Embodiments of the present invention employ complexly shaped, high-surface-area channels for separation and purification of molecules, including important biopolymers such as proteins, glycoproteins, polysaccharides, and other molecular components of living cells. The relatively large internal surface areas of the complexly shaped channels employed in embodiments of the present invention provide, in comparison to traditional, simply shaped separation channels, increased heat dissipation during electrokinetic separation, and a decreased tendency for bulk-solution flow. Heat dissipation prevents high temperatures that can denature proteins and that can induce thermal currents within the separation channel. Bulk-solution flow within a separation channel can overwhelm the generally linear, electrical-potential-induced migration of molecules that leads to efficient and well-resolved molecular separations. The complexly shaped channels employed in various embodiments of the present invention can be readily manufactured at microscale dimensions for use in microscale devices, at millimeter-scale dimensions for inclusion in microfluidics devices, and may also be used in larger scale, traditional separation and purification systems.