KR101739323B1 - Protein stability analysis method using protein folding thermodynamic - Google Patents
Protein stability analysis method using protein folding thermodynamic Download PDFInfo
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Abstract
The present invention relates to a method for measuring conformational entropy of a biomolecule, a method for measuring free energy of a biomolecule, and a method for measuring a free energy difference between two states of the same biomolecule. Unlike conventional structural methods, the method of the present invention can produce reliable results without distortion by multi-local energy walls and efficiently calculate protein folding free energy by applying an energy method. The present invention can be used to describe protein-folding and protein ligand binding thermodynamics, predict their stability, and establish biological therapeutic strategies.
Description
The present invention relates to a method for analyzing a morphological change of a protein using an energy method.
The formation of protein folding and protein-protein, protein-ligand complexes involves a change in the shape of protein backbone and side chains in form entropy. Decrease in shape entropy is a major thermodynamic instability factor for protein folding [1]. Form entropy is also a key component of protein-ligand-coupled thermodynamics [2]. Recent NMR studies show how protein-ligand binding affinities involved in gene regulation and signaling are regulated through shape entropy [35]. Therefore, accurate evaluation of shape entropy is important in experimental studies, stability prediction, and structure-based design of biotherapy. However, the calculation of form entropy for complex biomolecules is known to be a difficult problem, and there are difficulties in deriving important thermodynamic quantities through computational methods [6-10]. The main difficulty in calculating the shape entropy is that it can not be computed through the protein structure and instead it has to compute the configuration integral, Z, which is the potential part of the distribution function. In the protein-water system, Z is the Boltzmann factor for the coordination of protein and water
Here, the 3N -dimensional vector r represents the protein form by the constituent atom N. f = Eu + Δ μ is the solvent-leveled effective energy of the inner-protein energy Eu and the solvation free energy, and defines the free-energy topography in protein form space [11]. A more simplified calculation method is required to obtain the coordinate integration Z of a complex biomolecule such as a protein. According to the quasi-harmonic method, which is the most widely used approach, the quadratic form of the effective energy f is transformed into a 3N × 3N covariance matrix σ iajb = Δr a- i r b j (i, j = 1, ..., N; a, b = x, y or z) [13-15].
In the following, bar represents the average of protein forms.
Here, I represents a unit matrix,
Numerous papers and patent documents are referenced and cited throughout this specification. The disclosures of the cited papers and patent documents are incorporated herein by reference in their entirety to better understand the state of the art to which the present invention pertains and the content of the present invention.
The present inventors have made extensive efforts to develop analytical methods for thermodynamically quantifying the morphological changes of various biomolecules, particularly proteins. As a result, it can be concluded that the derivation of the reliable results without distortion by the multi-local energy walls, unlike the conventional structural methods, can be achieved by using the energy method of formulating the protein type entropy estimating the Gaussian fluctuation in the horizontal axis and vertical axis of the free energy topography And found that the protein folding free energy can be efficiently calculated, thereby completing the present invention.
Accordingly, an object of the present invention is to provide a method for measuring conformational entropy of biomolecules.
Another object of the present invention is to provide a method for measuring free energy of biomolecules.
It is another object of the present invention to provide a method for measuring free energy difference between two states of the same biomolecule.
Other objects and advantages of the present invention will become more apparent from the following detailed description of the invention, claims and drawings.
According to one aspect of the present invention, the present invention provides a method for measuring conformational entropy of biomolecules comprising the steps of:
(a) measuring the solvent-averaged effective energy of a biomolecule to be analyzed:
(b) measuring fluctuations of the effective energy using the solvent-leveled effective energy measured in the step (a); And
(c) determining the shape entropy of the biomolecule by using the variation of the effective energy measured in the step (b).
The present inventors have made extensive efforts to develop analytical methods for thermodynamically quantifying the morphological changes of various biomolecules, particularly proteins. As a result, it can be concluded that the derivation of the reliable results without distortion by the multi-local energy walls, unlike the conventional structural methods, can be achieved by using the energy method of formulating the protein type entropy estimating the Gaussian fluctuation in the horizontal axis and vertical axis of the free energy topography And found that the protein folding free energy can be calculated efficiently.
The term "biomolecule" as used herein refers to a series of macromolecules present in vivo, such as proteins, oligonucleotides, polysaccharides, and the like. These polymers are affected by the three dimensional morphology and state change tendency due to their size, charge of constituent residues, hydrophobicity, formation of covalent and noncovalent bonds, and may become a cause of various diseases when these types and trends are abnormal. According to a specific embodiment of the present invention, the biomolecule to be analyzed in the present invention is a protein.
Since protein conformational anomalies (eg, misfolding) cause protein aggregation disorders such as Alzheimer's disease, Parkinson's disease and
As used herein, the term "form entropy" refers to the entropy associated with the number of forms that a molecule has in a different state, and more specifically, the entropy that reflects the energy state of a particular form of the molecule it means.
As used herein, the term "measurement " is intended to encompass a series of deductive and inductive processes that derive unknown values utilizing specific data, and are used interchangeably with calculation, prediction, identification, and determination. Therefore, the term measurement in the present invention includes all of experimental measurement, relationship establishment between plural variables, and computational calculation according to the established relationship.
As used herein, the term "effective energy" means the amount of energy after mathematically correcting various factors affecting the total energy. As used herein, the term " solvent-averaged effective energy "means an effective energy considering the effect of a solvent on the energy state of the molecule. For example, in the case of a protein dissolved in water, Water < / RTI > and water-water interactions.
According to a specific embodiment of the present invention, step (a) of the present invention is performed by measuring the intra-molecular energy and the solvation free energy of the biomolecule. More specifically, it is performed using the following equation:
Where f is the solvent-leveled effective energy, Eu is the internal energy of the biomolecule, and [ mu] is the solvated free energy.
According to a more specific embodiment of the invention, the solvation free energy is determined using the following equation:
Wherein, Δ μ is the solvated free energy for, ρ is the water, the number density (number density), k B is the Boltzmann's constant, θ (x) is the Heaviside (Heaviside) step function, h (r) is the total , And c ? (R) is a direct association function.
According to a specific embodiment of the present invention, step (b) of the present invention is carried out using the following equation:
In the above equation,? F is the effective energy variation, f is the solvent-leveled effective energy,
According to a specific embodiment of the present invention, step (c) of the present invention is carried out using the following equation:
In the above equation,
According to another aspect of the present invention, there is provided a method for measuring free energy of a biomolecule comprising the steps of:
(a) the average solvent-averaged effective energy of biomolecules; And measuring the conformational entropy of the biomolecule;
(b) determining the free energy of the biomolecule using the average solvent-leveled effective energy measured in the step (a) and the shape entropy.
The concept "solvent-averaged effective energy" and conformational entropy of a biomolecule used in the present invention have already been described above, so that description thereof is omitted in order to avoid excessive redundancy.
According to a specific embodiment of the present invention, step (b) of the present invention is carried out using the following equation:
F o =
In the above equation, F o is the free energy,
According to another aspect of the present invention, the present invention provides a method for measuring free energy difference between two states of the same biomolecule comprising the steps of:
(a) a difference in average solvent-averaged effective energy between biomolecules in the first and second states; And measuring a difference in conformational entropy between biomolecules in the first and second states;
(b) determining a free energy difference between biomolecules of the first state and the second state using the average solvent-leveled effective energy difference measured in the step (a) and the shape entropy difference.
As used herein, the terms "first state" and "second state" refer to mutually different physico-chemical states in which the same biomolecules are present in time in the living body. The first and second states have different three-dimensional structures that are spectroscopically separated according to temperature, covalent bonding, noncovalent interaction, reaction with surrounding water molecules, and the like. For example, folding of a protein composed of the same amino acid This is the state and the unfolded state. The difference in free energy between the first state and the second state provides important information on the mechanism of the change of state of biomolecules, the orientation, and the stability of biomolecules. The present inventors have found that protein folding free energy can be derived using a probability distribution of solvent-averaged protein effective energies.
According to a specific embodiment of the present invention, step (b) of the present invention is carried out using the following equation:
ΔF o = Δ
In the above equation,? F o is the free energy difference between biomolecules in the first and second states,?
The features and advantages of the present invention are summarized as follows:
(a) The present invention provides a method for measuring the shape entropy of a biomolecule, a method for measuring free energy of a biomolecule, and a method for measuring a free energy difference between two states of the same biomolecule.
(b) The method of the present invention is able to derive reliable results without distortion by multi-local energy walls unlike conventional structural methods by applying an energy method to biomolecule type analysis and efficiently calculate free energy of protein folding .
(c) The present invention can be used to describe protein-folding and protein ligand-binding thermodynamics, predict their stability, and establish biological therapeutic strategies.
Figure 1A is a graph showing the CRMSD relative to the NMR structure (except the terminal residues) as a function of simulation time. The time zones corresponding to the different clusters (clusters 1-6) are indicated by different colors. FIG. 1B is a diagram showing a result of projecting a mass-weighted displacement trajectory in a two-dimensional space over first and second main axes of a mass-weighted covariance matrix. FIG. The dotted curve refers to the area sampled by simulation, but according to the parametric method, the area is the most sampled area. In addition, a representative form of six clusters is shown. Each protein structure was color-coded from blue to red from the N-terminus to the C-terminus according to its sequence. For comparison, the NMR structure is shown in clear gray.
2A is a diagram showing a probability density function P (d1) (black solid line curve) of the first main coordinate d1. The curve of the red dotted line indicates that it matches the Gaussian function. Contribution to P ( d1 ) from the protein forms belonging to clusters 1-6 was indicated together (lower panel) and shifted vertically to avoid overlapping of the curves. FIG. 2B shows a result corresponding to the probability density function P (d2) of the second main coordinate.
FIG. 3A shows a probability density function W ( f ) (black solid line curve) for the effective energy f . The curve of the red dotted line indicates that it matches the Gaussian function. The contribution of W ( f ) from the protein form belonging to clusters 1-6 was shown and shifted vertically to avoid overlap of curves.
4A is a graph showing the probability density function P ( Eu ) of the inner-protein energy Eu (upper panel). The contribution of P ( Eu ) from the protein form belonging to clusters 1-6 is shown in the lower panel and shifted vertically to avoid overlap of curves. Figure 4b shows the results corresponding to the probability density function P ([Delta] [ mu] ) of solvation free energy [Delta] [ mu ].
5 shows a representative folded state form (Fig. 5C) from the NMR structure (Fig. 5A) of HP-36 (PDB ID: 1), the NMR structure of the typical folded state form (Fig. 5B) and the locus UNFOLD1-UNFOLD10 from the locus FOLD1- ) ≪ / RTI > NMR structure.
6 is a graph showing a probability distribution function.
7 is a graph showing a standard error.
Fig. 8 is a schematic diagram showing the principle of calculation of free energy of protein folding according to the present invention.
Hereinafter, the present invention will be described in more detail with reference to Examples. It is to be understood by those skilled in the art that these embodiments are only for describing the present invention in more detail and that the scope of the present invention is not limited by these embodiments in accordance with the gist of the present invention .
Example
Implementation 1: Measurement of shape entropy
The present inventors have attempted to use an energy-based method to measure protein form entropy. This method starts from the reconstruction of the following coordinate integrals, focusing on the effective energy f , not the protein structure:
The above equation is expressed on the basis of the density function W (f) α∫drδ (ff (r)) of the effective energy normalized to be ∫d f W ( f ) = 1. (Due to the use of normalized W (f)
The fundamental assumption in the energy approach is the Gaussian assumption for W ( f ). In this case, the protein form entropy can be estimated as follows:
In this equation, the effective energy variation? F = f -
Experimental Method
MD simulation
An entire atom, explicit-water MD simulation for HP-36 was performed from the structure revealed by NMR at T = 300 K and P = 1 bar (PDB ID: 1 [18]). For water, the ff99SB force field [32] and the TIP3P model [33] were used. HP-36 was dissolved in 6693 water molecules and two Cl - ion clusters. After a standard minimization and equilibration procedure, a 20-ns time-of-production run was performed. The short-range non-bonding interactions were cut off at 10 Å, while long-range electrostatic interactions were processed by the particle mesh Ewald method [34]. Berendsen thermostats and pressure regulators with 1.0 and 2.0 ps coupling constants were used to control temperature and pressure [35]. 40,000 protein forms were taken from the 20-ns trajectory at 0.5ps time intervals and used for further analysis. The DSSP program [36] was used to calculate the secondary structure. RMSD-based K- means clustering analysis of 2.5 Å cut-off was introduced to determine representative protein forms and to demonstrate the presence of distinct multi-local energy walls in free energy terrains [37].
Type entropy based on structural approach
The covariance matrices fused to the quasi - harmonization method were calculated using the simulated protein form as follows. First, to eliminate external (translational and rotational) degrees of freedom, each protein form was geometrically matched to the initial shape using least squares. The backbone (N, C α , C) atoms other than terminal terminal atoms were used in least squares. Since then the average position
The mass-weighted covariance matrix M 1/2 αM 1/2 is constructed by a diagonal matrix M iajb = δ ij δ ab m i containing the mass mi of the constituent atoms replaced by equation (3)
? = U T (M 1/2 ? M 1/2 ) U (7)
U is called the principal axis matrix, and its ι th column vector u ι is the ι th principal axis. Specific value λ ι is the mass in a direction - shown by the square fluctuation-weighted average. The λ ι was sort ι th spindle to have a maximum value of ι th.
The mass-weighted 3 N- dimensional displacement vector M 1/2 Δr (t) from the mean shape at time t can be expressed as:
Here, the coefficient d ι ( t ), which is expressed as τ th, is the projection of the instantaneous form on the ι th principal axis at time t , which is referred to as the principal coordinate:
The loci of the first and second main coordinates are shown in Fig.
Type entropy based on energy method
Through the simulated protein form, the effective energy f = E u + Μ μ and its distribution W ( f ): E u is based on the applied force field, while μ μ is the 3D-RISM theory [38 , 39]. When W ( f ) is close to the Gaussian function, the protein type entropy
This leads to the derivation of the total association function h ν (r) and the direct association function c ν (r). Where χ νν ' (r) is the site-site water sensitivity function calculated from the genetically identical RISM theory [40] and d ν (r) = u ν (r) / ( k B T) + h ν (r) - c ν (r). Then the solvation free energy Δ μ was derived from the following equation [38,39]:
Where ρ is the number density of water and θ (χ) is the Heaviside step function.
Experiment result
We performed MD simulations on the folded protein villin headpiece subdomain (HP-36) to obtain the amount needed to examine the structure and energy approach [18]. The simulation was performed for 20 ns (T = 300 K, P = 1 bar) under ambient conditions starting from the NMR structure (PDB ID: 1 VII [18]) in which 40,000 protein forms were obtained at 0.5 ps time intervals. Based on these protein forms, a covariance matrix for starting the quasi-harmonic method was calculated and the density function W ( f ) of the effective energy f necessary for the energy approach was obtained. Over the simulated time scale, the NMR structure remained stable at 1.7 ± 0.3 A, the mean (± standard deviation) C α -RMSD value (FIG. 1a), and the simulated form was considered to correspond to the folded phase.
In order to investigate more specific characteristics of the folded morphology, six different clusters were derived as a result of classifying the simulated structure based on the cluster analysis (Fig. 1 and Table 1). The largest cluster (46.3%) of the simulated form was most similar to the NMR structure in the radius of rotation, both end distances and α-helix content. As can be inferred from the representative form shown in FIG. 1B, the overall structure of the other clusters was also similar to the NMR structure, but in particular several detailed differences such as both end distance and a-helix content were evident (Table 1). This shows that there is a distinct multi-local energy wall in the free energy topography of the folded HP-36. The transition between these local energy walls can be investigated through principal component analysis [19] and the mass-weighted displacement trajectory M 1/2 Δr ( t ) as the mass-weighted covariance matrix M 1/2 αM 1 / 2 < / RTI > (FIG. 1B). The fundamental approach in the quasi-coherence method is to predict the multivariate Gaussian distribution of protein morphology variability (Eqs. (1) and (2)). However, the presence of multi-local energy walls (Figure 1b) in free energy terrains, which are more often referred to in the simulation process, is inconsistent with these figures. In fact, this shows a probability distribution of the protein form along the main axis, which is largely deviated from the Gaussian form (Figs. 2a and 2b). The quasi-harmonization method efficiently integrates these multiplexed energy walls into a single wide wall (dashed lines in Figs. 2a and 2b), thereby overestimating the shape entropy value. Furthermore, in the conventional quasi-harmonization method, the main modes are independently considered, and possible associative effects are not considered. In order to demonstrate the existence of such associations, the protein form space, which was hardly sampled through simulation, was marked with a dotted circle (Fig. 1b), which can not be estimated with the prediction distribution shown in Figs. 2a and 2b alone. The area, such as the dotted circle in FIG. 1B, does not have an overall effect on shape entropy, but according to the parametric method, the area is the most sampled region because it is close to the minimum of the first and second major axes. For this reason, form entropy based on parametric methods is much larger than would be expected from the actual form of free energy terrain. On the other hand, only the actual sampled protein form by simulation contributes to the density function W ( f ). In particular, W ( f ) is hardly affected by areas that are not well sampled in shape space. Despite the presence of a distinct multiple energy wall (Fig. 1b) through simulation, the inventors have found that the density function W ( f ) is very close to a single Gaussian function (Fig. These results, despite their respective distributions for Eu , deviate significantly from the Gaussian function (Fig. 4). The observed Gaussian properties are indicated by the central limit principle, which is associated with the largest number of significant deletions of the similar energy terms of the Hamiltonian type. In particular, a deletion of between Eu and Δ μ particularly true, which internal protein and protein-shows the reflecting competition between water interaction and [20], whereby substantially the same distribution as the mirror image of each other (Fig. 4). The fact that W ( f ) follows the central marginal principle confirms that this is not well applied to small molecules, while the number of terms contributing to Hamiltonian equations is small. This fact is shown in FIG. S1 which shows W ( f ) of the four free amino acids systematically deviating from the Gauss equation.
Implementation 2: Measurement of free energy
We focus our attention on two states A and B (for example, Δ F 0 ) that determine an equilibrium relative population defined by (C A / C B ) eq through the relationship of equation (2) F 0 A - F 0 B between the standard free energy difference? F 0 = F 0 A - F 0 B between the folded state and the unfolded state, where? Is the folding free energy.
The standard free energies F 0 A and F 0 B represent the free energies for an ideal solution with the same reference concentration C 0 = M / V, where M and V are the number and volume of proteins, respectively. Thus, ΔF 0 can be defined as the difference between the free energy for an ideal solution of M proteins in state B, which is dissolved in the same volume V as the free energy for the ideal solution of M proteins in state A dissolved in volume V .
Next, we took a snapshot of the excess solution in the X state (where X represents A or B). A sample of the M protein type can then be obtained at state X, characterized by the effective energy f iX (i X = 1, .., M). The distribution function for each given sample of M effective energy is
Where M represents the average over the samples. (15) is derived by introducing the number of effective energies belonging to the density of the state n X ( f ), that is, the interval ( f, f + df ), for each sample with M effective energy { f iX }
<Log ∫ d f n X ( f ) e -> f > M, which is the "quenched" mean at the temperature at which the system does not freeze at the local free energy bottoms (in the case of proteins at physiological temperatures) The average in-log ∫ d f <n X ( f )> is equal to M e- βf . This gives the following equation (16): < RTI ID = 0.0 >
After introducing the normal probability distribution function, equation (17) is obtained.
Thus, the explicit dependence on M disappears and it is sufficient to deal with the normal distribution function W x ( f ) instead of the density of states in determining the standard free energy difference.
Here we have introduced a central assumption in the present approach; That is, it is assumed that the distribution function W x ( f ) is very close to the Gaussian distribution.
(
Thus, Eq. (19) shows that the system can detect differences in free energy terrain in two states (TΔS conf )
In our previous work, equations (19) and (20) were derived by first rewriting the configuration integrals in terms of the normalized quadrature function Wx ( f )
However, it is not reasonable to use the normal distribution function Wx ( f ) instead of the denormalized density of states in the corrected coordinate integration. In this study, the rationalization of the use of the normal distribution function Wx ( f ) in determining the standard free energy difference is explicitly explained through the derivation of equation (17).
The approach proposed here is referred to as an energy method because it is based on the statistical distribution of the effective energy f = E u + G solv . The main obstacle in this method is to measure the effective energy for a sufficient number of protein forms to establish a distribution function W ( f ) that can test the Gaussian property. This can be achieved not only by the protein form, but also by combining molecular dynamics simulations that generate the intraprotein energy E u and the theory of integral equations that enable the calculation of the solvation free energy, G solv , for each of the simulated forms . This energy approach is closely related to the random energy model, where the energy probability distribution is assumed to be a Gaussian function and the resulting entropy is expressed in terms of energy waves.
Finally, we note that the Helmholtz free energy is basically equal to the Gibbs free energy, since the pressure-volumetric term is usually negligible under physiological conditions. Therefore equations (19) and (20) in which F (Helmholtz free energy) is replaced by G (Gibbs free energy) can actually be applied.
Experimental Method
Simulation of molecular dynamics
Collapsed state simulation. Initial coordinates for HP-36 were obtained via the NMR structure. Specified water molecule dynamics simulations under all atomic, neutral pH conditions were performed with
Unfold state simulation. The following unfolded state simulations were performed from the thermally denaturated structures. We first performed a 20 ns NVT ensemble simulation after heating the system to a certain volume above T = 600 K after 200 ps NPT ensemble simulation at T = 300 K and P = 1 bar mentioned above. This led to an annealing simulation up to T = 300K at 50k intervals and a 1ns NVT ensemble simulation was performed at each intervening temperature. After this, a 1 ns NVT ensemble equilibrium simulation was performed at T = 300 K and P = 1 bar. Finally we performed a 5 μs production run at T = 300 K and P = 1 bar. The entire procedures were repeated 10 times at different random initial velocities to create 10 independent unfolded state trajectories. Structural analysis and solvation free energy calculations were performed on the last 1 μs trajectory (4-5 μs) derived from each of the 10 independent 5 μs actual operations.
Structural analysis . 100,000 protein forms with 10 ps time intervals were obtained from each of the 3 folded state trajectories and 10 unfolded state trajectories of 1 μs length. If the minimum distance between heavy atoms is less than 5.4 A and the distance is applied to the residues forming the hydrophobic core of HP-36, the hydrophobic contact will be greater than or equal to four residues, Lt; / RTI > We calculated the secondary structure content using the DSSP program in the AMBER11 distribution. K-means-based root mean square deviation (rmsd) clustering analysis was performed to obtain a representative protein form. The MMTSB tool set was used to analyze the cutoff value 4.0 for C alpha and C beta atoms in the protein.
Calculation of solvation free energy : The 3D-RISM (three-dimensional reference interaction site model) theory was applied to calculate the solvation free energy for each of the simulated protein forms. According to this theory, the 3D distribution function g ν (r) of the position ν of the water at the position r around the protein is consistently d ν (r) = -u ν (r) / (k B T) + h ν ν (r) is obtained through the 3D-RISM equation (10) and closure relation (22).
(h ν (r) = g ν (r) - 1 is the 3D overall correlation function of the water position ν). c ? (r) is the corresponding direct correlation function; χ νν ' (r) represents a site-site water susceptibility function that is treated as an input for this theory; And u ν (r) is the interaction potential generated by the protein atoms. The procedures were used to solve the above equations as well as the yield function for the TIP3P water model calculated from a consistent RISM theory dielectrically. The solvation free energy can then be calculated using the following analytical formula (23).
Where θ (x) is the Heaviside step function and ρ is the number density of the water.
Because of the similar nature of the closure relation, it is inevitable that the absolute value of the solvation free energy calculated from the 3D-RISM theory depends on the closed relationship used. On the other hand, the relative value of solvation free energy is quite accurate due to the elimination of errors. Since only the relative values of solvation free energy are input to the standard free energy difference (Eq. (8)), it is expected that the experimental results of the present invention will not be significantly affected by the inherent constraints of the 3D-RISM theory.
Statistical analysis
Gauss method. Our central assumption is that the distribution function W ( f ) has a Gaussian form. We mean,
Block-Averaging Method. We can calculate the mean effective energy f , TS conf = (β / 2) f 2 , and G 0 =
Bootstrap method. For large n, the number of blocks N b = N sim / n decreases for a given length N sim of the trajectory of the simulation. To improve the error estimate for large n, we use the blocked samples x =
B = 100 was used for bootstrapping.
Propagation of Errors . The standard error (σ ste ) for θ θ = θ folded- θ unfolded can be estimated from Eq. (26), which can be observed in the folded and unfolded state.
Experiment result
Folding-state simulation
We have calculated the folding free energy of the protein vinilin headpiece subdomain (HP-36) at physiological conditions (T = 300 K and P = 1 bar) to illustrate the applicability and utility of the energetic method. HP-36 is the shortest, natural, thermostable spiral protein that automatically folds on the microstructural scale and is the best model system for studying protein folding (previous studies have shown that HP-35 without N-terminal methionine But the physical properties of HP-35 and HP-36 are similar). The NMR-derived folding structure of HP-36 (PDB ID: 1VII) contains three short spirals tightly surrounding the hydrophobic core (Fig. 5A).
The inventors performed three independent folding-state simulations of each 1 μs length named FOLD1-FOLD3. A representative protein structure is shown in Figure 5B. The NMR structure was stable during the time scale of the simulation: the average C ? Rmsd value for the NMR structure (except the terminal residues) was ~ 2 Å. The radius of gyration (Rg) was similar to that of the NMR structure as observed in the NMR structure, close to the average of the inherent hydrophobic core contacts and the surrounding three short spirals, ~ 90% or more (Table 1: Structural characteristics).
Unfolding - state simulation
Generating unfolded proteins in physiological states is a serious problem because this form is virtually unattainable as the folded state simulation continues. We have performed unfolding simulations of high temperatures in NMR structures to initiate unfolded-state simulations for thermodynamically denatured protein forms. After performing the short annealing simulation, 5 μs operation was performed at T = 300 K and P = 1 bar.
The entire experiment was repeated to yield 10 independent 5 μs trajectories, corresponding to an accumulated simulation time of 50 μs. No folding of the HP-36 was observed in any trajectory over the time scale of the simulation. In this experiment, the protein form obtained from the final 1 μs trajectory (4 -5 μs) from each 5 μs production run was considered to belong to the unfolded state at T = 300 K, and the initial 4 μs trajectory was considered high temperature ) Unfolded state to T = 300 K unfolded state as a relaxation process. The 10 independent unfolded-state trajectories of each 1 μs length are referred to herein as UNFOLD1-UNFOLD10. Representative protein structures in this locus are shown in Figure 1c. The unfolded structure is characterized by a very large C ? Rmsd value (~ 7 A) in the NMR structure and rarely (~ 10-20%) hydrophobic core contact as observed in the NMR structure, (~ 0 to 70%, depending on the spiral and trajectory) form a secondary structure (Table 1).
Distribution of effective energy
FOLD1-FOLD3 and U NFOLD1-UNFOLD10 From each 1 μs long trajectory, 100,000 protein forms were analyzed at 10 ps time intervals. The internal energy ( E u) of each form of protein was calculated directly during the simulation. Solvation free energy (G solv ) was obtained by applying the 3D-RISM theory to the simulated protein form. The Eu and G solv values were combined to obtain W ( f ) = E u + G solv of the effective energy f . It can be seen that both the folded and unfolded W ( f ) curves (FIGS. 6A and 6D, respectively) are very similar to the Gaussian curves. In fact, both the skewness as well as the excess jurtosis of W ( f ) were very small in both the folded and unfolded-state trajectories (Table 2: asymmetry and excess kurtosis of the effective energy distribution function). E u and G solv are somewhat heterogeneous and their shape is different in different trajectories (Figures 6b and 6c for folded state trajectories and Figure 6e for unfolded state trajectories And 6f).
The Hamiltonian is essentially due to the central limit theory because many of them are pairwise sums of many similar energy terms, many of which are mutually exclusive (the relevance of the central limit theory to protein variation is Trion, MM Large Rev. Lett. 1996, 77, 1905-1908). ≪ / RTI > In particular, the cancellation between protein interactions (Eu) and protein-water interactions (G solv ) was pronounced, resulting in probability distributions P (E u ) and P (G solv ) a through Fig. 6b, 6c on the state trajectory, the trajectory stored in the counter P (E u) mainly lower Eu region P (G solv), P ( G solv) , which peak is further located in the high G solv area , And the weight is also the same)
The anti-correlation between P (Eu) and P (G solv ) can also be seen in Figures 6e and 6f for the unfolded state trajectory. This reflects competition between protein-protein interactions and protein-water interactions. For example, if the hydrogen bond of a protein is broken and water is replaced by water, Eu is increased while G solv is decreased, and the inverse is also the same. Therefore, when the cancellation between Eu and G solv is large, a gentler Gaussian variation is obtained at f = E u + G solv .
Folding thermodynamics
The Gaussian characteristic of the W (f) curve in both the folded and unfolded states of the HP-36 is the mean of the distribution
The calculated folding free energy, ΔG O = -2.5 kcal / mol (standard error 2.0 kcal / mol), is in agreement with the experimental range of -2.3 to -3.2 kcal / mol (depending on the experimental method) ΔG O = -3.1 kcal / mol, -2.3 kcal / mol in the triplet-life time experiment, -3.2 kcal / mol in the case of urea denaturation, -2.4 kcal / mol in the case of guanidinium chloride modification, -2.9 kcal / mol in spectroscopy)
While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the same is by way of illustration and example only and is not to be construed as limiting the scope of the present invention. Accordingly, the actual scope of the present invention will be defined by the appended claims and their equivalents.
Claims (12)
(a) the average solvent-averaged effective energy of biomolecules; And measuring the conformational entropy of the biomolecule; And
(b) determining the free energy of the biomolecule using the average solvent-leveled effective energy and the shape entropy measured in the step (a) using the following equation:
In the above equation, F ° is the free energy of the biomolecule,
(a) a difference in average solvent-averaged effective energy between biomolecules in the first and second states; And measuring a difference in conformational entropy between biomolecules in the first and second states; And
(b) determining a difference between the mean solvent-leveled effective energy measured in step (a) and the shape-type entropy difference using the following equation, and determining a free energy difference between biomolecules in the first state and the second state, :
In the above equation,? F ° is a free energy difference between biomolecules in the first state and the second state,
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