An individual-based model is presented which describes the spatial and temporal evolution of phytoplankton growth in terms of a Lagrangian ensemble of cells affected by various physical and biological forcing factors. The motion of cells develops according to a turbulent velocity field which simulates the Antarctic mixed layer during the summer. The cell growth is a function of the irradiance regime, nutrient availability and the vertical position of the individual with respect to the other cells (in order to evaluate the self-shading effect). The values of photosynthetic parameters used to simulate the photophysiological response of the organisms are derived from measurements collected in the Ross Sea. In contrast to previous individual-based descriptions, all the physical and biological processes involved are explicitly reproduced in their dynamical features. Coupling different mixing levels with photoacclimation strategies leads to a wide range of photophysiological responses which underline the role of individual physiological histories in determining the growth of the population as a whole. Simulated photosynthetic parameters, chlorophyll a concentrations and integrated primary production correspond closely to in situ data and confirm that photoacclimation to low irradiance and strong mixing regimes may be considered as crucial factors in the photosynthetic performance of Antarctic phytoplankton.