1. Coupled optimization of structures of homologous proteins. Elber explores the empirical observation that homologous proteins (proteins of the same family) fold to similar structures and combines this observation with global optimization of an energy function. Significant improvement (compared to the use of energy function only) was demonstrated for structure prediction of protein families (pancreatic hormones - ppt, and DNA binding proteins - homeodomains) . The averaging of sequences (on different members of the family) and the averaging of alternate transient conformations provides a new minimum with a significantly larger radius of attraction .
Even if the structure is known, questions may be left unanswered and new puzzles may appear. For example, the biologically active structure of the protein can be a rare fluctuation that is not observed in the average experimental structure. These fluctuations can be studied with the method of Molecular Dynamics. Elber develops theoretical approaches and algorithms to extend the scope of the Molecular Dynamics method and applies them to a variety of biophysical problems.
1. Mechanisms and dynamics of peptide folding. Peptides are short polymers of amino acids. They serve as model systems for nucleation sites in protein folding. It is believed that protein folding proceeds via a time sequence of nuclei of structures. The identity and the physical forces that hold the initiators of structure are a topic of intense investigations by theorists and experimentalists. He performed atomically detailed simulations of peptide folding  using a novel algorithm for global optimization of structure. The results indicate that long-range electrostatic attraction and the local propensity of the proline are the prime initiators of the folding process.
2. Algorithms for long time dynamics. The usual approach of Molecular Dynamics is limited to time scales of a few nanoseconds, far shorter than the time scales of many biophysical processes. Elber developed a new technique to compute approximate molecular dynamic trajectories at very extended time scales. The method is based on a stochastic difference equation that models numerical errors. Elber has formulated the theory, provided numerous examples for Newtonian mechanics , and further exploited properties of Brownian trajectories . He is employing the new methodology to investigate ion channels and conformational transitions in proteins.
 Simultaneous and coupled energy optimization of homologous proteins: A new tool for structure prediction. Folding and Design 2 (1997), 247-259 (with C. Keasar and J. Skolnick).
 Homology as a tool in optimization problems: Structure determination of 2D hetero-ploymers. J. Phys. Chem. 99 (1995), 11550 (with C. Keasar).
 Kinetics of peptide folding: Computer simulations of SYPFDV and peptide variants in water. J. Mol. Biol. 272 (1997), 423-442 (with D. Mohanty, D. Thirumalai, D. Beglov, and B. Roux).
 Calculation of classical trajectories with a very large time step: Formalism and numerical examples. J. Chem. Phys. 105 (1996), 9299-9315 (with R. Olender).
 Yet another look at the steepest descent path. J. Mol. Struct. Theochem and Proc. WATOC Symp. (1997), 398-399,63-72. (with R. Olender).