It´s not my discipline. But I´ve learnt, that normally the sequence predicts the structure (state of minimal free energy, see Nobel price for Anfinsen 1973). But some proteins show different shapes (metamorphic proteins) and are still working.

There are some softwares that can do it. The most famous is MODELLER, but also exist I-Tasser, Phyre2..... They commonly search for proteins with 3D structure in the Protein Data Bank and compare their sequences with your sequence. After found good matches, these programs use the structural information of the template (protein with PDB) to guide the construction of your 3D protein. 

It is important to notice that there are other ways, such as ab initio methods that use only biophysics and biochemistry laws to create your protein, but you have to do many steps of validation to your model. You can use these kinds of methods when there is not the structure of any protein with similar sequence. Also, these software that I talk above can use these methods when the template that you use do not have some parts of your sequence.

This has been a subject of great interest for some time. The "Critical Assessment of Protein Structure" (CASP) is a consortium of scientist who have been organizing contests since 1994 aimed at testing methods for ab initio protein structure prediction from sequence. See their home page http://predictioncenter.org/ for the latest and archived results. A great variety of methods have been tested and evaluated. Generally, "consensus" techniques wherein multiple methods arrive at the same result are usually the most reliable. Regarding specific programs, Rosetta developed by David Baker's group is particularly interesting. It has been used, among other thing, to successfully design new stable protein folds. See  http://www.sciencemag.org/news/2016/07/protein-designer-aims-revolutionize-medicines-and-materials and https://www.rosettacommons.org/software. Also, if you have any experimental information (chemical cross linking, residues known to be in the same catalytic or binding site, even just one or two assigned inter-molecular NOEs, NMR assignments for the backbone C, CA, N an HN atoms, distance restraints from paramagnetic effect, etc), these data can be incorporated in to many structure prediction algorithms. Hope this helps.

Keith

A significant new enhancement to the methodologies available for protein structure prediction was recently published by David Baker and colleagues. See Ovchinnikov et al. "Protein structure determination using metagenome sequence data" (2017) Science 355, 294 - 298 (http://science.sciencemag.org/content/355/6322/294) and the perspective piece, Soding "Big-data approaches to protein structure prediction" Science 355, 248 - 249 (http://science.sciencemag.org/content/355/6322/248). Briefly, residues likely to interact in the 3D structures of proteins belonging to the same family are identified by correlated mutations of residues pairs using large sequence alignments. The authors describe a statistical approach that greatly improves the alignment method by predicting which correlations are due to direct contacts between residue pairs, as opposed that are the result of "indirect chains of interactions".  After identifying the models that are highly likely to be correct, Ovchinnikov et al. report models for 614 protein families with previously unknown structures. Some of the structures predicted by this method have been subsequently confirmed X-ray crystallography; these include relatively complex proteins such as cytochrome bd oxidase and both the monomer and dimer forms of fumarate hydratase. So far, no structures predicted by this method and classified as very likely to be correct have been shown to incorrect by experimental structures. The metagenomic correlation method is available in Rosetta. Rosetta outperformed all other methods in the recent CASP12 http://predictioncenter.org/casp12/zscores_final.cgi