CN116092600A - Single GPU copy exchange free energy calculation method and system - Google Patents
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Abstract
The invention discloses a single GPU copy exchange free energy calculation method, which comprises the following steps: s1, performing analog decomposition on a replica exchange MD into two-dimensional Gibbs sampling: the variable of one dimension is defined as x; the other dimension is the free energy f corresponding to each window; defining a joint probability characterization copy exchange MD simulation; s2, defining a specific window j and a conformation x based on the joint probability m Is realized by Monte Carlo or by molecular dynamics simulation; s3, defining a specific conformation x based on joint probability m Conditional probability of window j; s4, based on a specific window j, a conformation x m Conditional probability of (1) specific conformation x m Conditional probability of window j and randomThe approximation policy calculates the free energy of single GPU copy exchange. Corresponding systems and applications are also disclosed, implementing copy exchange enhanced sampling policies in ABFEP/RBFEP based on a monolithic GPU card.
Description
Technical Field
The invention belongs to the technical field of computer-aided drug design, and particularly relates to a single GPU copy exchange free energy calculation method and system.
Background
In drug development, rationally designed drug candidate compounds are challenging and the implementation process can be understood to address complex multi-objective tasks. Taking the study of oral administration of a novel coronavirus main protease inhibitor as an example, preclinical development requires the establishment of various experimental tests to detect the binding of compounds to the main protease (IC 50<10 nm), the virus inhibition effect (EC 50<5 um), half-life (> 8 h), solubility (> 5 mg/mL), toxicity, etc. Therefore, in practical research, hundreds of compounds need to be designed for iterative optimization to find molecules meeting each target task. In the whole iterative optimization, the interaction efficacy of the compound and the target protein is ensured to be the most basic requirement, so that most of preclinical experiments are spent on detecting the activity of the compound and the target protein.
In recent years, the ability of compounds to bind to target proteins has been predicted in silico, with representative methods being ABFEP/RBFEP. Compared with traditional empirical methods dock, semi-empirical MM-GBSA and the like, the ABFEP/RBFEP physical background is strict, and the calculation result is more accurate and reliable. In fact, the formula derivation work of ABFEP/RBFEP has been completed in the last 80 th century, subject to various conditions, and its main application scenario is limited to academia, with few use cases in industry. In this century, the level of software and hardware of a computer is greatly improved, and particularly after 2011, the GPU technology gradually replaces a CPU to become a main angle in the field of computation; on the other hand, the crystal structure of the target protein also increases in a blowout manner, and the appearance of alpha Fold2 also provides reliable structure prediction for proteins which cannot be crystallized temporarily. Therefore, ABFEP/RBFEP is gradually landing, playing an increasingly important role in industry.
Performing the ABFEP/RBFEP calculation requires MD analog sampling at a specific potential energy, current analog sampling strategies include the traditional MD method (fig. 1 a) and the replica-switched MD method (fig. 1 b). For the traditional MD simulation method, the sampling of each window (different lambda values represent different windows) is independent, with no conformational exchange between the windows. The advantage of this strategy is that it supports serial-parallel computing and is easy to deploy. For the MD sampling method of copy exchange, the conformations between the windows can be exchanged under the condition of meeting the careful balance, thereby achieving the effect of enhancing the sampling.
For traditional kinetic simulations, as discussed above, the obvious disadvantage is that sampling cannot be enhanced, and the simulation of most windows tends to be tied to near local minima of the potential energy surface. As shown in fig. 2, when simulation is performed in window 1, the sample (sphere representation) is tied to the left side of the potential energy plane due to the presence of the high potential barrier. Although the MD approach of replica swapping can achieve enhanced sampling, it has two distinct disadvantages: serial and time consuming are not supported. Additional GPU/CPU computation interactions affect the efficiency of parallelism because of the fine balance condition determination at a particular simulation time point. Some copy exchange methods also introduce some windows of high temperature, which further increases the computational effort. As shown in fig. 1b, to implement copy exchange, each window must be simulated simultaneously, so that parallel computation of multiple GPUs is indispensable. If there is only one GPU card, the existing copy switch policy cannot be implemented.
Thus, the above-mentioned prior art does have to propose a better solution.
Disclosure of Invention
The invention aims to provide a single GPU copy exchange free energy calculation method and system, and copy exchange enhanced sampling strategy in ABFEP/RBFEP is realized based on a single GPU card. The principle of computation is that the replica switched MD simulation can be seen as a two-dimensional gibbs sampling: the variable of one dimension is defined as x, representing the conformation of the study system (under classical mechanical framework, the system momentum can be counteracted when calculating thermodynamic properties); the other dimension is the free energy f corresponding to each window. Therefore, the copy exchange MD simulation is characterized by defining a joint probability, and the calculation result of the exchange free energy is obtained by implicitly expressing the thermodynamic temperature beta.
The invention provides a single GPU copy exchange free energy calculation method, which comprises the following steps:
s1, performing analog decomposition on a replica exchange MD into two-dimensional Gibbs sampling: the variable of one dimension is defined as x; the other dimension is the free energy f corresponding to each window; defining a joint probability characterization copy exchange MD simulation;
s2, defining a specific window j and a conformation x based on the joint probability m Conditional probability of (2), andand the conformation x m Sampling under this conditional probability is achieved by monte carlo or by molecular dynamics simulation;
s3, defining a specific conformation x based on the joint probability m Conditional probability of window j;
s4, based on a specific window j, a conformation x m Conditional probability of (1) specific conformation x m The conditional probability of window j and the random approximation strategy calculate the free energy of single GPU copy exchange.
Preferably, the joint probability of S1 is:
wherein pi j The other terms to the right of the equation satisfy the boltzmann distribution, which represents the probability of the system being in the j window.
Preferably, the specific window j, conformation x in S2 m The conditional probability of (2) is defined as:
the conformation x m Sampling under this conditional probability is achieved by monte carlo or by molecular dynamics simulation.
Preferably, for Monte Carlo implementation, the new conformation x n The reception probability of (2) satisfies:
preferably, for molecular dynamics simulation implementation, the conformation x is implemented in a specific window using open source Gromacs software m Molecular dynamics analog sampling of (a);
preferably, a specific conformation x is defined in S3 m The conditional probability of window j is:
where s represents the total number of windows.
Preferably, p (f i |x m ) S discrete values (i=1, …, s), the jump of the samples of window j is judged by equation (5):
where r is a random number between 0 and 1 and k is the minimum value that satisfies the inequality.
Preferably, the S4 includes: assuming θ is to be solved for, the following holds:
M(θ)＝b (6)；
constructing a random variable N (·, θ) such that E [ N (·, θ) ]=M (θ); according to the random approximation,
the θ value can be iteratively obtained by equation (7):
θ t+1 ＝θ t -γ t (N(·，θ t )-b) (7)；
the purpose of gibbs sampling is to look for a suitable f-value, let { p (f 1 )，…，p(f s ) Equal to { pi } 1 ，…，π s (where pi) i The value is used to freely define the number of samples per window; using stochastic approximation, the initial free energy value f is updated iteratively and optimized according to equation (8):
wherein k is t Representing the system at the kth window, f at time t t Representing the free energy corresponding to each window.
A second aspect of the invention provides a single GPU replica swap free energy computing system, comprising:
a decomposition module for decomposing the replica switched MD simulation into two-dimensional gibbs samples: the variable of one dimension is defined as x; the other dimension is the free energy f corresponding to each window; defining a joint probability characterization copy exchange MD simulation;
a first conditional probability module for defining a specific window j, a constellation x based on the joint probabilities m And the conformation x m Sampling under this conditional probability is achieved by monte carlo or by molecular dynamics simulation;
a second conditional probability module for defining a specific constellation x based on the joint probabilities m Conditional probability of window j;
a calculation module for constructing a conformation x based on a specific window j m Conditional probability, specific conformation of (c)
x m The conditional probability of window j and the random approximation strategy calculate the free energy of single GPU copy exchange.
A third aspect of the present invention is to provide an application of the single GPU replica swap free energy computing method in kinetic simulation.
The system, the method and the application provided by the invention have the following beneficial technical effects:
the invention innovatively provides a single GPU copy exchange free energy calculation method, realizes the enhanced sampling dynamics simulation of the single GPU, and can be realized by setting pi i The value freely defines the number of samples per window and the initial free energy can be updated and optimized by stochastic approximation.
Drawings
FIG. 1 is a schematic diagram of a traditional kinetic simulation and replica exchange MD simulation according to the prior art; wherein FIG. 1 (a) is a schematic diagram of a conventional kinetic simulation; FIG. 1 (b) is a schematic diagram of a replica switch MD simulation;
FIG. 2 is a schematic diagram of the principle that conventional kinetic methods would bind around the local minima of the potential energy plane in the presence of a high potential barrier according to the prior art;
FIG. 3 is a flow chart of a single GPU copy swap free energy computing method according to the present invention;
FIG. 4 is a diagram of a single GPU copy swap free energy computing system architecture, shown in accordance with the present invention;
FIG. 5 is a flow chart illustrating the system operating principle and the single GPU copy switch implementation policy principle according to the preferred embodiment of the present invention;
FIG. 6 is a graph of RBFEP thermodynamic cycle according to a preferred embodiment of the present invention;
fig. 7 is a graph of RBFEP values versus simulation time for two compounds calculated in accordance with a conventional kinetic simulation and a single GPU copy exchange strategy, according to a preferred embodiment of the present invention.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
The terms used in the examples are as follows a:
ABFEP: absolute binding free energy perturbation
RBFEP: relative binding free energy perturbation
GPU: graphics processor
MD: molecular dynamics
Example 1
As shown in fig. 3, a method for calculating free energy of single GPU copy exchange is provided, which includes:
s1, performing analog decomposition on a replica exchange MD into two-dimensional Gibbs sampling: the variable of one dimension is defined as x, and represents the conformation x of a research system, and under the classical mechanical framework, the system momentum can be counteracted when thermodynamic properties are calculated; the other dimension is the free energy f corresponding to each window; defining a joint probability characterization replica switch MD simulation:
wherein pi j The probability of the system in the j window is represented, and other terms on the right of the equation meet the Boltzmann distribution;
s2, defining a specific window j and a conformation x m The conditional probability of (2) is defined as:
the conformation x m Sampling under this conditional probability is achieved by monte carlo or by molecular dynamics simulation; for Monte Carlo implementation, the new conformation x n The reception probability of (2) satisfies:
for molecular dynamics simulation implementation, the embodiment utilizes open source Gromacs software to implement conformation x in a specific window pair m Molecular dynamics analog sampling of (a);
s3, defining a specific conformation x m The conditional probability of window j is:
wherein s represents the total number of windows; due to p (f i |x m ) S discrete values (i=1, …, s), so the jump in the samples of window j is judged by equation (5):
where r is a random number between 0 and 1, and k is a minimum value satisfying the establishment of the inequality;
s4, the step is also the core of the corresponding solution strategy of the method. It can be seen that S f needs to be set at S3 i The magnitude of the value. If f i The difference between the current free energy value and the actual free energy value of the i window is large, so that the sampling in the i window is insufficient; if f i Equal to the actual free energy of the i window, then the samples in the i window satisfy pi i . For how to select reasonable f i The value, this embodiment adopts a random approximation strategy. Assuming θ is to be solved for, the following holds:
M(θ)＝b (6)；
a random variable N (·, θ) is constructed such that E [ N (·, θ) ]=m (θ). Then, based on the stochastic approximation, the θ value can be iteratively obtained by equation (7):
θ t+1 ＝θ t -γ t (N(·，θ t )-b) (7)；
the purpose of gibbs sampling is to look for a suitable f-value, let { p (f 1 )，…，p(f s ) Equal to { pi } 1 ，…，π s (where pi) i The value is used to freely define the number of samples per window; with stochastic approximation, the initial free energy value f can be updated iteratively and optimized according to equation (8):
wherein k is t Representing the system at the kth window, f at time t t Representing the free energy corresponding to each window.
Example two
As shown in fig. 4, there is provided a single GPU replica swap free energy computing system, comprising:
a decomposition module 101 for decomposing the replica switched MD simulation into two-dimensional gibbs samples: the variable of one dimension is defined as x and represents the conformation x of the research system; the other dimension is the free energy f corresponding to each window; defining a joint probability characterization replica switch MD simulation:
wherein pi j The probability of the system in the j window is represented, and other terms on the right of the equation meet the Boltzmann distribution;
a first conditional probability module 102 for defining a specific window j, conformationx m The conditional probability of (2) is defined as:
sampling of the conformation x under this conditional probability is achieved by monte carlo or by molecular dynamics simulation; for Monte Carlo implementation, the new conformation x n The reception probability of (2) satisfies:
for molecular dynamics simulation implementation, the embodiment utilizes open-source Gromacs software to realize molecular dynamics simulation sampling of x in a specific window;
a second conditional probability module 103 for defining a specific conformation x m The conditional probability of window j is:
wherein s represents the total number of windows; due to p (f i |x m ) S discrete values (i=1, …, s), so the jump in the samples of window j is judged by equation (5):
where r is a random number between 0 and 1, and k is a minimum value satisfying the establishment of the inequality;
the calculation module 104 is configured to take a random approximation policy, and assume that θ is to be solved so that the following equation holds:
M(θ)＝b (6)；
a random variable N (·, θ) is constructed such that E [ N (·, θ) ]=m (θ). Then, based on the stochastic approximation, the θ value can be iteratively obtained by equation (7):
θ t+1 ＝θ t -γ t (N(·，θ t )-b) (7)；
the purpose of gibbs sampling is to look for a suitable f-value, let { p (f 1 )，…，p(f s ) Equal to { pi } 1 ，…，π s (where pi) i The value is used to freely define the number of samples per window; with stochastic approximation, the initial free energy value f can be updated iteratively and optimized according to equation (8):
wherein k is t Representing the system at the kth window, f at time t t Representing the free energy corresponding to each window.
Example III
The application of the single GPU copy exchange free energy calculation method in dynamics simulation is provided.
Referring to fig. 5, the working principle of the single GPU copy swap free energy computing system and the single GPU copy swap implementation strategy diagram. The entire simulation flow is shown in fig. 5: in window 1, sampling is performed by conventional kinetic simulation, and the left black sphere represents the conformation obtained by sampling; at a certain time point, judging whether the conformation can jump to other windows or not, and if the free energy used in calculating the judging standard is not updated; assuming that the condition of jumping from window 1 to window 2 is satisfied, the gray conformation is swapped to window 2 and the free energy is updated by the stochastic approximation method; the traditional dynamics simulation is carried out on the window 2, and the potential barrier of the window 2 is low, so that the left and right sides of the potential energy surface can be sampled to obtain conformations (gray balls); sampling happens right at a certain time point, and jump standards are calculated according to updated free energy; assuming that the condition of jumping from window 2 to window 1 is satisfied, the conformation is swapped to window 1 and the free energy is updated. It can be seen that a black sphere appears on the right side of the window 1, achieving the effect of enhanced sampling.
In summary, the technique achieves enhanced sampling dynamics simulation of a single GPU, which can be achieved by setting up
π i The value freely defines the number of samples per window and the initial free energy can be updated and optimized by stochastic approximation.
TYK2 is a non-receptor tyrosine kinase that plays a key role in downstream signaling by responding to various cytokines in the human body. Currently, various scientific research institutions are devoted to researching TYK2 inhibitors, and considerable treatment effects are expected to be obtained in the fields of immunity, tumors and the like. As shown in fig. 6, two compounds active with TYK2 were selected and subjected to RBFEP calculation by single GPU copy swap method.
As shown in fig. 7, the red line represents the change in RBFEP values over time for two compounds calculated by conventional kinetic simulation, and the 5 red lines represent that we repeated 5 independent simulations to calculate standard deviation and determine the repeatability of the calculation. Green represents the change in RBFEP values calculated by the single GPU copy swap policy over time, we have also repeated 5 independent calculations. As can be seen, the convergence of the results of the conventional kinetic simulation calculations is poor, and 5 simulations give a maximum of-4.01 kcal/mol and a minimum of-4.52 kcal/mol, which differ by 0.5kcal/mol. For the single GPU copy switching strategy, the 5 computations tend to converge, and the difference between the maximum and minimum values is only 0.19kcal/mol. Compared with the traditional method, the calculation repeatability of the strategy is better due to the fact that copy exchange enhanced sampling is considered.
As shown in Table 1, the calculated values given by the conventional kinetic method are-4.20 kcal/mol, and the standard deviation is 0.18kcal/mol (data in brackets). While the RBFEP value predicted by the single GPU copy-exchange strategy is-4.14 kcal/mol, which is closer to the experimental value-3.89 kcal/mol. Compared with the traditional method, the standard deviation is reduced by more than 2 times and is only 0.07kcal/mol. In summary, the single GPU copy exchange strategy realizes RBFEP/ABFEP calculation on 1 GPU card, and can also perform high-order activity calculation under the condition of limited hardware resources; the single GPU copy exchanging method optimizes the free energy of each window through random approximation, so that the sampling of each window truly meets the set value of a user; compared with the traditional method, the single GPU copy exchange strategy realizes enhanced sampling in dynamic simulation, and the calculated value is closer to the experimental value and the standard deviation is smaller.
TABLE 1
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention. It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (10)
1. A single GPU replica swap free energy computing method, comprising:
s1, performing analog decomposition on a replica exchange MD into two-dimensional Gibbs sampling: the variable of one dimension is defined as x; the other dimension is the free energy f corresponding to each window; defining a joint probability characterization copy exchange MD simulation;
s2, defining a specific window j and a conformation x based on the joint probability m And the conformation x m Sampling under this conditional probability is achieved by monte carlo or by molecular dynamics simulation;
s3, defining a specific conformation x based on the joint probability m Conditional probability of window j;
s4, based on a specific window j, a conformation x m Conditional probability of (1) specific conformation x m The conditional probability of window j and the random approximation strategy calculate the free energy of single GPU copy exchange.
2. The method for calculating free energy of single GPU copy swap according to claim 1, wherein the joint probability in S1 is:
wherein pi j The other terms to the right of the equation satisfy the boltzmann distribution, which represents the probability of the system being in the j window.
3. A method according to claim 2, wherein the specific window j, conformation x in S2 m The conditional probability of (2) is defined as:
the conformation x m Sampling under this conditional probability is achieved by monte carlo or by molecular dynamics simulation.
4. A single GPU replica swap free energy computing method according to claim 3, wherein for a monte carlo implementation, the new constellation x n The reception probability of (2) satisfies:
5. a single GPU replica swap free energy computing method according to claim 3, wherein for molecular dynamics simulation implementations, the conformation x is implemented in a particular window pair using open source Gromacs software m Molecular dynamics analog sampling of (a).
6. A method of single GPU copy swap free energy computing according to claim 4 or 5, wherein a specific constellation x is defined in S3 m The conditional probability of window j is:
where s represents the total number of windows.
7. A single GPU replica swap free energy computing method according to claim 6, wherein p (f i |x m ) S discrete values (i=1, …, s), the jump of the samples of window j is judged by equation (5):
where r is a random number between 0 and 1 and k is the minimum value that satisfies the inequality.
8. A single GPU replica swap free energy computing method according to claim 7, wherein s4 comprises: assuming θ is to be solved for, the following holds:
M(θ)＝b (6)；
constructing a random variable N (·, θ) such that E [ N (·, θ) ]=M (θ); according to the random approximation,
the θ value can be iteratively obtained by equation (7):
θ t+1 ＝θ t -γ t (N(·，θ t )-b) (7)；
the purpose of gibbs sampling is to look for a suitable f-value, let { p (f 1 )，…，p(f s ) Equal to { pi } 1 ，…，π s (where pi) i The value is used to freely define the number of samples per window; using stochastic approximation, the initial free energy value f is updated, iterated and optimized according to equation (8):
wherein k is t Representing the system at the kth window, f at time t t Each representation isThe free energy corresponding to each window.
9. A single GPU replica switched free energy computing system for implementing the method of any of claims 1-8, comprising:
a decomposition module (101) for decomposing the replica switched MD simulation into two-dimensional gibbs samples: the variable of one dimension is defined as x; the other dimension is the free energy f corresponding to each window; defining a joint probability characterization copy exchange MD simulation;
a first conditional probability module (102) for defining a specific window j, a constellation x, based on said joint probabilities m And the conformation x m Sampling under this conditional probability is achieved by monte carlo or by molecular dynamics simulation;
a second conditional probability module (103) for defining a specific constellation x based on the joint probabilities m Conditional probability of window j;
a computation module (104) for constructing a constellation x based on a specific window j m Conditional probability of (1) specific conformation x m The conditional probability of window j and the random approximation strategy calculate the free energy of single GPU copy exchange.
10. Use of a single GPU replica swap free energy computing method according to any of claims 1-8 in kinetic simulation.
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