Synchronous coefficient of drag alteration
Synchronous coefficient of drag alteration (SCODA) is a biotechnology method for purifying, separating and/or concentrating bio-molecules. SCODA has the ability to separate molecules whose mobility (or drag) can be altered in sync with a driving field. This technique has been primarily used for concentrating and purifying DNA, where DNA mobility changes with an applied electrophoretic field. Electrophoretic SCODA has also been demonstrated with RNA and proteins. Theory As shown below, the SCODA principle applies to any particle driven by a force field in which the particle's mobility is altered in sync with the driving field. SCODA principle For explanatory purposes consider an electrophoretic particle moving (driven) in an electric field. Let: (1) and (2) denote an electric field and the velocity of the particle in such a field. If is constant the time average of . If is not constant as a function of time and if has a frequency component proportional to the time average of need not be zero. Consider the following example: (3) Substituting (3) in (2) and computing the time average, , we obtain: (4) Thus, it is possible to have the particle experience a non-zero time average velocity, in other words, a net electrophoretic drift, even when the time average of the applied electric field is zero. Creation of focusing field geometry Consider a particle under a force field that has a velocity parallel to the field direction and a speed proportional to the square of the magnitude of the electric field (any other non-linearity can be employed): (5) The effective mobility of the particle (the relationship between small changes in drift velocity with respect to small changes in electric field ) can be expressed in Cartesian coordinates as: (6) (7) Combining (5), (6) and (7) we get: (8) (9) Further consider the field E is applied in a plane and it rotates counter-clockwise at angular frequency , such that the field components are: (10) (11) Substituting (10) and (11) in (8) and (9) and simplifying using trigonometric identities results in a sum of constant terms, sine and cosine, at angular frequency . The next calculations will be performed such that only the cosine terms at angular frequency will yield non-zero net drift velocity - therefore we need only evaluate these terms, which will be abbreviated and . The following is obtained: (12) (13) Let and take the form of a small quadrupole field of intensity that varies in a sinusoidal manner proportional to such that: (14) (15) Substituting (14) and (15) into (12) and (13) and taking the time average we obtain: (16) (17) which can be summarized in vector notation to: (18) Equation (18) shows that for all positions the time averaged velocity is in the direction toward the origin (concentrating the particles towards the origin), with speed proportional to the mobility coefficient k, the strength of the rotating field E and the strength of the perturbing quadrupole field . DNA concentration and purification DNA molecules are unique in that they are long,