Explain the algorithmic modifications required to implement the Needleman-Wunsch global alignment algorithm using affine gap penalties (differentiating between gap opening and gap extension costs). Provide a step-by-step walkthrough of the initialization and recurrence relations for the scoring matrices (M, Ix, Iy). Calculate the time and space complexity for aligning two protein sequences of length N and M, and propose a heuristic method to reduce space complexity if exact traceback is not required for the full alignment.