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We construct a functor that associates to any dg cooperad of dg commutativealgebras (satisfying some conditions) an augmented commutative algebra. Whenapplied to the cohomology operad of Francis Brown's moduli spaces it producesan algebra that formally models the algebra of multiple zeta values. We provethat there is an injection from the graded dual of theGrothendieck-Teichmueller Lie algebra into the indecomposables of the algebraassociated to the Gerstenhaber cooperad, and that there is a morphism from thealgebra associated to Brown's moduli spaces to the algebra associated to theGerstenhaber cooperad which is surjective on indecomposables.

Formal weights in Kontsevich's formality construction and multiple zeta values