Small angle X-ray scattering (SAXS) is an important tool for investigating the structure of proteins in solution. We present a novel ab initio method representing polypeptide chains as discrete curves used to derive a meaningful three-dimensional model from only the primary sequence and SAXS data. High resolution structures were used to generate probability density functions for each common secondary structural element found in proteins, which are used to place realistic restraints on the model curve's geometry. This is coupled with a novel explicit hydration shell model in order to derive physically meaningful three-dimensional models by optimizing against experimental SAXS data. The efficacy of this model is verified on an established benchmark protein set, and then it is used to predict the lysozyme structure using only its primary sequence and SAXS data. The method is used to generate a biologically plausible model of the coiled-coil component of the human synaptonemal complex central element protein.