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Antibody affinity maturation is a natural optimization process in which B cells acquire mutations through somatic hypermutation (SHM), undergo selection for improved antigen binding, and iteratively evolve toward higher affinity. Computationally modeling this process requires capturing both biologically plausible mutations and antigen-specific selection. However, existing mutation models do not directly optimize binding, while affinity optimization often neglects realistic mutation trajectories. We introduce iGC (in silico Germinal Centers), a two-stage reinforcement learning (RL) framework for antigen-specific antibody optimization. Stage 1 learns an SHM mutation prior from parent-child pairs in B-cell lineage trees and adapts it to a target affinity-maturation dataset. Stage 2 initializes an RL policy from this prior and optimizes antigen binding with Kullback-Leibler (KL) regularization toward the frozen prior. To prevent reward exploitation, including repetitive high-reward substitutions and structurally tolerated framework mutations, we introduce a Reward-Tax Meta-Gradient objective. RewardNet smooths the affinity landscape, while TaxNet penalizes reward overexploitation, jointly defining a learned meta-reward for policy optimization. We evaluate iGC on mutation prediction, SHM consistency, affinity optimization, and mutation diversity. The mutation prior more than doubles the strongest baseline in mutation-site prediction. Following RL optimization, iGC maintains SHM sequence structure. It also achieves a strong exploration-exploitation balance, yielding competitive reward-diversity products across candidate-selection cutoffs. These results demonstrate that iGC integrates biologically plausible mutation generation with antigen-specific affinity selection, providing an in silico framework for iterative antibody affinity maturation.