where 
  
    
      
        
          δ
          
            i
            ,
            j
          
        
      
    
    {\displaystyle \delta _{i,j}}
   denotes the Kronecker delta. The physical interpretation of the various terms in the above master equation is straight forward: the terms on the first line describe the growth of fibrils via monomer addition with rate constant 
  
    
      
        
          k
          
            +
          
        
      
    
    {\displaystyle k_{+}}
   (elongation). The terms on the second line describe monomer dissociation, i.e. the inverse process of elongation.
k
          
            
              o
              f
              f
            
          
        
      
    
    {\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.