PDB id 1A19) was obtained from the database Protein Data Bank. The structure was prepared for MD, Cys82 residue was mutated to spin-labeled cystein. New residue SLHG was added to parameter files used for simulation; the parameters were combined from (Stendardo E *et al*, 2010), CHARMM-cgenff and UFF, and optimized to reproduce average geometry of spin label known from X-Ray (Shapiro A. B. et al., 1979)). Explicit solvent model was used, with TIP3 water. After equilibration (NPT ensemble with Langevin method for temperature control), a series of annealing steps has been performed. Annealing ended up in clearly observable two kinds of distinct dynamical behavior of spin label, more and less ordered. For them, the production runs of lengths of 20 ns at 330 K, and 10 ns at 300 K, were performed.

The initial structure of the complex barnase-barstar (PDB id 1AY7) was also obtained from the Protein Data Bank. Spin-labeled complex was reconstructed by Targeted MD using already built model of labeled Barstar. Both dynamical states of spin label attached to Barstar, discovered by annealing, upon virtual Barnase 'binding', yielded trajectory with disordered motional state absent. Trajectories of length of 20 ns at 330 K and 10 ns at 300 K were calculated, and used for determination of order parameters.

All calculations were performed using the software packages NAMD & VMD (Phillips J.C., *et al*, 2005; Humphrey W., *et al*, 1996).

**Figure 17.** Autocorrelation function calculated from MD trajectories (squares) of Barstar (gray) and its complex with Barnase (black), and corresponding two-exponential model fits (line).

It is straightforward to compute coordinate autocorrelation function from MD trajectory. Its long time asymptotic limit is referred as generalized order parameter, as it does not rely on azimuthal motion symmetry, which is the case of McConnel's parameter *S*. This method of order parameter definition is commonly used in NMR and referred to as Model Free approach (Lipari, G.; Szabo, 1982; K.K. Frederick, K. A. Sharp., 2008). Two-exponential decomposition of autocorrelation function obtained for free Barstar yielded fast-component

*et al*, 2005; Humphrey W., *et al*, 1996).

files used for simulation; the parameters were combined from (Stendardo E *et al*, 2010), CHARMM-cgenff and UFF, and optimized to reproduce average geometry of spin label known from X-Ray (Shapiro A. B. et al., 1979)). Explicit solvent model was used, with TIP3 water. After equilibration (NPT ensemble with Langevin method for temperature control), a series of annealing steps has been performed. Annealing ended up in clearly observable two kinds of distinct dynamical behavior of spin label, more and less ordered. For them, the

The initial structure of the complex barnase-barstar (PDB id 1AY7) was also obtained from the Protein Data Bank. Spin-labeled complex was reconstructed by Targeted MD using already built model of labeled Barstar. Both dynamical states of spin label attached to Barstar, discovered by annealing, upon virtual Barnase 'binding', yielded trajectory with disordered motional state absent. Trajectories of length of 20 ns at 330 K and 10 ns at 300 K

All calculations were performed using the software packages NAMD & VMD (Phillips J.C.,

**Figure 17.** Autocorrelation function calculated from MD trajectories (squares) of Barstar (gray) and its

It is straightforward to compute coordinate autocorrelation function from MD trajectory. Its long time asymptotic limit is referred as generalized order parameter, as it does not rely on azimuthal motion symmetry, which is the case of McConnel's parameter *S*. This method of order parameter definition is commonly used in NMR and referred to as Model Free approach (Lipari, G.; Szabo, 1982; K.K. Frederick, K. A. Sharp., 2008). Two-exponential decomposition of autocorrelation function obtained for free Barstar yielded fast-component

complex with Barnase (black), and corresponding two-exponential model fits (line).

production runs of lengths of 20 ns at 330 K, and 10 ns at 300 K, were performed.

were calculated, and used for determination of order parameters.

order parameter (apparent correlation time 3.2 ns for Bs, or 5.4 for complex) to be significantly different from one for Barstar-Barnase complex (0.89 *vs* 0.97). McConnel's azimuthal order parameters calculated along entire trajectories were lower, *S* = 0.67 for the Bs, and *S* = 0.93 for the BnBs complex, which is consistent with motion anisotropy (azimuthal and generalized order parameters coincide when motion is axially symmetrical). The exact calculation by averaging along the trajectory shown *S* = 0.67 for the free Barstar, and *S* = 0.93 for the complex. This is expected, as all the EPR spectra for Barstar and its complex with Barnase presented above were simulated using non-axial model (but with several order parameters). On the other hand, the value of azimuthal order parameter *S* is in good agreement, as expected, with the experimental value obtained from the temperature-viscosity dependence of EPR spectra. The detailed trajectory analysis for free Barstar showed that it is nonuniform in sense of spin label motion. Namely, some parts of trajectory demonstrated much less disorder in this motion, and order parameter computed from them appeared to be 0.91, which is in good agreement with McConnel's order parameter determined experimentally by TVD for 2nd state EPR spectra component.

**Figure 18.** A. Experimental EPR spectrum of TEMPO radical in DPPC at 37.6°C (heavy line) and simulated spectrum (fine line) at X band (microwave frequency 9.15 GHz). All necessary parameters for simulation are summarized in Table 1. Center field B0 = 3260 G, and scan range is 49 G. B. The simulated EPR spectrum (fine line) of TEMPO radical in lipid phase. Parameters are in Table 1. C. The simulated EPR spectrum (fine line) of TEMPO radical in aqueous phase. Parameters are in Table 1.
