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In the standard approach to lattice proteins the models based on nearestneighbor interaction are used. In this kind of models it is difficult toexplain the existence of secondary structures --- special preferredconformations of protein chains.  In the present paper a new lattice model of proteins is proposed which isbased on non-local cooperative interactions. In this model the energy of aconformation of a polymer is equal to the sum of energies of conformations offragments of the polymer chain of the length five.  It is shown that this quinary lattice model is able to describe atqualitative level secondary structures of proteins: for this model allconformations with minimal energy are combinations of lattice models ofalpha--helix and beta--strand. Moreover for lattice polymers of the length notlonger that 38 monomers we can describe all conformations with minimal energy.

Quinary lattice model of secondary structures of polymers