Contraction of striated muscles is regulated by tropomyosin strands that run continuously along actin-containing thin filaments. Tropomyosin blocks myosin-binding sites on actin in resting muscle and unblocks them during Ca2+-activation. This steric effect controls myosin-crossbridge cycling on actin that drives contraction. Troponin, bound to the thin filaments, couples Ca2+-concentration changes to the movement of tropomyosin. Ca2+-free troponin is thought to trap tropomyosin in the myosin-blocking position, while this constraint is released after Ca2+-binding. Although the location and movements of tropomyosin are well known, the structural organization of troponin on thin filaments is not. Its mechanism of action therefore remains uncertain. To determine the organization of troponin on the thin filament, we have constructed atomic models of low and high-Ca2+ states based on crystal structures of actin, tropomyosin and the "core domain" of troponin, and constrained by distances between filament components and by their location in electron microscopy (EM) reconstructions. Alternative models were also built where troponin was systematically repositioned or reoriented on actin. The accuracy of the different models was evaluated by determining how well they corresponded to EM images. While the initial low and high-Ca2+ models fitted the data precisely, the alternatives did not, suggesting that the starting models best represented the correct structures. Thin filament reconstructions were generated from the EM data using these starting models as references. In addition to showing the core domain of troponin, the reconstructions showed additional detail not present in the starting models. We attribute this to an extension of TnI linking the troponin core domain to actin at low (but not at high) Ca2+, thereby trapping tropomyosin in the OFF-state. The bulk of the core domain of troponin appears not to move significantly on actin, regardless of Ca2+ level. Our observations suggest a simple model for muscle regulation in which troponin affects the charge balance on actin and hence tropomyosin position.