amanitin Although the ferromagnetic particles and T DNA liga
Although the ferromagnetic particles and T4 amanitin on the particles were heated by the ac magnetic field, the average temperature of the reaction solution as a whole was kept suitably low for the annealing of DNA ends (16°C). Indeed, no appreciable increase in the temperature of the reaction solution was detected since the volume fraction of the heat-dissipating ferromagnetic particles in the solution (final volume fraction after mixing the solutions for the reaction) was as low as 3.2 × 10−3%. We analyzed heat transfer between ferromagnetic particles and the solvent fluid surrounding the particles in order to understand the thermal conditions in the present experiment in more detail. Since the volume fraction of the particles was very low in the present experiment, the particles can be assumed to be thermally isolated from each other. The steady-state temperature distribution around a spherical particle obtained by solving the heat conduction equation is:where r, a, T, and T are, respectively, the distance from the center of a particle, the radius of the particle, the surface temperature of the particle and the ambient temperature, which corresponds to the average temperature of the reaction solution (16°C) in the present experiment. The volume fraction of regions around particles, the temperature of which is higher than a certain threshold, T, obtained from Eq. (1) is given bywhere is the volume fraction of particles. When the amplitude of the ac magnetic field was 30kA/m, which corresponds to the maximum field amplitude in the present study, the particle\'s surface temperature estimated above was 27°C, in which case, the volume fraction of the regions around the particles heated to 17°C or higher (volume fraction of fluid regions where the temperature increase is higher than 1°C) calculated by Eq. (2) is as low as 4.2% and therefore we suppose that the annealing of DNA ends was efficiently carried out almost without being affected by heat dissipation from the magnetic particles. However, in the present case, phosphodiester bonds between DNA fragments are formed by DNA ligase immobilized on the surface of magnetic particles and therefore annealed DNA fragments have to travel through the higher temperature region to the particle\'s surfaces (see Fig. 1). Now we compare DNA ligation under an ac magnetic field and that in the absence of a magnetic field, noting that the temperature of small regions including magnetic particles is locally increased under an ac magnetic field at the ambient temperature of 16°C in the former case, whereas the temperature is uniform throughout the reaction solution in the latter case. When the surface temperature of magnetic particles in the former case is equal to the ambient temperature in the latter case, the activities of DNA ligase in those cases are equal to each other since DNA ligase is immobilized on the surface of magnetic particles. Comparing the ligation efficiency under the ac magnetic field as a function of the particle\'s surface temperature (inset in Fig. 4) and the temperature dependence of the ligation efficiency in the absence of a magnetic field (Fig. 3), we found that the ligation efficiency under the ac magnetic field was always higher than that in the absence of a magnetic field at the same temperature. The ligation efficiency under the ac magnetic field increased with an increase in the particle\'s surface temperature, while the ligation efficiency under a zero magnetic field in the same temperature range (20–27°C) decreased with an increase in the ambient temperature. Therefore the difference between the ligation efficiencies in those cases increased with an increase in the temperature. The present result clearly shows that DNA ligase immobilized on ferromagnetic particles is activated by heating with an ac magnetic field having much less effect on the annealing of DNA ends than the case of uniform heating. If the field amplitude is increased further, although the activity of DNA ligase may increase, the effect of heat dissipation from ferromagnetic particles on DNA annealing may become more significant at the same time and therefore, it is supposed that the ligation efficiency may reach the maximum at a higher field amplitude.