We present a comprehensive 5-43 GHz VLBA study of the blazar 3C 273 initiated after an onset of a strong $gamma$-ray flare in this source. We have analyzed the kinematics of new-born components, light curves, and position of the apparent core to pinpoint the location of the $gamma$-ray emission. Estimated location of the $gamma$-ray emission zone is close to the jet apex, 2 pc to 7 pc upstream from the observed 7 mm core. This is supported by ejection of a new component. The apparent core position was found to be inversely proportional to frequency. The brightness temperature in the 7 mm core reached values up to at least $10^{13}$ K during the flare. This supports the dominance of particle energy density over that of magnetic field in the 7 mm core. Particle density increased during the radio flare at the apparent jet base, affecting synchrotron opacity. This manifested itself as an apparent core shuttle along the jet during the 7 mm flare. It is also shown that a region where optical depth decreases from $tausim1$ to $tau<<1$ spans over several parsecs along the jet. The jet bulk flow speed estimated at the level of 12c on the basis of time lags between 7 mm light curves of stationary jet features is 1.5 times higher than that derived from VLBI apparent kinematics analysis.
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