Amyloids are aggregates of proteins characterised by a fibrillar morphology of 7–13 nm in diameter, a beta sheet (β-sheet) secondary structure (known as cross-β) and ability to be stained by particular dyes, such as Congo red. In the human body, amyloids have been linked to the development of various diseases. Pathogenic amyloids form when previously healthy proteins lose their normal structure and physiological functions (misfolding) and form fibrous deposits in amyloid plaques around cells which can disrupt the healthy function of tissues and organs. Such amyloids have been associated with (but not necessarily as the cause of) more than 50 human diseases, known as amyloidosis, and may play a role in some neurodegenerative diseases. Some of these diseases are mainly sporadic and only a few cases are familial. Others are only familial. Some are iatrogenic as they result from medical treatment. Prions are an infectious form of amyloids that can act as a template to convert other non-infectious forms. Amyloids may also have normal biological functions; for example, in the formation of fimbriae in some genera of bacteria, transmission of epigenetic traits in fungi, as well as pigment deposition and hormone release in humans.Amyloids have been known to arise from many different proteins. These polypeptide chains generally form β-sheet structures that aggregate into long fibers; however, identical polypeptides can fold into multiple distinct amyloid conformations.
k
          
            
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    {\displaystyle k_{\rm {off}}}
   is the rate constant of monomer dissociation. The terms on the third line describe the effect of fragmentation, which is assumed to occur homogeneously along fibrils with rate constant 
  
    
      
        
          k
          
            −
          
        
      
    
    {\displaystyle k_{-}}
  . Finally, the terms on the last line describe primary and secondary nucleation respectively.