Among other aspects, the present invention relates to cell culture conditions for producing high molecular weight vWF, in particular, highly multimericWF with a high specific activity and ADAMTS13 with a high specific activity. The cell culture conditions of the present invention can include, for example, a cell culture medium with an increased copper concentration and/or cell culture supernatant with a low ammonium (NH4+) concentration. The present invention also provides methods for cultivating cells in the cell culture conditions to express high molecular weight vWF and rA13 having high specific activities.