CN113125552B - A method for determining kinetic and thermodynamic parameters at solid-liquid interfaces - Google Patents
A method for determining kinetic and thermodynamic parameters at solid-liquid interfaces Download PDFInfo
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- ZKHQWZAMYRWXGA-KQYNXXCUSA-J ATP(4-) Chemical compound C1=NC=2C(N)=NC=NC=2N1[C@@H]1O[C@H](COP([O-])(=O)OP([O-])(=O)OP([O-])([O-])=O)[C@@H](O)[C@H]1O ZKHQWZAMYRWXGA-KQYNXXCUSA-J 0.000 description 7
- ZKHQWZAMYRWXGA-UHFFFAOYSA-N Adenosine triphosphate Natural products C1=NC=2C(N)=NC=NC=2N1C1OC(COP(O)(=O)OP(O)(=O)OP(O)(O)=O)C(O)C1O ZKHQWZAMYRWXGA-UHFFFAOYSA-N 0.000 description 7
- 108091023037 Aptamer Proteins 0.000 description 5
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Abstract
The invention discloses a method for measuring kinetic and thermodynamic parameters on a solid-liquid interface, which is characterized in that the kinetic and thermodynamic parameters (a binding/dissociation equilibrium constant K A/KD, gibbs free energy delta G DEG, surface coverage theta, a binding/dissociation rate constant K a/kd and a reaction activation energy E a) of a nucleic acid aptamer and a ligand thereof on the solid-liquid interface are obtained by analyzing and calculating the output frequency-time curve of a micro-cantilever sensor according to the frequency-time curve corresponding to ligand solutions with different concentrations to be measured and the frequency-time curve of ligand solutions with other concentrations to be measured at two different temperatures. The method overcomes the defects of expensive instruments, complicated operation, single parameter measurement and the like of the traditional method, has the advantages of high sensitivity, low cost, simple and quick operation, no need of marking and correction, capability of effectively avoiding systematic errors, one-time measurement of related parameters and the like, and is suitable for measuring dynamics and thermodynamic parameters of various nucleic acid aptamers and ligands thereof.
Description
Technical Field
The invention relates to the technical field of molecular dynamics/thermodynamics, in particular to a method for measuring dynamics and thermodynamic parameters of biochemical reaction on a solid-liquid interface.
Background
Nucleic acid aptamer (Nucleic ACID APTAMER) is an artificially synthesized RNA or DNA receptor molecule, and various target substances (small molecules, proteins and even cells) can be used as ligands. The nucleic acid aptamer has stable chemical property, is easy to synthesize, can be modified according to requirements, has high specificity and affinity for the ligand, and has become a common molecular recognition element in the development and application of biosensors.
When the biosensor is used for detecting an object to be detected in a solution, the occurrence place of the biosensor is a solid-liquid interface no matter the reaction occurs, the energy is transferred and the signal is converted. Therefore, the kinetics/thermodynamics of biochemical reaction on the solid-liquid interface can be quantitatively researched, the biosensing mechanism can be researched, the sensor performance can be perfected, the interface design and material optimization can be evaluated, and the design and the manufacture of the biosensor can be guided. While there is a lot of work to study the kinetics and thermodynamic behavior of aptamer and its ligand in solution, the diffusion layer on the solid-liquid interface and the steric effect of the capture probe will generate energy barriers, and the parameters obtained from the solution cannot describe the kinetics and thermodynamic behavior of biochemical reaction on the interface, while the kinetics and thermodynamic research methods on the solid-liquid interface are often limited by factors such as signal markers and temperature change range, so the development of biological interface sensing, especially the biological sensing system based on the reaction of aptamer and ligand, is highly needed to provide a method for rapidly measuring the kinetics and thermodynamic parameters of aptamer and ligand on the solid-liquid interface, so as to systematically study the kinetics and thermodynamic mechanism and physicochemical process on the solid-liquid interface.
In view of the foregoing, it is desirable to provide a method for determining kinetic and thermodynamic parameters at a solid-liquid interface to solve the above-mentioned problems.
Disclosure of Invention
In view of the limitations of the traditional method for measuring dynamic and thermodynamic parameters on an interface, the invention aims to provide a more direct, convenient and comprehensive method, which can directly and quickly obtain the required dynamic and thermodynamic parameters according to a frequency-time curve, and utilizes a micro-cantilever sensor as a detection platform to track the occurrence of a reaction on a solid-liquid interface in real time, so that a plurality of dynamic/thermodynamic parameters are extracted at one time, the modification or marking of an object to be measured is not needed, the mass sensitivity calibration is not needed, the measurement efficiency is improved, the measurement error is effectively avoided, and the measurement cost is reduced.
The invention is realized by the following technical scheme:
the invention provides a method for measuring dynamic and thermodynamic parameters on a solid-liquid interface, which comprises the following steps:
S100, providing a frequency-time curve diagram corresponding to each of a plurality of ligand solutions with different concentrations to be detected and a frequency-time curve diagram of another ligand solution with different concentrations to be detected at two different temperatures, wherein the ligand solutions with different concentrations to be detected at least comprise three ligand solutions with different concentrations to be detected;
S200, calculating to obtain dynamic and thermodynamic parameters on a solid-liquid interface according to frequency-time graphs corresponding to the ligand solutions with different concentrations to be detected, wherein the parameters at least comprise a binding equilibrium constant K A, a dissociation equilibrium constant K D, a Gibbs free energy delta G, a surface coverage theta, a binding rate constant K a and a dissociation rate constant K d;
s300, calculating to obtain the reaction activation energy E a according to a frequency-time curve diagram of the ligand solution with the other concentration to be detected at the two different temperatures.
Further, according to the frequency-time graphs corresponding to the ligand solutions with different concentrations to be detected, kinetic and thermodynamic parameters on the solid-liquid interface are calculated, wherein the parameters at least comprise a binding equilibrium constant K A, a dissociation equilibrium constant K D, a gibbs free energy Δg °, a surface coverage θ, a binding rate constant K a, and a dissociation rate constant K d, and the steps include:
S201, reading to obtain frequency change values delta f corresponding to the concentrations of the ligands to be detected according to the frequency-time graphs corresponding to the ligand solutions to be detected;
S202, calculating to obtain a reactive binding equilibrium constant K A according to frequency change values Deltaf corresponding to the concentrations of the multiple different ligands to be detected;
S203, calculating to obtain a dissociation equilibrium constant K D of the reaction according to the binding equilibrium constant K A of the reaction;
S204, calculating to obtain gibbs free energy delta G DEG of the reaction according to the binding equilibrium constant K A of the reaction;
S205, calculating to obtain surface coverage theta corresponding to the concentration of various ligands to be detected according to the binding equilibrium constant K A of the reaction;
s206, calculating to obtain a combination rate constant k a of the reaction according to the frequency-time curve graphs and the corresponding surface coverage theta corresponding to the ligand solutions with different concentrations to be detected;
S207, calculating to obtain a dissociation rate constant k d according to the combination rate constant k a of the reaction.
Further, the calculating the binding equilibrium constant K A according to the frequency change value Δf corresponding to the concentrations of the plurality of different ligands to be detected includes:
according to the frequency change value delta f corresponding to the concentration of the multiple different ligands to be detected, the method passes through the formula The binding equilibrium constant K A of the reaction was calculated.
Wherein [ L ] is the concentration of the ligand to be detected, and A is a constant reflecting the number of maximum reaction sites on the interface.
Further, the calculating the dissociation equilibrium constant K D of the reaction according to the binding equilibrium constant K A of the reaction includes:
The dissociation equilibrium constant K D for the reaction is calculated by equation K D＝1/KA based on the binding equilibrium constant K A for the reaction.
Further, the calculating gibbs free energy Δg° of the reaction according to the binding equilibrium constant K A of the reaction includes:
The gibbs free energy Δg° of the reaction is calculated from the formula Δg° = -RTlnK A according to the binding equilibrium constant K A of the reaction.
Where R is the ideal gas constant, r= 8.314J/(mol·k), and T is the absolute temperature (K) at which the experiment was performed.
Further, the calculating the surface coverage θ corresponding to the concentrations of the plurality of different ligands to be detected according to the binding equilibrium constant K A of the reaction includes:
According to the binding equilibrium constant K A of the reaction, the reaction is carried out by the formula And calculating to obtain the surface coverage theta corresponding to the concentration of the various ligands to be detected.
Further, the calculating the binding rate constant k a according to the frequency-time graph and the corresponding surface coverage θ corresponding to each of the ligand solutions with different concentrations to be measured includes:
S2061, reading and obtaining the slope b of the frequency-time curve corresponding to the concentration of the ligand to be detected according to the frequency-time curve corresponding to the ligand solution to be detected;
s2062, according to the slope b of the frequency-time curve corresponding to the concentrations of the multiple different ligands to be detected, the frequency change value delta f corresponding to the concentrations of the multiple different ligands to be detected and the corresponding surface coverage theta, passing through the formula The binding rate constant k a of the reaction was calculated.
Further, the calculating the dissociation rate constant k d according to the binding rate constant k a of the reaction includes:
From the binding rate constant k a of the reaction, the dissociation rate constant k d is calculated by the formula k d＝ka/KA.
Further, the two different temperatures include a first preset temperature T 1 and a second preset temperature T 2, and calculating, according to a frequency-time graph of another ligand solution to be measured at the two different temperatures, a reaction activation energy E a includes:
S301, obtaining a frequency-time curve slope b 1 at the first preset temperature T 1 and a frequency-time curve slope b 2 at the second preset temperature T 2 according to the frequency-time curve graph of the ligand solution with the other concentration to be detected at the two different temperatures;
S302, calculating to obtain an activation energy E a according to the first preset temperature T 1, the second preset temperature T 2, the frequency-time curve slope b 1 at the first preset temperature T 1 and the frequency-time curve slope b 2 at the second preset temperature T 2.
Further, the calculating the activation energy E a according to the first preset temperature T 1, the second preset temperature T 2, the frequency-time curve slope b 1 at the first preset temperature T 1, and the frequency-time curve slope b 2 at the second preset temperature T 2 includes:
According to the first preset temperature T 1, the second preset temperature T 2, the slope b 1 of the frequency-time curve at the first preset temperature T 1 and the slope b 2 of the frequency-time curve at the second preset temperature T 2, the method is as follows The activation energy E a was calculated.
Where R is the ideal gas constant, r= 8.314J/(mol·k).
The implementation of the invention has the following beneficial effects:
1. the method can directly and quickly obtain the required dynamics and thermodynamic parameters according to the frequency-time curve, and the determination method of the required data curve is simple, convenient and quick, does not need complex instrument operation, and can directly detect the ligand in the solution without marking the ligand based on the micro-weighing detection mode of the micro-cantilever sensor;
2. the method provided by the invention can extract a plurality of kinetic and thermodynamic parameters at one time according to the data acquired by one micro-cantilever sensor, so that systematic errors caused by a plurality of tests and a plurality of instruments are avoided;
3. The method provided by the invention does not need to calibrate the mass sensitivity of the micro-cantilever sensor, simplifies the experimental steps and improves the measurement efficiency;
4. The micro-cantilever sensor used in the invention has extremely high sensitivity, overcomes the limitation that other methods can only detect macromolecules, and is used for researching the interaction mechanism of small molecules with low molecular weight and the nucleic acid aptamer thereof on an interface.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions and advantages of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are only some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for determining kinetic and thermodynamic parameters at a solid-liquid interface according to an embodiment of the present invention.
Fig. 2 is a flowchart of step S200 provided in an embodiment of the present invention.
Fig. 3 is a flowchart of step S300 provided in an embodiment of the present invention.
Fig. 4 is a schematic diagram of a detection system based on a micro-cantilever sensor according to an embodiment of the present invention.
FIG. 5 shows frequency-time curves obtained from the reaction of Adenosine Triphosphate (ATP) and its aptamer at the solid-liquid interface at different ATP concentrations [ L ] at the same temperature.
FIG. 6 is a graph of [ L ]/[ delta ] f [ L ] for calculating the binding/dissociation equilibrium constant K A/KD, the Gibbs free energy ΔG DEG using the data obtained in FIG. 5, according to an example of the present invention.
FIG. 7 is a graph of b- [ L ]. DELTA.f/θ for calculating a surface coverage θ, a binding rate constant k a, and a dissociation rate constant k d using the data obtained in FIG. 5, provided by an embodiment of the present invention.
FIG. 8 is a graph showing the frequency versus time for the measurement of the same ATP concentration at different temperatures, respectively, in accordance with an embodiment of the present invention.
The reference numerals correspond to 1-buffer solution, 2-ligand solution, 3-sample injection valve, 4-reaction cavity, 41-sample injection port, 42-sample outlet, 5-detection cavity, 6-micro cantilever beam chip, 7-temperature control device, 8-constant pressure pump, 9-waste liquid outlet, 10-computer and 11-data collector.
Detailed Description
The present invention will be described in further detail with reference to examples for the purpose of making the objects, technical solutions and advantages of the present invention more apparent. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a method for measuring dynamic and thermodynamic parameters on a solid-liquid interface, referring to fig. 1 to 8, the method for measuring the dynamic and thermodynamic parameters on the solid-liquid interface comprises the following steps:
S100, providing a frequency-time curve diagram corresponding to each of a plurality of ligand solutions with different concentrations to be detected and a frequency-time curve diagram of another ligand solution with different concentrations to be detected at two different temperatures, wherein the ligand solutions with different concentrations to be detected at least comprise three ligand solutions with different concentrations to be detected;
S200, calculating to obtain dynamic and thermodynamic parameters on a solid-liquid interface according to frequency-time graphs corresponding to the ligand solutions with different concentrations to be detected, wherein the parameters at least comprise a binding equilibrium constant K A, a dissociation equilibrium constant K D, a Gibbs free energy delta G, a surface coverage theta, a binding rate constant K a and a dissociation rate constant K d;
s300, calculating to obtain the reaction activation energy E a according to a frequency-time curve diagram of the ligand solution with the other concentration to be detected at the two different temperatures.
Further, according to the frequency-time graphs corresponding to the ligand solutions with different concentrations to be detected, kinetic and thermodynamic parameters on the solid-liquid interface are calculated, wherein the parameters at least comprise a binding equilibrium constant K A, a dissociation equilibrium constant K D, a gibbs free energy Δg °, a surface coverage θ, a binding rate constant K a, and a dissociation rate constant K d, and the steps include:
S201, reading to obtain frequency change values delta f corresponding to the concentrations of the ligands to be detected according to the frequency-time graphs corresponding to the ligand solutions to be detected;
S202, calculating to obtain a reactive binding equilibrium constant K A according to frequency change values Deltaf corresponding to the concentrations of the multiple different ligands to be detected;
S203, calculating to obtain a dissociation equilibrium constant K D of the reaction according to the binding equilibrium constant K A of the reaction;
S204, calculating to obtain gibbs free energy delta G DEG of the reaction according to the binding equilibrium constant K A of the reaction;
S205, calculating to obtain surface coverage theta corresponding to the concentration of various ligands to be detected according to the binding equilibrium constant K A of the reaction;
s206, calculating to obtain a combination rate constant k a of the reaction according to the frequency-time curve graphs and the corresponding surface coverage theta corresponding to the ligand solutions with different concentrations to be detected;
S207, calculating to obtain a dissociation rate constant k d according to the combination rate constant k a of the reaction.
As shown in fig. 2, the calculating the binding equilibrium constant K A according to the frequency change value Δf corresponding to the concentrations of the plurality of different ligands to be detected includes:
according to the frequency change value delta f corresponding to the concentration of the multiple different ligands to be detected, the method passes through the formula The binding equilibrium constant K A of the reaction was calculated. Wherein [ L ] is the concentration of the ligand to be detected, and A is a constant reflecting the number of maximum reaction sites on the interface.
The calculating the dissociation equilibrium constant K D of the reaction according to the binding equilibrium constant K A of the reaction includes:
The dissociation equilibrium constant K D for the reaction is calculated by equation K D＝1/KA based on the binding equilibrium constant K A for the reaction.
The calculation of the Gibbs free energy ΔG DEG of the reaction according to the binding equilibrium constant K A of the reaction comprises:
The gibbs free energy Δg° of the reaction is calculated from the formula Δg° = -RTlnK A according to the binding equilibrium constant K A of the reaction.
Where R is the ideal gas constant, r= 8.314J/(mol·k), and T is the absolute temperature (K) at which the experiment was performed.
The calculating the surface coverage theta corresponding to the concentration of the ligands to be detected according to the binding equilibrium constant K A of the reaction comprises the following steps:
According to the binding equilibrium constant K A of the reaction, the reaction is carried out by the formula And calculating to obtain the surface coverage theta corresponding to the concentration of the various ligands to be detected.
The calculating a binding rate constant k a of the reaction according to the frequency-time curve graphs corresponding to the ligand solutions with different concentrations to be detected respectively comprises:
S2061, reading and obtaining the slope b of the frequency-time curve corresponding to the concentration of the ligand to be detected according to the frequency-time curve corresponding to the ligand solution to be detected;
s2062, according to the slope b of the frequency-time curve corresponding to the concentrations of the multiple different ligands to be detected, the frequency change value delta f corresponding to the concentrations of the multiple different ligands to be detected and the corresponding surface coverage theta, passing through the formula The binding rate constant k a of the reaction was calculated.
The calculating the dissociation rate constant k d according to the binding rate constant k a of the reaction includes:
From the binding rate constant k a of the reaction, the dissociation rate constant k d is calculated by the formula k d＝ka/KA.
As shown in fig. 3, the two different temperatures include a first preset temperature T 1 and a second preset temperature T 2,
The calculating reaction activation energy E a according to the frequency-time curve graph of the ligand solution with the other concentration to be measured at the two different temperatures comprises:
S301, obtaining a frequency-time curve slope b 1 at the first preset temperature T 1 and a frequency-time curve slope b 2 at the second preset temperature T 2 according to the frequency-time curve graph of the ligand solution with the other concentration to be detected at the two different temperatures;
S302, calculating to obtain an activation energy E a according to the first preset temperature T 1, the second preset temperature T 2, the frequency-time curve slope b 1 at the first preset temperature T 1 and the frequency-time curve slope b 2 at the second preset temperature T 2.
Further, the calculating the activation energy E a according to the first preset temperature T 1, the second preset temperature T 2, the frequency-time curve slope b 1 at the first preset temperature T 1, and the frequency-time curve slope b 2 at the second preset temperature T 2 includes:
According to the first preset temperature T 1, the second preset temperature T 2, the slope b 1 of the frequency-time curve at the first preset temperature T 1 and the slope b 2 of the frequency-time curve at the second preset temperature T 2, the method is as follows The activation energy E a was calculated. Where R is the ideal gas constant, r= 8.314J/(mol·k).
As shown in fig. 4 to 8, a method for determining kinetic and thermodynamic parameters at a solid-liquid interface according to the present invention specifically comprises:
1) An amino-modified aptamer (sequence 5'-ACCTGGGGGAGTATTGCGGAGGAAGGTTTT-NH 2 -3') was conjugated to polydopamine microspheres.
2) Uploading to the detection area of the micro-cantilever chip by a micro-printer.
3) The micro-cantilever beam chip is put into a detection system for sealing treatment, and the micro-cantilever beam sensor has the advantages of low cost, small volume and good repeatability by adopting a detection chip based on the micro-cantilever beam technology, can directly detect the ligand in the solution without marking the ligand, and outputs continuous signals in real time so as to realize complete tracking of the reaction process.
4) As shown in fig. 4, the sample channel of the sample valve 3 is turned into the buffer solution 1, the constant pressure pump 8 is started, the system becomes negative pressure, the buffer solution fills the detection cavity 5 through the sample inlet 41, flows out from the sample outlet 42, and finally is discharged through the waste liquid outlet 9. And applying negative pressure at the tail end of the sampling pipe by using a constant pressure pump, so that the buffer solution flows into a main flow channel of the reaction cavity. The gas residue in the system is reduced by utilizing a negative pressure sample injection mode, and the sample injection is rapid.
5) The method comprises the steps of recording signals acquired by a data acquisition unit in real time by a computer, observing the reaction progress through the signals, namely adding ATP solution (dissolved in a binding buffer solution) with a certain concentration (L 1) into a system after resonance frequency is stable, recording a frequency-time curve and frequency change Deltaf 1, adding dissociation solution into the system after frequency is stable, carrying out interface regeneration, detecting the addition of other two concentration systems (L 2 and L 3) by the same method after the frequency is restored to an initial baseline level, and respectively obtaining the frequency-time curve and frequency change (Deltaf 2 and Deltaf 3) under the two concentrations, as shown in figure 5. The frequency-time curve graph corresponding to the ligand solution to be measured is obtained by sequentially adding the ligand solution to be measured, the measuring method is simple, convenient and quick, complex instrument operation is not needed, sample injection is only needed after the output frequency is stable, multiple groups of experimental data are extracted at one time by using one micro-cantilever sensor, and system errors caused by multiple experiments and multiple instruments are avoided.
6) As shown in FIG. 6, the frequency change Δf corresponding to the different ligand concentrations [ L ] in FIG. 5 is read and is taken into the formulaThe binding equilibrium constant K A＝7.42ⅹ10-3M-1 is obtained by [ L ]/Δf=2.85x10 -3[L]+3.85ⅹ10-9.
7) The resulting K A was taken into the formula K D＝1/KA and the dissociation equilibrium constant K D =1.3 μm was calculated.
8) Bringing the obtained K A into the formula DeltaG DEG= -RTlnK A, calculating the Gibbs free energy DeltaG DEG= -33.5kJ/mol.
9) Bringing the resulting K A into the formulaThe surface coverage θ at each ATP concentration [ L ] was calculated.
10 In FIG. 5, the slope b of the frequency-time curve after addition of the different ligand concentrations [ L ] to the system is read, combined with the frequency variation Δf and the surface coverage θ, and brought into the formulaIn (1) to obtainI.e. k a＝660M-1s-1.
11 The resulting k a is taken into the formula k d＝ka/KA and the dissociation rate constant k d,kd＝0.00089s-1 is calculated as shown in fig. 7.
12 As shown in fig. 8, under different conditions of T 1 (299K) and T 2 (293K), ATP solutions of the same concentration l=1μm were added to the system, and the slopes b 1 and b 2 were read, respectively, and were brought into the formulaThe activation energy E a =38.0 kJ/mol was calculated.
The embodiment of the invention has the following beneficial effects:
1. the method can directly and quickly obtain the required dynamics and thermodynamic parameters according to the frequency-time curve, and the determination method of the required data curve is simple, convenient and quick, does not need complex instrument operation, and can directly detect the ligand in the solution without marking the ligand based on the micro-weighing detection mode of the micro-cantilever sensor;
2. the method provided by the invention can extract a plurality of kinetic and thermodynamic parameters at one time according to the data acquired by one micro-cantilever sensor, so that systematic errors caused by a plurality of tests and a plurality of instruments are avoided;
3. The method provided by the invention does not need to calibrate the mass sensitivity of the micro-cantilever sensor, simplifies the experimental steps and improves the measurement efficiency;
4. The micro-cantilever sensor used in the invention has extremely high sensitivity, overcomes the limitation that other methods can only detect macromolecules, and is used for researching the interaction mechanism of small molecules with low molecular weight and the nucleic acid aptamer thereof on an interface.
While the invention has been described with respect to preferred embodiments thereof, it will be understood by those skilled in the art that various modifications and additions may be made without departing from the scope of the invention. Those skilled in the art will appreciate that many modifications, adaptations and variations of the present invention can be made using the techniques disclosed herein without departing from the spirit and scope of the invention, and that many modifications, adaptations and variations of the present invention are within the scope of the invention as defined by the appended claims.
Claims (10)
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