KR102039793B1 - A Method for Predicting a Binding of Biological Molecules - Google Patents

Abstract

)을 측정하는 방법에 관한 것이다. 본 발명은 또한 자유에너지 측정을 통해 수성 환경에서의 제1 분자 및 제2 분자의 결합여부를 예측하는 방법을 제공하며, 이를 통해 생체 내(in vivo)와 같은 수성 환경에서 분자들 간의 결합 가능성을 왜곡 없이 높은 신뢰도로 정량 측정할 수 있어, 컴퓨터 상에서 질환 치료제를 스크리닝하거나 디자인하는 도구로서 유용하게 적용될 수 있다. According to the present invention, the amount of change in effective binding free energy ( f _u ) and standard binding free energy between the first molecule and the second molecule in an aqueous environment (

) Is a method of measuring. The present invention also provides a method for predicting the binding of a first molecule and a second molecule in an aqueous environment through free energy measurement, thereby determining the possibility of binding between molecules in an aqueous environment such as in vivo . It can be quantitatively measured with high reliability without distortion, and can be usefully applied as a tool for screening or designing a disease therapeutic agent on a computer.

Description

A Method for Predicting a Binding of Biological Molecules

The present invention relates to a method for predicting the formation of bonds of biomolecules by investigating the dynamic and thermodynamic properties of water molecules present on the interface between biomolecules.

Water is an active and indispensable component of cells. Understanding the different roles of water in determining the structure and dynamics of biomolecules and mediate interactions between them is very important ^{1 - 3.} The various functions of water in biological tissues stem from their ability to change their properties depending on which biomolecules they interact with. For example, the DNA sequence-dependent hydration tendency of water functions as a sequence-specific “hydration fingerprint” ⁴ ; Changes in water dynamics in the course of the substrate is bonded to the enzyme protein-ligand recognizing the important and ^5, Trans to cone (translocon) water ratio in the internal-bulk (non-bulk) action ranging from cone trans membrane This greatly affects the partitioning of hydrophobic regions of ^six . However, in recent years, despite the significant advance understanding of the behavior of a living body hydration water (hydrating water) around the molecule, and ^7-14, two water molecules in between the biomolecule has been modified to a certain extent by the interaction between the two bonding surfaces The extent to which these modified water molecules affect the binding affinity has not yet been explained. In this regard, water-mediated contact has been proposed to provide additional layers for biomolecule recognition by substantially complementing protein-protein direct contact ^{15 , 16} . It is important to adequately describe the interactions mediated by contact water molecules, and in fact, recent computer research is important to clearly analyze the interfacial water, which is critical for protein-protein interactions ¹⁸ and protein-ligand binding ¹⁹ . For example, contact surface water molecules are important for identifying trends observed in mutations affecting protein-protein binding affinity, ¹⁸ and in other studies contact surface in the range of water molecules ( N _wat ) 30-70. The consideration of water molecules significantly increased the relevance to the binding affinity experimental values in four different systems where the optimal value of N _wat depends on the unique system ¹⁹ . However, it is unclear how to distinguish these key contact surface water molecules from other water molecules, and whether there are other distinguishing features of the contact surface water molecules that appear during protein-protein complex formation.

We investigated the dynamic and thermodynamic properties of contact surface water in the varnase-barstar complex ¹⁵ . X-ray measurement reveals the presence of water that fills the gap between the binding surfaces ^{15 , 20} , which is a well-known paradigm in the study of protein-protein interactions and is an ideal method for analyzing contact surface water molecules. We performed molecular dynamics simulations to analyze the dynamic properties of contact surface water molecules. The inventors noted the rearrangement of hydrogen bonds, which is most important for protein-water interactions in that the protein-protein binding surface consists mostly of polar and charged residues ²¹ .

We performed statistical thermodynamic analysis to explain the kinetic properties of the contact surface water molecules. Finally, we would like to discuss the effect of contact surface water kinetics on interprotein binding affinity. The inventors have found that conventional approaches to water-mediated interactions that presume the separation of time units between protein and hydrated water kinetics cannot be successful due to the extremely slow kinetics of the contact surface water. We found it important to treat it as an integral part of the molecule. Thus, the present inventors attempted to consider the role of water in protein-protein interactions from a kinetic point of view.

Throughout this specification, many papers and patent documents are referenced and their citations are indicated. The disclosures of cited papers and patent documents are incorporated herein by reference in their entirety, and the level of the technical field to which the present invention belongs and the contents of the present invention are more clearly described.

The present inventors have made extensive efforts to develop a method for quantitatively measuring the binding potential between two molecules, for example, a protein, in an aqueous environment such as in vivo . As a result, the contact surface water molecules that form hydrogen bonds with both molecules are identified, and the number of molecules and the solvation free energy of each molecule are eliminated. The present invention has been completed by discovering that it is possible to obtain reliable results without distortion of coupling by measuring together.

Accordingly, an object of the present invention is to provide a method for measuring effective binding free energy ( f _u ) between a first molecule and a second molecule in an aqueous environment.

)을 측정하는 방법을 제공하는 데 있다.Another object of the present invention is to change the standard binding free energy of the first and second molecules in an aqueous environment (

It is to provide a method for measuring).

It is another object of the present invention to provide a method for predicting the binding of a first molecule and a second molecule in an aqueous environment.

Other objects and advantages of the present invention will become apparent from the following detailed description, claims and drawings.

); 및 상기 가교 물 단일 분자의 수(n)를 측정하는 단계를 포함하는 수성(aqueous) 환경에서의 제1 분자 및 제2 분자 간 유효 결합 자유에너지(effective binding free energy, f _u )를 측정하는 방법을 제공한다.According to one aspect of the present invention, the present invention provides a bridging water single molecule that forms a hydrogen bond with both the first molecule and the second molecule while being present at an interface formed between the first molecule and the second molecule. Solvation free energy in bulk

); And measuring the number ( n ) of the single molecules of the crosslinked water, wherein the effective binding free energy ( f _u ) between the first molecule and the second molecule in an aqueous environment is measured. To provide.

The present inventors have made extensive efforts to develop a method for quantitatively measuring the binding potential between two molecules, for example, a protein, in an aqueous environment such as in vivo . As a result, the contact surface water molecules that form hydrogen bonds with both molecules are identified, and the number of molecules and the solvation free energy of each molecule are eliminated. By measuring together, we found that reliable prediction is possible without distortion of coupling.

As used herein, the term “bulk state” refers to a bulky group of water molecules formed by forming a bond between a large amount of water molecules and not forming a bond with a molecule other than water, that is, a hydrogen bond or the like. It refers to the physicochemical state of each single water molecule.

As used herein, the term “solvation free energy” refers to a process in which solute particles are stabilized in a solution through a solute-solvent reaction after the solute particles move into a solvent having a constant temperature. Solvation free energy ”means free energy at standard state according to the solvation process.

The solvation free energy can be calculated through various methods known in the art, and the integration and decomposition calculation methods exemplarily applied in the present invention are described in detail in the following supplementary examples.

As used herein, the term “binding free energy” refers to free energy in a standard state according to a process in which two molecules in a free state form a bond, and when the amount of change in binding free energy is negative, It means that union occurs spontaneously.

As used herein, the term "measurement" is meant to encompass a series of deductive and inductive processes that derive unknown values using specific data, and therefore have the same meaning as "calculation", "prediction", "determination", "decision". Used as Thus, the term “measurement” in the present invention encompasses both experimental measurements, computational calculations on in silico and establishing relationships between a plurality of variables based thereon.

According to a specific embodiment of the invention, the method further comprises the step of measuring the gaseous energy ( E _u ) of the first molecule, the second molecule and the crosslinked water molecule.

)를 측정하는 단계를 추가적으로 포함한다. According to a specific embodiment of the present invention, the process of the present invention provides the solvation free energy of the first molecule, the second molecule and the crosslinked water molecule (

Further comprising the step of measuring).

According to a specific embodiment of the present invention, the effective binding free energy ( f _u ) between the first molecule and the second molecule is measured using the following equation:

); 상기 가교 물 단일 분자의 수(n); 제1 분자, 제2 분자 및 가교 물 분자의 기체상 에너지(E _u ); 및 제1 분자, 제2 분자 및 가교 물 분자의 용매화 자유 에너지(

)는 전산 시뮬레이션을 이용하여 측정된다. According to a more specific embodiment of the present invention, the solvation free energy in the bulk state of the bridging water single molecule (

); Number of the crosslinked water single molecules ( n ); Gas phase energy ( E _u ) of the first molecule, the second molecule, and the crosslinked water molecule; And the solvation free energy of the first molecule, the second molecule and the crosslinked water molecule (

) Is measured using computational simulation.

As used herein, the term “computational simulation” refers to a simulation that predicts and reproduces the behavior of a specific system through mathematical modeling using a plurality of computing devices forming one or a network. Specifically, the computational simulation is molecular dynamic simulation. Molecular dynamics simulation is a computational simulation that numerically calculates the trajectories of atoms or molecules in accordance with established physical laws and reproduces their physical motion.

According to a more specific embodiment of the invention, the number n of crosslinked water single molecules is determined using a snapshot of computational simulation.

According to a more specific embodiment of the present invention, at least one of the first molecule and the second molecule is a biomolecule.

As used herein, the term "biomolecule" refers to a series of macromolecules (macromolecule) existing in vivo, such as proteins, oligonucleotides, polysaccharides. These polymers have a structure in which monomer units are linearly bonded, but the overall three-dimensional shape is influenced by the size, charge of constituent residues, hydrophobicity, covalent and non-covalent bond formation, and the like.

According to a more specific embodiment of the invention, the biomolecule is a protein.

The term "protein" as used herein refers to a series of macromolecules (macromolecule) formed by binding amino acid residues to each other by peptide bonds. Proteins are linear molecules composed of consecutive bonds of amino acid units, but their overall size, charge or hydrophobicity of all or each constituent moiety, and covalent and non-covalent bond formation are affected by the three-dimensional shape and state change tendency. The present invention can be applied to screening a computer or designing a drug for a disease therapeutic agent that inhibits a target protein by quantifying the likelihood that the target protein and test substance specifically bind to the progress of a specific disease. Therefore, according to one embodiment of the present invention, the first molecule and the second molecule may be target proteins and test substances, respectively.

As used herein, the term "test substance" refers to an unknown candidate substance used in screening and the like to specifically bind to a target protein, which is a first molecule, or to determine whether the binding protein affects its activity. The test substance includes, but is not limited to, compounds, nucleotides, peptides and natural extracts. Subsequently, when a binding free energy indicating a significant binding is formed as a result of measuring the binding between the target protein and the test substance in the environment where the test substance is treated, the test substance is determined as a candidate of a composition for preventing or treating a disease. Can be.

)을 측정하는 방법을 제공한다. According to another aspect of the invention, the present invention comprises the steps of measuring the effective binding free energy ( f _u ) between the first molecule and the second molecule in an aqueous environment using the method of the present invention Change in standard binding free energy of the first and second molecules in an aqueous environment, including

Provides a method of measuring).

)은 하기 수학식을 이용하여 측정한다: According to a specific embodiment of the present invention, the amount of change in the standard bond free energy between the first molecule and the second molecule (

) Is measured using the following equation:

= △E _u + △

- n

- T(△S_config + △S_ext)

= △ E _u + △

-n

T (△ S _config + △ S _ext )

는 결합 전후의 제1 분자, 제2 분자 및 가교 물 분자의 용매화 자유 에너지 변화량이며,

는 가교 물(bridging water) 단일분자의 벌크 상태에서의 용매화 자유에너지이고, n은 가교 물(bridging water) 단일분자의 수이며, T는 온도이고, △S_config는 결합 전후의 제1 분자, 제2 분자 및 가교 물 분자의 배치 엔트로피 변화량이며, ΔS_ext는 결합 전후의 외부 엔트로피 변화량이다.In the above formula, ΔE _u is the amount of change in the gas phase energy of the first molecule, the second molecule and the crosslinked water molecule before and after the bond,

Is the amount of change in the solvation free energy of the first, second and crosslinked water molecules before and after bonding,

Is the solvation free energy in the bulk state of bridging water single molecule, n is the number of bridging water single molecule, T is the temperature, ΔS _config is the first molecule before and after the bond, The batch entropy change of the second molecule and the crosslinked water molecule, and ΔS _ext is the change of external entropy before and after binding.

As used herein, the term “configurational entropy” is entropy related to the position, not the velocity or momentum, of the constituent particles, the number and arrangement of particles in the space occupied by the molecule, ie the internal degrees of freedom of the solute. entropy determined by freedom).

As used herein, the term "external entropy" refers to entropy determined by the reduction of the degree of freedom of the outside (position and direction) during the complex formation process.

)을 측정하는 단계를 포함하는 수성 환경에서의 제1 분자 및 제2 분자의 결합여부를 예측하는 방법을 제공한다. According to another aspect of the present invention, the present invention provides a method for changing the standard binding free energy of a first molecule and a second molecule in an aqueous environment using the method of the present invention.

It provides a method for predicting the binding of the first molecule and the second molecule in an aqueous environment comprising the step of measuring).

According to a specific embodiment of the present invention, the method of the present invention determines that the binding probability of the first molecule and the second molecule increases when the amount of change in the standard binding free energy is negative.

The features and advantages of the present invention are summarized as follows:

)을 측정하는 방법을 제공한다.(a) The present invention provides the amount of change in effective binding free energy ( f _u ) and standard binding free energy between the first and second molecules in an aqueous environment (

Provides a method of measuring).

(b) The present invention provides a method for predicting the binding of the first molecule and the second molecule in an aqueous environment through free energy measurement.

(c) The present invention can quantitatively measure with high reliability without distorting the possibility of binding between molecules in an aqueous environment such as in vivo , thereby being usefully applied as a tool for screening or designing a disease therapeutic agent on a computer. Can be.

로 나타낸 결과를 보여준다. 각 패널의 점선 곡선은 가우스 분포를 나타낸다. 가우스 분포와 가까운 정도는 가우스 분포에 대해 0의 값을 가지는 skewness(s) 및 excess kurtosis(k)을 통해 측정하였다. 1 is a diagram showing the structure of the Varnase-Basta complex.
2a Illustration of single HB water, double HB water and crosslinked water, with dashed lines representing hydrogen bonds. FIG. 2B is a snapshot of the varase-vasta complex structure and hydrate, showing the distribution of single HB water (cyan), double HB water (orange) and crosslinked water (red).
3 is a diagram illustrating a thermodynamic cycle for obtaining trapping free energy. Process (1) (‘Process (1)’)i-th water molecules and solutesu′ (Varnase-vasta complex + hydration-i-th water molecules) shows the solvation process. Process (2) ("Process (2)"i-th solute water molecules at specific locations and in vacuumuIt shows the process of transition to a specific direction in the vicinity. Process (3) ("Process (3)" means soluteu(= Soluteu′ +i-th represents the solvation process of water molecules). Using the Gibbs free energy change in these processes, the transfer free energy is -ΔG _(One) + ΔG ₍₂₎ + ΔG ₍₃₎It may be represented as.
4 is Figure 1 shows the time-related function of hydrogen-bonds over the logarithmic time axis for bulk water (blue), single HB water (blue), double HB water (orange), and crosslinked water (red). The dashed dashed line represents the interval corresponding to the algebraic function.
5 is a diagram illustrating a thermodynamic-kinetic relationship diagram. The top panel shows the time-sensitive (light yellow) hydrogen-bonding of hydrogen-bonds in which the function decreases from 0.3 to 0.1 for the single HB water (cyan), double HB water (orange) and crosslinked water (red) of FIG. Represents a time-related function. The bottom panel shows the hydrogen-bond survival time of individual water molecules.τi) And trapping free energy (G _i ^trapA scatter plot for. The center of the ellipse was determined by the mean, with the width and height 3.6 along each axis.σ(σIs the standard deviation).
6A is a schematic diagram of a thermodynamic-kinetic relationship diagram of hydrated water. Single HB water (cyan), double HB water (orange) and crosslinked water (red) are shown along with the location of bulk water (blue) to graphically represent the bottom panel of FIG. Figure 6b is a color representation of the charge distribution on the surface of the protein, the positive and negative charge is shown in blue and red, respectively.
FIG. 7 is a plot showing the thermodynamic-kinetic relationship of hydrates to varase monomers (FIG. 7A) and varases in the complex (FIG. 7B). The top panel shows the hydrogen bond time-related function for the algebraic time base of single HB water (cyan) and double HB water (orange). The lower panel is a thermodynamic-kinetic relationship focused on the time interval (light yellow in the upper panel), with the time-related function decreasing from 0.3 to 0.1. Scatter plots of the hydrogen bond survival time and trapping free energy of individual molecules contributing to this relaxation were shown, the center of the ellipse was determined as the mean, and the width and width were determined as 3.6 along the axis.
FIG. 8 is a plot showing the thermodynamic-kinetic relationship of hydrates to batha monomer (FIG. 8A) and batha (FIG. 8B) in the complex. The top panel shows the hydrogen bond time-related function for the algebraic time base of single HB water (cyan) and double HB water (orange). The lower panel is a thermodynamic-kinetic relationship focused on the time interval (light yellow in the upper panel), with the time-related function decreasing from 0.3 to 0.1. Scatter plots of the hydrogen bond survival time and trapping free energy of individual molecules contributing to this relaxation were shown, the center of the ellipse was determined as the mean, and the width and width were determined as 3.6 along the axis.
9 shows cos for the magnitude of the electrostatic field E (FIG. 9A) and the angle between the dipole vector of the water and the electrostatic field (FIG. 9B) for single HB water (cyan), double HB water (orange) and crosslinked water (red).θ Represents the probability distribution of the values.
FIG. 10 shows the varase-buster complex plus crosslinked product (FIG. 10A), varase monomer (FIG. 10B), and varaster monomer (FIG. 10C).f _uProbability distribution forW(f _u)

Show the results shown. The dashed line curve in each panel represents the Gaussian distribution. The closeness to the Gaussian distribution was measured by skewness (s) and excess kurtosis (k) with zero values.

Hereinafter, the present invention will be described in more detail with reference to Examples. These examples are only for illustrating the present invention in more detail, it will be apparent to those skilled in the art that the scope of the present invention is not limited by these examples in accordance with the gist of the present invention. .

Example

Experiment method

molecule kinetics  simulation

We performed an exist-water molecular dynamics simulation for varase-vasta complexes and free varase and vasta proteins (FIG. 1). The initial complex structure was modeled based on X-ray structure as described in document 22 (PDB ID: 1 BRS ¹⁵ ), and the starting structures of the free varase and bathar simulations were derived from the NMR structures (1 BNR ²³ respectively). And 1 BTA ²⁴ ). The complex structure was solvated with 23,477 water molecules and neutralized with 4 Na ⁺ counter ions in a cube box with an initial side length of 95.4 mm 3; The glass Varna (Basta) is solvated, and Cl 2 for the cube in the box of the initial length of side 81.7Å (69.5Å) to 14 346 (8397) of water ^molecules was neutralized with (6 Na ⁺⁾ ions. All simulations were performed using AMBER14 suite ²⁵ with FF99SB force field ²⁶ for protein and TIP3P model ²⁷ for water. Temperature and the pressure was maintained at beren deusen (Berendsen) method T = 300K and P = 1 bar using ²⁸ respectively. Simulations were carried out using the same procedure described in Ref. 22, and three independent 1 μs production runs were performed, each starting at a different initial rate.

The inventors performed a pure-water simulation for kinetic quantitation of bulk water molecules. Three independent 100 ns simulations were performed on 2,539 water molecules at T = 300 K and P = 1 bar.

Hydrogen-bond rearrangement kinetics

The inventors have time t = hydrogen bonds found in 0 by quantifying the degree of survival to the time t since the time of the hydrogen bond-irradiation hydrogen bond rearrangement between were analyzed the association function, ²⁹ This protein and water of hydration can do. Hydrogen bonds are thought to form when the oxygen of water molecules is within 3.5 kW of the protein's heavy atom. Hydrated water was classified into three categories as shown in FIG. 2A: Water molecules forming a single hydrogen bond with a protein are called "single HB water". In FIG. 2B, the position of a single HB water in the simulation snapshot is represented by a cyan sphere, and their average number (± standard deviation) calculated from the total simulation trajectories for the complex is 325.7 ± 13.7 (number of water molecules and water The number of protein hydrogen bonds is summarized in Table 1). Water molecules that form two or more hydrogen bonds with the protein are called “double HB water” and the location of the double HB water in the snapshot is indicated by an orange sphere (FIG. 2B). There are 133.0 ± 8.0 double HB waters in the system, with an average number of hydrogen bonds to the protein being 2.4 ± 0.1. Finally, water molecules that form hydrogen bonds simultaneously with two proteins are called "bridging water." By definition, the crosslinked water is only present at the contact surface between the two proteins (red sphere in FIG. 2B). It was found that 19.6 ± 3.0 crosslinked water were present at the contact surface and the average number of water-protein hydrogen bonds was 2.9 ± 0.2. The time-related function of hydrogen bonding is defined as:

(1)

(One)

C ^α _{HB, indiv} ( t ) represents the individual contribution of each molecule, where α represents the form of water and parentheses represent the mean value of the water molecules of that form. For bulk water and single HB water, C ^α _{HB, indiv} ( t ) is 1 if one hydrogen bond found at time 0 survives to time 1. For double HB water and crosslinked water, C ^α _{HB, indiv} ( t ) is 1 if at least two hydrogen bonds found at time 0 survive to time 1.

Average number of water molecules and water-protein hydrogen bonds (mean ± standard deviation). Single HB water Double HB water Crosslinked water Number of water molecules 325.7 ± 13.7 133.0 ± 8.0 19.6 ± 3.0 Hydrogen bond number One 2.4 ± 0.1 2.9 ± 0.2

Trapping (trapping) free energy

We wanted to introduce the trapping free energy of the individual hydrates to quantify the strength of their binding to the protein surface. Trapping free energy refers to the reversible work (e.g., the strength of an average force) that transfers water molecules from infinite separation into a specific location and in a particular direction relative to the protein-protein complex. The inventors considered the process of transition in a specific direction relative to a fixed position and solute from two perspectives. First, through this, the trapping free energy of individual hydrates can be calculated using only a simulation snapshot as shown in FIG. 2B. Second, we tried to determine whether the trapping free energy calculated at time t = 0 could explain the extent to which the subsequent ( t > 0) dynamics of individual water molecules were delayed. The thermodynamic cycle shown in FIG. 3 was applied for this quantitation. In that cycle, the transition of the i- th water molecules to specific directions and in the vicinity of the solute was considered, including the desired hydrated water molecules (eg all water molecules shown in FIG. 2B). The solute excluding the i -th water molecule is represented by u '.

+

로 표시될 수 있다(

는 단일 물분자의 용매화 자유에너지/

는 용질의 용매화 자유에너지). 과정 (2)(‘Process (2)’에서, i-th 물 분자는 진공 내에서의 무한한 분리상태에서 특정 위치 및 용질 u′부근의 특정 방향으로 이동한다. 이 과정에 필요한 가역적인 일 ΔG ₍₂₎ = E _{u ’-i} 로 표시될 수 있다(E _{u ’-i} 는 용질 u′및 i-th 물 분자 사이의 상호작용 에너지). 과정 (3)(‘Process (3)’은 용질 u(=u′+ i)의 용매화 과정으로, ΔG ₍₃₎ =

로 표시될 수 있다. 열역학 사이클로부터, -ΔG ₍₁₎ + ΔG ₍₂₎ + ΔG ₍₃₎를 계산하여 트래핑 자유에너지를 얻을 수 있으므로, 다음과 같이 표현될 수 있다:Process (1) of FIG. 3 ('Process (1)' is an independent solvation process of i- th water molecule and solute u ', so the amount of Gibbs free energy change related thereto is Δ G ₍₁₎ = _).

+

Can be represented as

Is the solvation free energy of a single water molecule,

Is the solvation free energy of the solute). Step (2) (in the 'Process (2)', i -th water molecules moving in the space separated in a vacuum to a particular location and solute u 'specific direction in the vicinity. Reversible work required for this process Δ G ₍₂₎ = E _{u '-i} ( E _{u ' -i} is the interaction energy between solute u 'and i -th water molecules) Process (3) (' Process (3) 'is the solute Solvation of u (= u ′ + i ), Δ G ₍₃₎ =

It may be represented as. From the thermodynamic cycle, trapping free energy can be obtained by calculating -Δ G ₍₁₎ + Δ G ₍₂₎ + Δ G ₍₃₎ , which can be expressed as:

(2)

(2)

는 3D-RISM 이론³⁰을 통해 계산하였다(보충 실시예 참조). 용매화 자유에너지의 원자분해에 기반한

-

를 계산하는 효율적인 방법도 보고되었다^{31 , 32}. 유리 바르나제 및 바스타 단백질 부근의 수화 물의 트래핑 자유에너지도 유사한 방법으로 측정할 수 있다.We calculate the interaction energy E _{u '-i} through the force field, solvating free energy

Was calculated via 3D-RISM theory ³⁰ (see Supplemental Examples). Based on atomic decomposition of solvation free energy

-

An efficient way of calculating ^{31 and 32 has} also been reported. The trapping free energy of hydrated water near free varase and basta protein can also be measured in a similar manner.

Recently, several computer analysis method for the evaluation of the thermodynamic function of the individual molecules of the water of hydration has been developed ^33-41. However, these methods usually require additional separate simulations. For example, in order to apply the heterogeneous solvation theory ^{33 to 35} , there are limitations to applying protein atoms in the direction of sample water molecules and the direction of a given protein form when the simulation is performed. During this additional simulation, the hydrate is replaced with the bulk water. Analysis can be complicated. On the other hand, the trapping free energy analysis method of the present invention applying the integrated equation theory (3D-RISM) is more efficient in that it can be applied using only snapshots obtained by unlimited equilibrium simulation.

Standard combined free energy

Conventional approach

Standard binding free energies can be expressed in statistical thermodynamic representations as described in references 22 and 42:

(3)

(3)

Δ X represents the amount of change in X during the formation of the complex from two free proteins (labeled 1 and 2): Δ X _{= X complex - (X 1 +} X 2). f _u = Eu + G _u ^solv includes the gaseous energy ( E _u ) and the solvation free energy of the solute u ( G _u ^solv ), where u is the complex or one of the two free proteins excluding the hydrate, bar ) Represents the mean value of the simulated configuration; Δ S _config represents the configuration entropy associated with the degrees of freedom of the solute, and Δ S _ext represents the amount of entropy change due to the reduction of external (position and direction) degrees of freedom due to complex formation. Δ S _ext confers standard state dependence, where a standard concentration (1 M) is chosen.

The gaseous energy E _u was calculated from the force field applied in the simulation ( E _u for free protein represents only the energy inside the protein, while E _u for the complex also contains the inter-protein interaction energy). To calculate the solvation free energy G _u ^solv was applied to the 3D-RISM Theory ³⁰ (see Supplementary embodiment). It was the energetically approach to define the layout entropy S _config expressed Through the statistical properties of the ^{43, 44,} fu. In particular, when the probability distribution W ( fu ) of f _u shows a Gaussian curve, it can be expressed as:

(4)

(4)

Mean relaxation time and trapping free energy (mean ± standard deviation). Bulk water Single HB water Double HB water Crosslinked water Relaxation time < τ _i > ^a 5.1 ± 1.6 28.1 ± 10.1 133.0 ± 8.0 19.6 ± 3.0 (<log10 τ _i >) ^b (0.69 ± 0.13) (1.42 ± 0.16) 2.4 ± 0.1 2.9 ± 0.2 Trapping free energy ^c 0 -4.5 ± 3.4 -8.0 ± 4.1 -12.5 ± 4.7

(calculated using the individual relaxation times τ _i in ^a p seconds; statistical values calculated using ^b log10 τ _i ; ^c kcal / mol)

이다. 바르나제-바스타 복합체의 외부 엔트로피 ΔS_ext는 종래에 보고된 값인 -6.8±0.1 kcal/mol를 적용하고²², 에너지론적인 접근을 결합과정까지 확장한 결과 종래 보고된 바와 유사한 값을 얻었다⁴⁵. k _B is Boltzmann's constant

to be. Varna claim External entropy ΔS _ext of Basta complex is applied to a value of -6.8 ± 0.1 kcal / mol, and ²² as reported in prior art, as a result of the expansion energy theoretical approach to the joining process to obtain a similar value as the conventional report ^45.

object Water molecules  Substantial inclusion

에 대한 식 (3)에서 나타난 f _u = E _u +

를 다음의 식으로 대체하였다:A statistical thermodynamic formula of binding free energy that allows the actual inclusion of certain solvent molecules is introduced in Ref. 42.

F _u in Equation (3) for = E _u +

Is replaced by the following equation:

(5)

(5)

는 단일 물 분자의 용매화 자유에너지이다. S _config는 이후 식 (4)와 (5)를 조합하여 계산하였다.In the above formula, solute u now clearly includes the target water molecules (ie E _u contains interactions with these water molecules), n is the number of water molecules contained,

Is the solvation free energy of a single water molecule. S _config was then calculated by combining Equations (4) and (5).

Results and Discussion

Hydrogen-bond rearrangement kinetics

The inventors investigated the kinetics and thermodynamic properties of the hydrates surrounding the Varnase-Basta complex through molecular dynamics simulation and statistical thermodynamic analysis. In particular, we wanted to investigate the properties of the contact surface water molecules between the two proteins during complex formation. This was done by comparing the dynamics of the contact surface water and the hydrated water around the free protein. For this purpose, simulations and assays for free varase and basta proteins were also performed. We focused on rearrangement of hydrogen bonds, which is a very important protein-water interaction due to the wide hydrophobicity of the protein-protein binding surface ²¹ .

4 shows the time-related function of hydrogen bonds, which quantifies the extent to which hydrogen bonds found at time t = 0 survive the subsequent time t . For water molecules with a single hydrogen bond with the protein (single HB water; see FIG. 2 and Table 1), a significant slowdown in relaxation kinetics was observed compared to bulk water (average relaxation times are compared in Table 2). For water molecules (double HB water) that form two or more hydrogen bonds with the protein, the hydrogen bond rearrangement is slower. In the water-molecules of crosslinked water molecules, which form hydrogen bonds simultaneously with the two proteins, the relaxation was extremely slow (about 1,000 times slower). In addition, the relaxation curve was irregular, resulting in a three-fold logarithmic decrease with time.

thermodynamics- kinetics  Relationship

To account for the slow relaxation of the hydrate, a statistical thermodynamic analysis was introduced. Focusing on long time intervals (light yellow portion of the top panel of FIG. 5) where the time-related function decreases from 0.3 to 0.1, selects water molecules that contribute to relaxation by measuring the hydrogen bond survival time ( τ _i ) of individual molecules It was. For each of these water molecules, trapping free energy ( G _i ^trap ) was calculated using a simulation snapshot at t = 0. Trapping free energy can be thought of as a practical possibility characterized by how strongly each water molecule is trapped on the surface of the biomolecule: the more negative the trapping free energy is, the closer it is to the protein complex than in the bulk of the water molecule. By stability, it is more "trapped" in protein complexes. The lower panel of FIG. 5 shows a scatter plot of relaxation time and trapping free energy of individual water molecules (average relaxation time and trapping free energy shown in Table 2 were derived through this function, Since the distribution of relaxation time τ _i is well represented on the logarithmic axis (Fig. 5 lower panel), the statistical value calculated as log ₁₀ τ _i in Table 2 is disclosed). The resulting “thermodynamic-kinetic relationship” clearly shows that trapping free energy ( G _i ^trap ) at t = 0 can be used as an expression phrase for the degree of delay ( τ _i ) of the hydration of a subsequent hydrate. there was.

6a schematically shows a thermodynamic-kinetic relationship diagram. Single HB water showed slower kinetics than bulk water because single HB water is more stable near the protein surface, indicating that the hydrogen bond between water and protein is stronger than the hydrogen bond between water molecules. Can be. The slower kinetics of double HB water can be similarly understood, with further stabilization due to the additional water-protein hydrogen bonds. Why, then, is the crosslinked product that forms a number of hydrogen bonds similar to double HB water with proteins (Table 1)? The inventors have found that single and double HB water molecules have similar thermodynamic as well as kinetic properties regardless of whether they are present in the vicinity of the monomer or protein-protein complex (FIGS. 7 and 8). The “red site” appearance of the crosslinked product in the scheme is due to the formation of the protein-protein contact surface. Regarding this particular factor affecting only this contact surface, the inventors noted the electrostatic complementarity of the Varnase-Basta bonding surface (FIG. 6B) which generates a strong electrostatic field in the contact surface water. Indeed, it was found that the crosslinked water had a stronger electrostatic field compared to single and double HB water and the dipole vectors of water were arranged along the more electrostatic field (FIG. 9). Therefore, no change in hydration kinetics of the non-contacting surface sites is necessarily observed before and after bonding (FIGS. 7 and 8), while the strong electrostatic field generated at the bonding contacting surface acts as an additional stabilizing element of the crosslinked water, thereby making it extremely slow ( Nanosecond units), resulting in hydrogen bond relaxation (Table 2). In order to investigate how the transition of hydration kinetics occurs during the coupling process, spontaneous coupling simulation should be performed.

Trapping free energy is an important quantitative data not only for investigating the formation of binding contacts from the water's point of view, but also for studying the rearrangement of hydrated water from unbound proteins to binding complexes. Varna claim - Basta complex contact surface water is particularly known for stationary systems, but ^46, the coupling since the observed electrostatic complementarity a number of protein complexes on the surface ^{47 and 48,} the hydrophobic protein to slow water relaxation an extremely-common protein contact surface features were estimated to be ^{47 and 48.}

"Traditional" coupled thermodynamics

를 결정하는 인자들 중에서[식 (3)], Δf _u = ΔE _u + Δ

는 두 가지 이유로 중요한 역할을 한다. 우선, 일반적으로 단백질과 같은 복합체 고분자의 배치(ΔS _config) 및 외부(ΔS _ext) 엔트로피는 계산하기 어렵다. 다음으로, 복합체 형성 과정에서 ΔS _config 및 ΔS _ext는 대개 음의 값이므로

을 증가시키게 되어 결합이 일어나지 않도록 하기 때문에, 결합의 동력은 Δf _u 에서 유래하여야 한다. 실제로, 유효 결합 자유에너지⁴⁹라고 불리는 Δf _u 는 MM-PBSA(molecular-mechanics Poisson-Boltzmann surface area)와 같은 생체분자 결합의 컴퓨터 분석에 있어 주요 정량값이다^50-52.

Of the factors determining [Eq. (3)], Δ f _u = Δ E _u + Δ

Plays an important role for two reasons. First, the general arrangement of a composite polymer such as a protein (Δ S _config) and outer (Δ S _ext) entropy, it is difficult to calculate. Next, Δ S _config and Δ S _ext are usually negative values during complex formation.

The increases are not occur because this combination, the power of the combination is to be derived from Δ f _u. Indeed, Δ f _u , called effective binding free energy ⁴⁹ , is the main quantitative value in computer analysis of biomolecule binding, such as molecular-mechanics Poisson-Boltzmann surface area (MM-PBSA) ^50-52 .

를 계산하였다(이는 하나의 복합체 및 두 개의 유리 단백질에 대한 분리된 계산을 수행하여 3궤적 방법이라 불린다. 결합 열역학 수치 값은 복합체 및 유리 단백질의 독립적인 궤적 및 오차전파 법칙에 기초하여 계산된 표준오차와 함께 기재된다). 에너지 기여(ΔE _u )는 역장으로부터 직접적으로 계산하였으며, 용매화 기여(Δ

)는 3D-RISM 이론을 이용하여 계산하였다(보충 실시예 참조). 이를 통해

= 25.7±2.6 kcal/mol를 도출하였는데, 이는

를 양의 값으로 만들어 실험적 관찰과 명백히 불일치한다(

= 18.9 kcal/mol)⁵³. 흥미롭게도, 바르나제-바스타 복합체에서 양의 유효 결합 자유에너지 값은 MM-PBSA 계산을 통해 이미 보고된 바 있다(

= +14 kcal/mol⁵⁴,

= +3.6 kcal/mol⁵⁵, 이들 값의 차이는 MM-PBSA 계산 시 복합체의 시뮬레이션으로부터 복합체 및 단량체 배치를 모두 도출하는 단일궤적 방법의 사용; 상이한 역장의 이용; 및 용매화 자유에너지의 상이한 추정 때문일 수 있다).By averaging the values of Δ f _u for the simulated protein form

(This is called a three-track method by performing separate calculations for one complex and two free proteins. Binding thermodynamic numerical values are standard calculated based on the independent trajectory and error propagation laws of the complex and free protein. With errors). The energy contribution (Δ E _u ) was calculated directly from the force field and the solvation contribution (Δ

) Was calculated using 3D-RISM theory (see Supplemental Examples). because of this

= 25.7 ± 2.6 kcal / mol, which is

Is positively inconsistent with experimental observations (

= 18.9 kcal / mol) ⁵³ . Interestingly, positive effective binding free energy values in the Varnase-Basta complex have already been reported through the MM-PBSA calculation (

= +14 kcal / mol ⁵⁴ ,

= +3.6 kcal / mol ⁵⁵ , the difference between these values is the use of a single trajectory method that derives both the complex and monomer batches from the simulation of the complex in calculating the MM-PBSA; The use of different force fields; And different estimates of solvation free energy).

Assumptions on the Traditional Way

Here, the inventors tried to verify the assumptions underlying the equation (3) for the standard binding free energy. To simplify the matter, we considered only canonical ensemble and ignored external entropy that did not change the point. We started with the coordination integral, which is an important part of the segmentation function in solute-solvent systems:

(6)

(6)

와 E _tot = E _u + E _uv + E _v를 적용함으로써, 식(6)을 통해 자연스럽게 도출되는 엔트로피 S_tot=

가 된다. 이는 용질(S_config) 및 용매 (

에 포함) 엔트로피가 분리되어 있는 식(3)에 반한다. r _u and r _v mean solute and solvent degrees of freedom, respectively; β = 1 / ( k _B T ) means the inverse of the temperature; E _u , E _uv and E _v mean solute energy, solute-solvent interaction energy and solvent-solvent interaction energy, respectively. Z _tot is a key element in free energy simulations. The change in free energy F _tot = -k _B T log Z _tot (e.g. mutations) was calculated through a simulation in which solute and solvent degrees of freedom were clearly controlled. However, equation (6) cannot be the basis of equation (3): for example, probability distribution p _tot ( r _u , r _v ) =

And by applying E _tot = E _u + E _uv + E _v , the entropy S _tot = naturally derived through Eq.

Becomes This is because the solute (S _config ) and the solvent (

Contrary to equation (3) in which entropy is separated.

(r _u)에 의존적인 용질-배위의 관점에서 다음과 같이 계산될 수 있다:In order to arrive at equation (3) from equation (6), the average value for the solvent degrees of freedom must first be calculated. These mean calculations yield solvation free energy for a given solute coordination r _u .

In terms of solute-coordination dependent on ( r _u ), it can be calculated as follows:

(7)

(7)

는 순수 용매에 대한 배위적분이다. 이제, 용매 자유도의 평균값을 도출한 뒤의 배위적분은 다음과 같이 표현될 수 있다: here,

Is the coordination integral with respect to the pure solvent. Now, the coordination integral after deriving the mean value of the solvent degrees of freedom can be expressed as:

(f _u = E _u +

) (8)

( f _u = E _u +

) (8)

를 도입함으로써, 연관된 엔트로피는 용질 배치 엔트로피 S_config에 대한 식을 정의하는 -k _B∫dr _u p(r _u)logp(r _u)로 표현될 수 있다. 따라서, 식(3)이 용매 자유도의 평균값에 기반하고 있음은 명백하다(식(8)로부터 식(3)이 도출되는 과정은 참고문헌 22 및 42에 기재되어 있다). “전통적인”방법에 의할 때 이러한 사전 평균(pre-averaging)에 기초하게 되며, PBSA 및 3D-RISM과 같은 특정 방법을 참고하지 않았다.

By introducing, the associated entropy can be expressed as −k _B ∫d r _u p ( r _u ) log p ( r _u ) which defines the equation for solute batch entropy S _config . Thus, it is evident that Eq. (3) is based on the average value of the solvent degrees of freedom (the process by which Eq. (3) is derived from Eq. (8) is described in references 22 and 42). The “traditional” method is based on this pre-averaging and does not refer to specific methods such as PBSA and 3D-RISM.

의 비현실적인 양의 값의 기원이라고 추측하였다. In practical applications of traditional methods, only protein forms obtained through simulation trajectories are used, replacing all water molecules with an equilibrium continuum model (PBSA) or molecular distribution function (3D-RISM). This treatment is usually justified due to the difference in time scale between typical water kinetics (picoseconds) and protein form motion (nanoseconds) ¹⁶ (eg due to the rapid equilibrium of the surrounding water). However, because we cannot superficially handle the water on the biomolecule contact surface because of the extremely slow cross-linking-water relaxation, we believe that

It is assumed that the origin of the unrealistic amount of.

Inclusion of crosslinked water

= -34.2±2.1kcal/mol을 얻었는데, 이는 결합의 동력이 된다. 이러한 결과는 결합 열역학에 있어 접촉면 물의 동력학을 고려할 필요성을 보여준다.In order to investigate the effects of the inclusion of slow crosslinks, we considered the protein coordination obtained from the simulation trajectory of the complex as well as the crosslinks located at the contact surface: the number of crosslinks (n) depends on the simulation snapshot and the average value was 19.6. ± 3.0 (Table 1). Now these crosslinked products are regarded as structural parts of the complex, and the equation (5) was substituted to calculate the f _u value for the complex. The result is a negative value

= -34.2 ± 2.1 kcal / mol, which is the power of the bond. These results show the need to consider the dynamics of contact surface water in coupling thermodynamics.

를 계산하였다. 이를 위해서는 배치(ΔS_config) 및 외부(ΔS_ext) 엔트로피 기여를 추정해야 했다. 배치 엔트로피에 대해 본 발명자들은 f _u의 변동의 관점에서 ΔS_config를 표현하는 에너지적 방법을 사용하였다^{43 ,44}. 특히, f _u의 확률 분포 W(f _u)가 가우스 곡선일 때, S_config는 단순히 f _u의 변동의 평균제곱이 된다(식(4)). 실제로, 바르나제-바스타 복합체 및 가교 물의 W(f _u)는 가우스 분포에 잘 수렴되어 TΔS_config = - 4.5 ±18.5 kcal/mol가 도출된다. 외부 엔트로피 ΔS_ext의 도출에는 참조문헌 22에서 보고한 방법으로 계산한 추정값 TΔS_ext = - 6.8 ±0.1 kcal/mol를 이용하였으며, 이는 참조문헌 45에서 보고된 값과 유사하다. 이들 결과를 조합하여

= - 22.9 ±18.60를 도출하였는데, 이는 실험값(-18.9 kcal/mol)과 합리적인 일치를 보인다⁵³ (

의 큰 표준오차는 TΔS_config의 표준오차에서 기인한다).Binding free energy to verify how the crosslinked material is substantially included by comparison with experimental values

Was calculated. This required estimating batch (ΔS _config ) and external (ΔS _ext ) entropy contributions. The inventors arranged for entropy used a method of expressing the energetically ΔS _config in terms of variation in the f _u ^{43, 44.} In particular, when the distribution of _u f W (f _u) is the Gaussian curve, S _config is simply the average of the square of the variation in the f _u (formula (4)). Indeed, W ( f _u ) of the varase-vasta complex and crosslinked water converge well to the Gaussian distribution resulting in TΔS _config = −4.5 ± 18.5 kcal / mol. For the derivation of the external entropy ΔS _ext , an estimate TΔS _ext = −6.8 ± 0.1 kcal / mol calculated by the method reported in Ref. 22 was used, which is similar to the value reported in Ref. 45. Combining these results

= - 22.9 ± 18.60 were obtained for which experimental data shows an (-18.9 kcal / mol) and reasonable match ⁵³ (

The large standard error of is due to the standard error of TΔS _config ).

supplement Example - Solvation  Calculation method of free energy

Integral equation theory .

를 계산하였다^{56 ,57}. 3D-RISM 이론은 용질 부위의 위치 r에서의 물의 3차원적 분포함수 g _γ(r)를 수득하기 위한 통계역학-기반 적분 방정식이다(여기서 용질은 바르나제-바스타 복합체, 바르나제 단량체, 바스타 단량체 또는 이들 단백질에 실제로 다루어지는 물 분자를 추가한 것이다. 이 경우, 물 분자는 실제 용질의 일부로 간주되는 물과 그 밖에 용질을 둘러싼 다른 물 분자의 두 가지로 나뉜다). 이 이론에서 3D-RISM 함수를 풀면 분포 함수도 함께 도출된다.For each simulated solute configuration, 3D-RISM was applied to solvate free energy.

^{56 and 57} were calculated. The 3D-RISM theory is a statistical dynamic-based integral equation for obtaining the three-dimensional distribution function g _γ ( r ) of water at the position r of the solute site, where the solute is a varase-vasta complex, a varase monomer, a vasta monomer Or adding water molecules that are actually addressed to these proteins, in which case the water molecules are divided into two, water which is considered part of the actual solute and other water molecules surrounding the solute). In this theory, solving the 3D-RISM function leads to the distribution function.

(9)

(9)

(10)

10

Wherein d _γ ( r ) = -u _γ ( r ) / ( k _B T ) + h _γ ( r ) -c _γ ( r ), where h _γ ( r ) = g _γ ( r ) -1 and c _γ ( r ) is the total and direct correlation functions, respectively; χ _{γγ '} (r) represents the water-to-position water sensitivity function that can be obtained through simulation of pure water or by calculating the integral equations; u _γ ( r ) indicates the solute-solvent interaction potential for a given solute configuration. We solved this equation by the method reported in Ref. 57.

The solvation free energy can also be calculated by the following Kirkwood charge formula ⁵⁸ .

(11)

(11)

Where λ is the maximum interaction at λ = 0, u _γ (r; λ = 0) with no solute-solvent interaction, λ = 1, u _γ (r; λ = 1) = u _γ (r) It is a charge parameter that is slowly switched on depending on the interaction. g _γ (r; λ) represents the distribution function in the parameter λ and can be calculated via 3D-RISM theory using the interaction probability u _γ (r; λ).

Decomposition Method

-

의 기여를 평가해야 한다. 여기서, 용질 u(= u’+ i)와 u’의 차이는 i-th 물분자의 존재여부에 있다(도 3). 주어진 용질 배위에서 각각의 수화 물 분자의 트래핑 자유 에너지 계산을 위하여, 이들 물분자의 수 만큼 계산을 반복해야 한다(바르나제-바스타 복합체를 둘러싼 물분자는 평균 533개이다). 이러한 계산 상의 문제를 회피하기 위하여, 다음의 근사치를 이용하였다:To calculate the trapping free energy of Equation (2)

-

The contribution of must be evaluated. Here, the difference between the solute u (= u '+ i ) and u ' is in the presence of i- th water molecules (Fig. 3). In order to calculate the trapping free energy of each hydrated molecule in a given solute configuration, the calculation must be repeated by the number of these water molecules (the average number of water molecules surrounding the varase-vasta complex is 533). To avoid this computational problem, the following approximation was used:

(12)

(12)

은 i-th 물분자가 모든 수화 물분자를 포함하는 용질의 용매화 자유 에너지

에 대한 기여이다. 주어진 용질 배위에서 모든 수화 물 분자의

는 단일

의 단일 분해계산으로부터 얻을 수 있어 매우 효율적이다.here,

Solvation free energy of the solute in which the i -th water molecule contains all the hydrated water molecules

Is a contribution to. Of all hydrated molecules in a given solute configuration

Is a single

It is very efficient because it can be obtained from single decomposition calculation of.

로 이루어져 있다는 점에 기반한다. 이를 식 11에 적용하면, 용매화 자유 에너지의 정확한 원자 분해를 얻을 수 있다^{59 ,60} Decomposition of the solvation free energy ^{59 , 60} shows the possibility of interaction between the water position _γ and the solute atoms u _γ (r) is a further contribution paired with

Based on the fact that Applying this to Equation 11, accurate atomic decomposition of the solvation free energy can be obtained ^{59 , 60}

(13)

(13)

로 표시하였다. 일단

의 원자 분해가 이루어지면, i-th 물분자의 기여

는

=

를 이용하여 얻을 수 있다. 3개의 독립적인 1 ㎲ 궤적으로부터 100 ns 시간 간격으로 30개의 바르나제-바스타 복합체 배위의 물분자에 대해 식(12)의 유효성을 검사한 결과,

-

및

간의 피어슨 상관계수(R)가 0:85임을 발견함으로써

가

-

의 유용한 근사치가 될 수 있음을 알 수 있었다.Here, to emphasize that the contribution by the atom of the solute u

Marked as. First

Of atomic decomposition of i -th water molecules

Is

=

Can be obtained using The validity of equation (12) on water molecules of 30 varnase-vasta complex coordinations at 100 ns time intervals from three independent 1 μs trajectories,

-

And

By finding that the Pearson's correlation coefficient (R) is 0:85

end

-

It can be a useful approximation of.

conclusion

Water molecules are widely found in the interface between biomolecules and the contact surface water molecules should be considered as a complete part of the biomolecule. In the present invention, to provide a new consideration based on the dynamic point of view. The inventors found that "special" water molecules appeared at the site of the contact surface where the two biomolecules are crosslinked via hydrogen bonding, resulting in extremely slow hydrogen bond rearrangement. Analyzes of the thermodynamic-kinetic relationships show that the extremely slow nature of the crosslinked water is due not only to the number of hydrogen bonds but also to further stabilization due to the strong electrostatic fields between the bond surfaces. This role of slow contact surface water in determining binding affinity cannot be explained through water-mediated interactions that presuppose a rapid equilibrium of degree of freedom as in the prior art. Indeed, the inventors have observed that integrating biomolecules and contact surface cross-links allows for a significant measurement of binding affinity. The present invention shows the effect of hydration kinetics on interprotein binding thermodynamics.

Having described the specific part of the present invention in detail, it is apparent to those skilled in the art that the specific technology is merely a preferred embodiment, and the scope of the present invention is not limited thereto. Thus, the substantial scope of the present invention will be defined by the appended claims and equivalents thereof.

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Claims (13)

The solvation free energy in the bulk state of bridging water single molecule which exists in the interface formed between the first molecule and the second molecule and forms hydrogen bonds with both the first molecule and the second molecule (

); And measuring the number n of the crosslinked water single molecule,
A method for measuring effective binding free energy ( f _u ) between a first molecule and a second molecule in an aqueous environment using molecular dynamics simulation.
The method of claim 1, wherein the method further comprises measuring gas phase energy ( E _u ) of the first molecule, the second molecule and the crosslinked water molecule.
The method of claim 1, wherein the method comprises the solvation free energy of the first, second and

The method further comprises the step of measuring).
The method of claim 1, wherein the effective binding free energy ( f _u ) between the first molecule and the second molecule is measured using the following equation:

.
The solvation free energy of the bulk of the bridging water single molecule,

); Number of the crosslinked water single molecules ( n ); Gas phase energy ( E _u ) of the first molecule, the second molecule, and the crosslinked water molecule; And the solvation free energy of the first molecule, the second molecule and the crosslinked water molecule (

) Is measured using computational simulation.
6. The method of claim 5, wherein the computational simulation is molecular dynamic simulation.
6. The method of claim 5, wherein the number n of crosslinked water single molecules is measured using a snapshot of computational simulation.
The method of claim 1, wherein at least one of the first molecule and the second molecule is a biomolecule.
9. The method of claim 8, wherein said biomolecule is a protein.
10. The method of any one of claims 1 to 9 comprising measuring the effective binding free energy ( f _u ) between the first molecule and the second molecule in an aqueous environment. The amount of change in the standard binding free energy of the first molecule and the second molecule in the aqueous environment (

How to measure).
The method of claim 10, wherein the amount of change in the standard bond free energy between the first molecule and the second molecule (

) Is measured using the following equation:

= △ E _u + △

-n

T (△ S _config + △ S _ext )
In the above formula, ΔE _u is the amount of change in the gas phase energy of the first molecule, the second molecule and the crosslinked water molecule before and after the bond,

Is the amount of change in the solvation free energy of the first, second and crosslinked water molecules before and after bonding,

Is the solvation free energy in the bulk state of bridging water single molecule, n is the number of bridging water single molecule, T is the temperature, ΔS _config is the first molecule before and after the bond, The batch entropy change of the second molecule and the crosslinked water molecule, and ΔS _ext is the change of external entropy before and after binding.
The amount of change in the standard binding free energy of the first molecule and the second molecule in the aqueous environment using the method of claim 11

A method for predicting the binding of the first molecule and the second molecule in an aqueous environment comprising the step of measuring).
The method of claim 12, wherein the method determines that the binding probability of the first molecule and the second molecule increases when the amount of change in the standard binding free energy is negative.

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