* PIC is Africa's biggest pension fund (Adds Treasury comment, details): JOHANNESBURG, Feb 1 (Reuters) - The board of South Africa’s state-owned state pension fund resigned on Friday, citing destabilising allegations of wrongdoing against four directors, as the crisis at the biggest investor in Africa’s most industrialised economy deepens. The Public Investment Corporation (PIC), which has around 2 trillion rand ($150 billion) of civil servant pensions under management, is facing a judicial inquiry into corporate governance after an opposition party alleged that former chief executive Dan Matjila had misused funds and made careless investment decisions.