Theories of protein crystallization based on spheres that form close-packed crystals predict optimal assembly within a 'slot' of second virial coefficients and enhanced assembly near the metastable liquid-vapor critical point. However, most protein crystals are open structures stabilized by anisotropic interactions. Here, we use theory and simulation to show that assembly of one such structure is not predicted by the second virial coefficient or enhanced by the critical point. Instead, good assembly requires that the thermodynamic driving force be on the order of the thermal energy and that interactions be made as nonspecific as possible without promoting liquid-vapor phase separation.The need to crystallize proteins for X-ray studies has spurred the development of theories of protein crystallization. These theories are largely based on the behavior of spheres with short-range isotropic attractions, a representation motivated by two observations. First, phase diagrams for typical proteins and spherical colloids with short range attractions are structurally similar, possessing a metastable demixing transition between a vapor of solute (solute-poor solution) and a liquid of solute (solute-rich solution) [1][2][3][4]. Second, both proteins and spherical colloids tend to crystallize when the second virial coefficient, an orientationally-averaged measure of protein-protein attraction, lies in a defined 'crystallization slot ' [5-7]. On the computer, short-range isotropic spheres crystallize poorly above the metastable liquidvapor binodal and show enhanced nucleation rates near or below it [3,[8][9][10][11][12]. Such enhancement is indeed seen in some protein solutions [13][14][15]. However, other experiments show disparities with this picture. Proteins can crystallize readily above the binodal [16,17] and experience kinetically-impaired crystallization below it [18]. They can also lie in the crystallization slot and not crystallize [19]. In addition, although the structure of protein and colloid phase diagrams is similar, the microscopic nature of the stable solid is not: most proteins do not form close-packed crystals [20].These disparities motivate a theoretical approach to protein crystallization that acknowledges additional features of proteins' interactions, particularly their anisotropy [21][22][23][24][25][26]. Such studies suggest that rules for optimal assembly of open structures are different from the rules for optimal assembly of close-packed structures. Here we explicitly demonstrate this difference. We have used extensive equilibrium and nonequilibrium numerical simulations and quantitatively accurate mean-field theory to exhaustively determine the design rules for optimal assembly of a model patterned after the SbpA surface-layer protein. The latter forms a porous square lattice with a tetrameric repeat unit on the surface of the bacterium Lysinibacillus sphaericus, and in vitro on surfaces or in solution [27][28][29][30]. We impose a simple set of model protein interactions that stabilize the two conde...