The general master equation approach to amyloid fibril formation with secondary pathways has been developed by Knowles, Vendruscolo, Cohen, Michaels and coworkers and considers the time evolution of the concentration 
  
    
      
        f
        (
        t
        ,
        j
        )
      
    
    {\displaystyle f(t,j)}
   of fibrils of length 
  
    
      
        j
      
    
    {\displaystyle j}
   (here 
  
    
      
        j
      
    
    {\displaystyle j}
   represents the number of monomers in an aggregate).
The crystallographic structures show that short stretches from amyloid-prone regions of amyloidogenic proteins run perpendicular to the filament axis, consistent with the "cross-β" feature of amyloid structure. They also reveal a number of characteristics of amyloid structures – neighboring β-sheets are tightly packed together via an interface devoid of water (therefore referred to as dry interface), with the opposing β-strands slightly offset from each other such that their side-chains interdigitate. This compact dehydrated interface created was termed a steric-zipper interface. There are eight theoretical classes of steric-zipper interfaces, dictated by the directionality of the β-sheets (parallel and anti-parallel) and symmetry between adjacent β-sheets. A limitation of X-ray crystallography for solving amyloid structure is represented by the need to form microcrystals, which can be achieved only with peptides shorter than those associated with disease. Although bona fide amyloid structures always are based on intermolecular β-sheets, different types of "higher order" tertiary folds have been observed or proposed. The β-sheets may form a β-sandwich, or a β-solenoid which may be either β-helix or β-roll. Native-like amyloid fibrils in which native β-sheet containing proteins maintain their native-like structure in the fibrils have also been proposed.One complicating factor in studies of amyloidogenic polypeptides is that identical polypeptides can fold into multiple distinct amyloid conformations. This phenomenon is typically described as amyloid polymorphism. It has notable biological consequences given that it is thought to explain the prion strain phenomenon. Formation
Amyloid is formed through the polymerization of hundreds to thousands of monomeric peptides or proteins into long fibers.