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.
Note that the rate of secondary nucleation is proportional to the mass of aggregates, defined as 
  
    
      
        M
        (
        t
        )
        =
        
          ∑
          
            j
            =
            
              n
              
                1
              
            
          
          
            ∞
          
        
        j
        f
        (
        t
        ,
        j
        )
      
    
    {\displaystyle M(t)=\sum _{j=n_{1}}^{\infty }jf(t,j)}
  .