Molecular dynamics simulations of a calmodulin-peptide complex in solution

We have performed an 4-ns MD simulation of calmodulin complexed with a target peptide in explicit water, under realistic conditions of constant temperature and pressure, in the presence of a physiological concentration of counterions and using Ewald summation to avoid truncation of long-range electrostatic forces. During the simulation the system tended to perform small fluctuations around a structure similar to, but somewhat looser than the starting crystal structure. The calmodulin-peptide complex was quite rigid and did not exhibit any large amplitude domain motions such as previously seen in apo- and calcium-bound calmodulin. We analyzed the calmodulin-peptide interactions by calculating buried surface areas, CHARMM interaction energies and continuum model interaction free energies. In the trajectory, the protein surface area buried by contact with the peptide is 1373 A(2) approximately evenly divided between the calmodulin N-terminal, C-terminal and central linker regions. A majority of this buried surface, 803 A(2), comes from nonpolar residues, in contrast to the protein as a whole, for which the surface is made up of mostly polar and charged groups. Our continuum calculations indicate that the largest favorable contribution to peptide binding comes from burial of molecular surface upon complex formation. Electrostatic contributions are favorable but smaller in the trajectory structures, and actually unfavorable for binding in the crystal structure. Since nonpolar groups make up most of buried surface of the protein, our calculations suggest that the hydrophobic effect is the main driving force for binding the helical peptide to calmodulin, consistent with thermodynamic analysis of experimental data. Besides the burial of nonpolar surface area, secondary contributions to peptide binding come from burial of polar surface and electrostatic interactions. In the nonpolar interactions a crucial role is played by the nine methionines of calmodulin. In the electrostatic interactions the negatively charged protein residues and positively charged peptide residues play a dominant role.     

Dynamics and entropy of a calmodulin-peptide complex studied by NMR and molecular dynamics

All-atom, explicit water molecular dynamics simulations of calcium-loaded calmodulin complexed with a peptide corresponding to the smooth muscle myosin light chain kinase target were carried out at 295 and 346 K. Amide and side chain methyl angular generalized order parameters were calculated and analyzed in the context of the protein's structure and dynamics. The agreement between amide order parameters measured by NMR and those from the simulations was found to be good, especially at the higher temperature, indicating both better convergence for the latter and excellent transferrability of the CHARMM parameters to the higher temperature. Subtle dynamical features such as helix fraying were reproduced. A large range of order parameters for the nine calmodulin methionines was observed in the NMR, and reproduced quite well in the simulations. The major determinant of the methionine order parameter was found to be the proximity to side chains of aromatic residues. An upper bound estimate of the difference in backbone entropy between loop and helical regions was extracted from the order parameters using a model of motion in an effective potential. Although loop regions are more flexible than helical regions, it was found that the entropy loss per residue upon folding was only approximately 20% less for loops than for helices. Pairwise correlated motions, which could significantly lower entropy estimates obtained from order parameter analysis alone, were found to be largely absent.     

Temperature dependence of fast dynamics in proteins

The temperature dependence of the internal dynamics of recombinant human ubiquitin has been measured using solution NMR relaxation techniques. Nitrogen-15 relaxation has been employed to obtain a measure of the amplitude of subnanosecond motion at amide N-H sites in the protein. Deuterium relaxation has been used to obtain a measure of the amplitude of motion of methyl-groups in amino-acid side chains. Data was obtained between 5 and 55 degrees C. The majority of amide N-H and methyl groups show a roughly linear (R(2)>0.75) temperature dependence of the associated Lipari-Szabo model-free squared generalized-order parameter (O(2)) describing the amplitude of motion. Interestingly, for those sites showing a linear response, the temperature dependence of the backbone is distinct from that of the methyl-bearing side chains with the former being characterized by a significantly larger Lambda-value, where Lambda is defined as d ln(1 - O)/d lnT. These results are comparable to the sole previous such study of the temperature dependence of protein motion obtained for a calmodulin-peptide complex. This suggests that the distinction between the main chain and methyl-bearing side chains may be general. Insight into the temperature dependence is gathered from a simple two-state step potential model.     

Temperature change and complex dynamics

Density-dependent factors, such as population growth rate and migration, influence dynamic behaviour in ecological models. Temperature, an abiotic and density-independent factor, is also an important determinant of insect population growth. We investigated the endogenous dynamics of a density-dependent response-surface model that included temperature, based on time series for two aphid species. We investigated the effects of temperature and random noise on the model dynamics. In most cases, an increase in temperature resulted in a higher predicted equilibrium density; it could induce complex dynamics. Noise at the level of the natural variation in temperature resulted in extinctions in some models. Our results from these models indicate that aphid populations might become more abundant, and less stable in some circumstances, if there is climate warming. Received: 25 November 1996 / Accepted: 30 June 1997     

Backbone and side chain dynamics of mutant calmodulin-peptide complexes

The mechanism of long-range coupling of allosteric sites in calcium-saturated calmodulin (CaM) has been explored by characterizing structural and dynamics effects of mutants of calmodulin in complex with a peptide corresponding to the smooth muscle myosin light chain kinase calmodulin-binding domain (smMLCKp). Four CaM mutants were examined: D95N and D58N, located in Ca2+-binding loops; and M124L and E84K, located in the target domain-binding site of CaM. Three of these mutants have altered allosteric coupling either between Ca2+-binding sites (D58N and D95N) or between the target- and Ca2+-binding sites (E84K). The structure and dynamics of the mutant calmodulins in complex with smMLCKp were characterized using solution NMR. Analysis of chemical shift perturbations was employed to detect largely structural perturbations. 15N and 2H relaxation was employed to detect perturbations of the dynamics of the backbone and methyl-bearing side chains of calmodulin. The least median squares method was found to be robust in the detection of perturbed sites. The main chain dynamics of calmodulin are found to be largely unresponsive to the mutations. Three mutants show significantly perturbed dynamics of methyl-bearing side chains. Despite the pseudosymmetric location of Ca2+-binding loop mutations D58N and D95N, the dynamic response of CaM is asymmetric, producing long-range perturbation in D58N and almost none in D95N. The mutations located at the target domain-binding site have quite different effects. For M124L, a local perturbation of the methyl dynamics is observed, while the E84K mutation produces a long-range propagation of dynamic perturbations along the target domain-binding site.     

The role of electrostatic interactions in calmodulin-peptide complex formation

The complex between calmodulin and the calmodulin-binding portion of smMLCKp has been studied. Electrostatic interactions have been anticipated to be important in this system where a strongly negative protein binds a peptide with high positive charge. Electrostatic interactions were probed by varying the pH in the range from 4 to 11 and by charge deletions in CaM and smMLCKp. The change in net charge of CaM from approximately -5 at pH 4.5 to -15 at pH 7.5 leaves the binding constant virtually unchanged. The affinity was also unaffected by mutations in CaM and charge substitutions in the peptide. The insensitivity of the binding constant to pH may seem surprising, but it is a consequence of the high charge on both protein and peptide. At low pH it is further attenuated by a charge regulation mechanism. That is, the protein releases a number of protons when binding the positively charged peptide. We speculate that the role of electrostatic interactions is to discriminate against unbound proteins rather than to increase the affinity for any particular target protein.     

Redistribution and loss of side chain entropy upon formation of a calmodulin-peptide complex

The response of the internal dynamics of calcium-saturated calmodulin to the formation of a complex with a peptide model of the calmodulin-binding domain of the smooth muscle myosin light chain kinase has been studied using NMR relaxation methods. The backbone of calmodulin is found to be unaffected by the binding of the domain, whereas the dynamics of side chains are significantly perturbed. The changes in dynamics are interpreted in terms of a heterogeneous partitioning between structure (enthalpy) and dynamics (entropy). These data provide a microscopic view of the residual entropy of a protein in two functional states and suggest extensive enthalpy/entropy exchange during the formation of a protein-protein interface.     

Temperature dependence of protein-hydration hydrodynamics by molecular dynamics simulations

The dynamics of water molecules near the protein surface are different from those of bulk water and influence the structure and dynamics of the protein itself. To elucidate the temperature dependence hydration dynamics of water molecules, we present results from the molecular dynamic simulation of the water molecules surrounding two proteins (Carboxypeptidase inhibitor and Ovomucoid) at seven different temperatures (T=273 to 303 K, in increments of 5 K). Translational diffusion coefficients of the surface water and bulk water molecules were estimated from 2 ns molecular dynamics simulation trajectories. Temperature dependence of the estimated bulk water diffusion closely reflects the experimental values, while hydration water diffusion is retarded significantly due to the protein. Protein surface induced scaling of translational dynamics of the hydration waters is uniform over the temperature range studied, suggesting the importance protein-water interactions.     

Temperature dependence of vesicular dynamics at excitatory synapses of rat hippocampus

How vesicular dynamics parameters depend on temperature and how temperature affects the parameter change during prolonged high frequency stimulation was determined by fitting a model of vesicular storage and release to the amplitudes of the excitatory post-synaptic currents (EPSC) recorded from CA1 neurons in rat hippocampal slices. The temperature ranged from low (13 °C) to higher and more physiological temperature (34 °C). Fitting the model of vesicular storage and release to the EPSC amplitudes during a single pair of brief high–low frequency stimulation trains yields the estimates of all parameters of the vesicular dynamics, and with good precision. Both fractional release and replenishment rate decrease as the temperature rises. Change of the underlying ‘basic’ parameters (release coupling, replenishment coupling and readily releasable pool size), which the model-fitting also yields is complex. The replenishment coupling between the readily releasable pool (RRP) and resting pool increases with temperature (which renders the replenishment rate higher), but this is more than counterbalanced by greater RRP size (which renders the replenishment rate lower). Finally, during long, high frequency patterned stimulation that leads to significant synaptic depression, the replenishment rate decreases markedly and rapidly at low temperatures (<22 °C), but at high temperatures (>28 °C) the replenishment rate rises with stimulation, making synapses better able to maintain synaptic efficacy.     

Temperature dependence of the structure and dynamics of myoglobin. A simulation approach

The results of simulations of the structure and internal motions of carbonomonoxymyoglobin (MbCO) at two different temperatures (325 and 80 K) are presented and compared with experimental data. Properties calculated from the 120 ps trajectory at 325 K are used as a reference in the analysis of the motion of the protein at 80 K. Three separate 80 K molecular dynamics trajectories were calculated; they were started with different coordinate sets from the 325 K simulation and the lower temperature was achieved by scaling the velocities. The simulations yield results for the structural changes between 325 and 80 K that are in general accord with those from X-ray data. Both the experimental and calculated radii of gyration, distances from the center of mass and main-chain difference distance matrices show that there is a significant but inhomogeneous shrinkage with decreasing temperature. For the atomic fluctuations, by contrast, the calculated temperature dependence is very different from the X-ray results; i.e. the calculated root-mean-square backbone fluctuations decrease to 0.11 A at 80 K from 0.51 A at 325 K, while the fluctuations obtained from the X-ray B factors go from 0.56 A at 260 K to 0.47 A at 80 K. The smaller temperature dependence of the B factors suggests that there is significant conformational disorder in MbCO crystals at lower temperatures. This is in accord with the simulation results, which show that the protein is trapped in restricted regions of conformational space at 80 K, while at 325 K a much larger region is accessible to the protein. Analysis of the fluctuations at 325 K and 80 K shows that the room temperature flexibility of the protein is determined by the mobility of the loop regions and by side-chain torsional motions (in accord with earlier simulation results), while the low temperature fluctuations involve motion within a single well. Examination of the calculated iron atom fluctuations and comparison with Mossbauer data show good agreement. It is found that the dominant contribution to the iron motion arises from heme sliding; motion of the iron relative to the heme are much smaller.     

Temperature dependence of the electronic spin-lattice relaxation time in a 2-iron-2-sulphur model complex

The complex [Fe2S2(S2-o-xylyl)2]2- in DMF (dimethylformamide), DMSO (dimethylsulphoxide) or a 1:1 DMF/DMSO mixture, a model for the chromophore in the 2Fe-2S proteins (ferredoxins), has been reduced and studied by conventional EPR over a temperature range. The low-field feature of the spectrum, Hz, has been computer simulated in order to analyse the lineshape in terms of a convolution product of Lorentzian and Gaussian distributions. The Gaussian contribution to the linewidth and a fixed part of the Lorentzian contribution, which is a function of the solvent and the way it freezes, were measured at a low temperature (less than or equal to 100 K) and subtracted from the linewidths in the higher-temperature range (130-200 K). The variable Lorentzian contribution thus obtained was related to spin-lattice relaxation times. The spin-lattice relaxation times of the sample having 1:1 DMSO/DMF solvent were measured in the range 6 to 11 K by the saturating pulse technique and in the range 10 to 65 K by continuous saturation methods. Up to 65 K the results follow the law 1/T1 alpha T4.5, a relationship which is not readily interpreted in terms of a simple Debye model. At higher temperatures the results may be interpreted in terms either of a dominant Orbach mechanism involving excited states at approx. 900 +/- 50 cm-1 (DMSO, DMF) or 770 +/- 50 cm-1 (1:1 DMSO/DMF), or of a Raman process in which 1/T1 alpha T7.5. The former is compatible with the two-phonon process already described in some ferredoxins, especially those with little anisotropy (gy - gx approximately 0.0) which have characteristically high [J] values.     

Temperature dependence of fast carbonyl backbone dynamics in chicken villin headpiece subdomain

Temperature-dependence of protein dynamics can provide information on details of the free energy landscape by probing the characteristics of the potential responsible for the fluctuations. We have investigated the temperature-dependence of picosecond to nanosecond backbone dynamics at carbonyl carbon sites in chicken villin headpiece subdomain protein using a combination of three NMR relaxation rates: ¹³C′ longitudinal rate, and two cross-correlated rates involving dipolar and chemical shift anisotropy (CSA) relaxation mechanisms, ¹³C′/¹³C′-¹³C^α CSA/dipolar and ¹³C′/¹³C′–¹⁵N CSA/dipolar. Order parameters have been extracted using the Lipari-Szabo model-free approach assuming a separation of the time scales of internal and molecular motions in the 2–16°C temperature range. There is a gradual deviation from this assumption from lower to higher temperatures, such that above 16°C the separation of the time scales is inconsistent with the experimental data and, thus, the Lipari-Szabo formalism can not be applied. While there are variations among the residues, on the average the order parameters indicate a markedly steeper temperature dependence at backbone carbonyl carbons compared to that probed at amide nitrogens in an earlier study. This strongly advocates for probing sites other than amide nitrogen for accurate characterization of the potential and other thermodynamics characteristics of protein backbone.     

Temperature dependence of dynamics and thermodynamics of the regulatory domain of human cardiac troponin C

Binding of Ca(2+) to the regulatory domain of troponin C (TnC) in cardiac muscle initiates a series of protein conformational changes and modified protein-protein interactions that initiate contraction. Cardiac TnC contains two Ca(2+) binding sites, with one site being naturally defunct. Previously, binding of Ca(2+) to the functional site in the regulatory domain of TnC was shown to lead to a decrease in conformational entropy (TDeltaS) of 2 and 0.5 kcal mol(-1) for the functional and nonfunctional sites, respectively, using (15)N nuclear magnetic resonance (NMR) relaxation studies [Spyracopoulos, L., et al. (1998) Biochemistry 37, 18032-18044]. In this study, backbone dynamics of the Ca(2+)-free regulatory domain are investigated by backbone amide (15)N relaxation measurements at eight temperatures from 5 to 45 degrees C. Analysis of the relaxation measurements yields an order parameter (S(2)) indicating the degree of spatial restriction for a backbone amide H-N vector. The temperature dependence of S(2) allows estimation of the contribution to protein heat capacity from pico- to nanosecond time scale conformational fluctuations on a per residue basis. The average heat capacity contribution (C(p,j)) from backbone conformational fluctuations for regions of secondary structure for the regulatory domain of cardiac apo-TnC is 6 cal mol(-1) K(-1). The average heat capacity for Ca(2+) binding site 1 is larger than that for site 2 by 1.3 +/- 0.8 cal mol(-1) K(-1), and likely represents a mechanism where differences in affinity between Ca(2+) binding sites for EF hand proteins can be modulated.     

Temperature dependence of cytochrome photooxidation and conformational dynamics of Chromatium reaction center complexes

A temperature dependence of multiheme cytochrome c oxidation induced by a laser pulse was studied in photosynthetic reaction center preparations from Chromatium minutissimum. Absorbance changes and kinetic characteristics of the reaction were measured under redox conditions where one or all of the hemes of the cytochrome subunit are chemically reduced (E _h =+300 mV or E _h =–20 to -60 mV respectively). In the first case photooxidation is inhibited at temperatures lower than 190–200 K with the rate constant of the photooxidation reaction being practically independent on temperature over the range of 300 to 190 K (k=2.2×10⁵ s^-1). Under reductive conditions (E _h =–20 to -60 mV) lowering the temperature to 190–200 K causes the reaction to slow from k=8.3×10⁵ s^-1 to 2.1×10⁴ s^-1. Under further cooling down to the liquid nitrogen temperature, the reaction rate changes negligibly. The absorption amplitude decreases by 30–40% on lowering the temperature. A new physical mechanism of the observed critical effects of temperature on the rate and absorption amplitude of the multiheme cytochrome c oxidation reaction is proposed. The mechanism suggests a close interrelation between conformational mobility of the protein and elementary electron tunneling act. The effect of freezing conformational motion is described in terms of a local diffusion along a random rough potential.     

Temperature dependence of rotational dynamics of protein and lipid in sarcoplasmic reticulum membranes

We have investigated the relationship between function and molecular dynamics of both the lipid and the Ca-ATPase protein in sarcoplasmic reticulum (SR), using temperature as a means of altering both activity and rotational dynamics. Conventional and saturation-transfer electron paramagnetic resonance (EPR) was used to probe rotational motions of spin-labels attached either to fatty acid hydrocarbon chains or to the Ca-ATPase sulfhydryl groups in SR. EPR studies were also performed on aqueous dispersions of extracted SR lipids, in order to study intrinsic lipid properties independent of the protein. While an Arrhenius plot of the Ca-ATPase activity exhibits a clear change in slope at 20 degrees C, Arrhenius plots of lipid hydrocarbon chain mobility are linear, indicating that an abrupt thermotropic change in the lipid hydrocarbon phase is not responsible for the Arrhenius break in enzymatic activity. The presence of protein was found to decrease the average hydrocarbon chain mobility, but linear Arrhenius plots were observed both in the intact SR and in extracted lipids. Lipid EPR spectra were analyzed by procedures that prevent the production of artifactual breaks in the Arrhenius plots. Similarly, using sample preparations and spectral analysis methods that minimize the temperature-dependent contribution of local probe mobility to the spectra of spin-labeled Ca-ATPase, we find that Arrhenius plots of overall protein rotational mobility also exhibit no change in slope. The activation energy for protein mobility is the same as that of ATPase activity above 20 degrees C; we discuss the possibility that overall protein mobility may be essential to the rate-limiting step above 20 degrees C.     

Temperature dependence of protein dynamics: computer simulation analysis of neutron scattering properties

The temperature dependence of the internal dynamics of an isolated protein, bovine pancreatic trypsin inhibitor, is examined using normal mode analysis and molecular dynamics (MD) simulation. It is found that the protein exhibits marked anharmonic dynamics at temperatures of approximately 100-120 K, as evidenced by departure of the MD-derived average mean square displacement from that of the harmonic model. This activation of anharmonic dynamics is at lower temperatures than previously detected in proteins and is found in the absence of solvent molecules. The simulation data are also used to investigate neutron scattering properties. The effects are determined of instrumental energy resolution and of approximations commonly used to extract mean square displacement data from elastic scattering experiments. Both the presence of a distribution of mean square displacements in the protein and the use of the Gaussian approximation to the dynamic structure factor lead to quantified underestimation of the mean square displacement obtained.     

Exploration of the correlation between solvation dynamics and internal dynamics of a protein

Protein function is intimately related to the dynamics of the protein as well as to the dynamics of the solvent shell around the protein. Although it has been argued extensively that protein dynamics is slaved to solvent dynamics, experimental support for this hypothesis is scanty. In this study, measurements of fluorescence anisotropy decay kinetics have been used to determine the motional dynamics of the fluorophore acrylodan linked to several locations in a small protein barstar in its various structural forms, including the native and unfolded states as well as the acid and protofibril forms. Fluorescence upconversion and streak camera measurements have been used to determine the solvation dynamics around the fluorophore. Both the motional dynamics and solvent dynamics were found to be dependent upon the location of the probe as well as on the structural form of the protein. While the (internal) motional dynamics of the fluorophore occur in the 0.1-3 ns time domain, the observed mean solvent relaxation times are in the range of 20-300 ps. A strong positive correlation between these two dynamical modes was found in spite of the significant difference in their time scales. This observed correlation is a strong indicator of the coupling between solvent dynamics and the dynamics in the protein.