Loop entropy

Loop entropy is the <a href="/facts/Entropy/s52IXeFz">entropy</a> lost upon bringing together two <a href="/facts/Residue_(chemistry)/xE6sUTDa">residues</a> of a <a href="/facts/Polymer/eF32E50K">polymer</a> within a prescribed distance. For a single loop, the entropy varies logarithmically with the number of residues 
 
 
 
 N
 
 
 {\displaystyle N}
 
 in the loop

Δ
        S
        =
        α
        
          k
          
            B
          
        
        ln
        ⁡
        N
        
      
    
    {\displaystyle \Delta S=\alpha k_{B}\ln N\,}

where 
 
 
 
 
 k
 
 B
 
 
 
 
 {\displaystyle k_{B}}
 
 is the <a href="/facts/Boltzmann_constant/5DIejyR3">Boltzmann constant</a> and 
 
 
 
 α
 
 
 {\displaystyle \alpha }
 
 is a coefficient that depends on the properties of the polymer. This entropy formula corresponds to a <a href="/facts/Power_law/DhAjYwwz">power-law distribution</a> 
 
 
 
 P
 ∼
 
 N
 
 −
 α
 
 
 
 
 {\displaystyle P\sim N^{-\alpha }}
 
 for the probability of the residues contacting.
The loop entropy may also vary with the position of the contacting residues. Residues near the ends of the polymer are more likely to contact (quantitatively, have a lower 
 
 
 
 α
 
 
 {\displaystyle \alpha }
 
) than those in the middle (i.e., far from the ends), primarily due to <a href="/facts/Excluded_volume_effect/RaSyR2hC">excluded volume effects</a>.

Loop entropy open-in-new

Loop entropy