Sedimentation constant, also known as sedimentation coefficient, refers to the macromoleculeSettling velocityIs equal to the velocity per unit of centrifugal field.Or s=v/(ωtwo‧r)。S is the settlement coefficient, ω is the angular velocity of the centrifugal rotor（radian/Second), r is the distance to the center of rotation, and v is the settling velocity.The settlement coefficient is expressed as the settlement time per unit gravity, and is usually within the range of 1~500 × 10 to the 13th power second, 10-13This factor is called settlement unit s, that is, 1s=10-13Seconds, such ashemoglobinThe settlement coefficient of is about 4 × 10-13Seconds or 4s.Generally, the pure protein is between 1~20S, the larger nucleic acid molecule is between 4~100S, and the larger subCellular structureBetween 30 and 500S.
According to the definition of sedimentation coefficient by Svedberg (Swedish protein chemist, the founder of centrifugation) in 1924: the velocity of particles moving in the unit centrifugal force field.The settlement coefficient is expressed in time.
In fact, the S of protein, nucleic acid and other biological macromolecules is often 10-13Seconds, so the settlement coefficient is 10-13The second is called a Svedberg unit, abbreviated as S,dimensionIs seconds.
As it changes with the type of solvent and temperature, it is usually converted to the value in 20 ℃ pure water, and then the extrapolation is calculated when there is no intermolecular force and the concentration is zero.Sedimentation coefficient is determined by molecular weight, molecular shape and water, which is very important as a feature of biological macromolecules.[1]
Measurement principle
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Fundamentals
The measuring principle of sedimentation coefficient is to measure the sedimentation velocity of sample particles under a constant centrifugal force field.
Because the sample particles are so small that their sedimentation movement cannot be seen directly, the moving speed of the sample particles at the interface during centrifugation is regarded as the average of the sample particlesSettling velocity。Usually Schlieren and absorption are usedoptical system To record the interface settlement diagram.In the sedimentation diagram, the sample interface generally presents a symmetrical peak, and the highest point of the peak represents the interface position.
General settlement coefficientmeasurement accuracy It is ± 2%, but if the surface boundary pattern shows an asymmetric peak pattern, or if the settlement coefficient measurement accuracy is expected to reach ± 1% or less, it is not enough to use the highest point of the peak as the interface position. In this case, the second order distance method should be used to calculate the interface position.[1]
Formula derivation
When the object rotates around the central axis, it will be affected by the centrifugal force F.WhenMass of objectM, V, D, rangular velocityIs ω（radianNumber/second), we can get:
F=M‧ωtwoR or F=V ·D ·ωtwo‧r （1）
The above shows that:centrifugal forceIt is proportional to the mass, volume, density, square of centrifugal angular velocity and radius of rotation of the material.The greater the centrifugal force, the faster the centrifuged material settles.
In the process of centrifugation, the material to be centrifuged also needs to overcome buoyancy andfrictionOfHindrance。The buoyancy F 'and friction F' 'are respectively expressed by the following formula:
F'=V‧D'‧ωtwo‧r （2）
F''=μ‧dr/dt （3）
Where, D 'is the solution density, μ is the friction coefficient, and dr/dt is the settling speed (change of rotation radius in unit time).
Under certain conditions, there can be:
F=F'+F''
V‧D‧ωtwo‧r =V‧D'‧ωtwo‧r + μ‧dr/dt
dr/dt =V‧ωtwo‧r‧(D-D')/μ (4)
Equation (4) shows that,Settling velocityIt is directly proportional to the volume and density difference of the centrifuged material, and inversely proportional to μ.If S represents the unit force field (ωtwoSettlement speed under r=1), then
S=V‧(D-D')/μ
S is the settlement coefficient.
When centrifuging,macromoleculeSettling velocityOfmeasurement, equal to the velocity per unit of centrifugal field.Or s=v/(ωtwo‧r)。S is the settlement coefficient, ω is the angular velocity of the centrifugal rotor (radians/second), r is the distance to the rotation center, and v is the settlement velocity.The sedimentation coefficient is expressed as the sedimentation velocity per unit gravity. For biological macromolecules, the sedimentation coefficient is mostly (1~500) × 10-13Seconds.For the convenience of application, it is stipulated that 1 × 10-13The second is a unit (or 1S).The larger the sedimentation coefficient is, the more settlement occurs first during centrifugation.Generally, the pure protein is between 1~20S, the larger nucleic acid molecule is between 4~100S, and the larger subCellular structureBetween 30 and 500S.
Take protein as an example. If the density of protein solution is greater than the density of solvent when protein in solution is subjected to strong centrifugal action, protein molecules will sink. In the centrifugal field, when the net centrifugal force (centrifugal force minus buoyancy) that protein molecules are subjected to is balanced with the friction force of solvent, the strength of each unit of centrifugal field is fixed,This fixed value is the sedimentation coefficient.Settling velocityIt is expressed as the distance of particle sinking per unit time.[1]
Determination method
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Settlement coefficient through analysisCentrifugedetermination.
Usually, only tens of milligrams or even tens of micrograms of samples are needed to prepare 1~2ml solution, which is loaded into the analysis cell and analyzed for several hourscentrifugalA series of samples can be obtainedCentrifugal sedimentationFig.According to the settlement diagram, the content of samples can be determinedComponentsFor qualitative analysis, it can also measure the sedimentation coefficient and estimate the molecular size of each component, conduct sample purity verification and heterogeneity determination, and determine the relative content of each component.[1]
(1) Sample: Protein
(2) Sample solution and centrifugation: dissolve the sample inBufferUse a double tank analysis cell of certain specification to add solution and solvent at the same time.Balance the weight of the analysis tank and the balance tank so that the balance tank is less than 0.5g lighter than the analysis tank, and then load them into the analysis turntables respectively.Vacuum.Turn on Schlieren light source, select working speed and centrifuge at room temperature.When the rotating chamber reaches vacuum, the centrifuge starts to run and accelerate. At this time, the centrifuge pattern can be seen in the observation window.Centrifuge at constant speed after reaching the working speed.
Take protein as an example. After seeing the tip of the sample peak, you can take pictures at intervals.Shut down the machine after photographing, take out the sample solution, and clean the rotating head and the analysis cell.The image of Schlieren optical path sedimentation is obtained after strong contrast development and processing.
(3) SettlementImage measurement: Schlieren settlement diagram can be measured with a comparator,Reading microscope, or projector measurement.When measuring, place the negative of the sedimentation image on the measuring instrument so that the vertical line of the liquid level coincides with the vertical line in the measuring instrument, and then measure the positions of the internal reference hole, the liquid level, the interface peak tip, and the external reference hole with a cross mark. Read each image at least three times and take the average value.Measure each image in the same way and list the data.
(4) Calculation of settlement coefficient S: calculated by formula.[1]
image analysis
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If a fast settling peak is seen at the beginning of centrifugation, it will reach the bottom of the analysis cell within a few minutes. Generally, it is because the sample is partially polymerized to form a fast settling polymer.The cardiac image of the sample after centrifugation reaches the speed shows a symmetrical peak shape, and the sample can generally be considered as centrifugally homogeneous.But yessampleOther methods such as electrophoresis, chromatography and so on are also used to further test the true homogeneity of.Occasionally, some mixed samples will also give a symmetric peak.The peak shape usually expands with time, which is the result of sample diffusion.However, if the peak shape expands rapidly, the sample may be polydisperse.If several peaks appear in the centrifuge image, it means that there are several components in the sample, and each peak represents the sedimentation interface of the corresponding component, so the sedimentation coefficient value of each component can be measured.The concentration of components can be measured according to the peak area.
Sometimes the centrifugal image shows an asymmetric peak, which may be caused by the following conditions. ①The peaks of several components with similar settlement coefficients overlap; ②The sample is polydispersemolecular weight distributionUneven; ③Some strongly interactinghigh polymer, whichSettling velocityIt is highly dependent on concentration.If it is measured at high concentration, the peak shape is asymmetric due to the inconsistent settling velocity caused by the concentration change in the interface area.[2]
application
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Centrifuge, which separates samples according to their mass, density and friction coefficient, has been widely used in the research field of biomacromolecules.The settling constant reflects the physical properties of settling particles under certain conditions. When the conditions are certain, it is a constant, representing the settling characteristics and structure of biological macromolecules. It can study the self polymerization state and homogeneity of biological macromolecules, assembly mechanism of macromolecular complexes, etc.[3]
