All powers and duties connected with and incident to the appointment, removal, government, and discipline of the officers and members of the fire department and police department of any city of the metropolitan class in the State of Nebraska, under such rules and regulations as may be adopted by the city council, shall be vested in and exercised by the city council. Rules and regulations for the guidance of the officers and members of such departments, and for the appointment, promotion, removal, trial, or discipline of such officers and members, shall be such as the city council shall consider proper and necessary.