Antifreeze proteins (AFPs) are biopolymers capable of interfering with ice growth. Their antifreeze action is commonly understood considering that the AFPs, by pinning the ice surface, force the crystal-liquid interface to bend forming an ice meniscus, causing an increase in the surface free energy and resulting in a decrease in the freezing point ΔTmax. Here, we present an extensive computational study for a model protein adsorbed on a TIP4P/Ice crystal, computing ΔTmax as a function of the average distance d between AFPs, with simulations spanning over 1 µs. First, we show that the lower the d, the larger the ΔTmax. Then, we find that the water-ice-protein contact angle along the line ΔTmax(d) is always larger than 0°, and we provide a theoretical interpretation. We compute the curvature radius of the stable solid-liquid interface at a given supercooling ΔT ≤ ΔTmax, connecting it with the critical ice nucleus at ΔT. Finally, we discuss the antifreeze capability of AFPs in terms of the protein-water and protein-ice interactions. Our findings establish a unified description of the AFPs in the contest of homogeneous ice nucleation, elucidating key aspects of the antifreeze mechanisms and paving the way for the design of novel ice-controlling materials.