A universal entropic pulling force caused by binding.

Abstract

We report an entropic pulling force that commonly occurs in systems with molecular or macroscopic binding. A particle binding to an object produces an entropic pulling force on the object because the bound particle tends to escape from this object to gain more entropy. This entropic pulling effect leads to an entropic force of ~ <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>k</mi></mrow> <mrow><mi>B</mi></mrow> </msub> <mi>T</mi> <mo>/</mo> <msub><mrow><mi>l</mi></mrow> <mrow><mi>b</mi></mrow> </msub> </math> , where <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>k</mi></mrow> <mrow><mi>B</mi></mrow> </msub> </math> is the Boltzmann constant, T is temperature, and <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub><mrow><mi>l</mi></mrow> <mrow><mi>b</mi></mrow> </msub> </math> is the binding length. We validate this entropic pulling effect through simulations and experiments. In macroscopic experiments, a particle bound to a bead-chain on a vibration platform, where mechanical vibration mimics thermal noise, produces an entropic force. In single-molecule magnetic-tweezers experiments, multivalent ions binding to DNA exert an entropic force to enlarge the DNA's diameter, detected through precise measurement of DNA twist change and twist-diameter coupling. The reported entropic force has biological and technological implications. Cells may utilize this entropic force to disassemble protein aggregates in neurodegenerative diseases, while engineered molecular machines could harness it to exert controlled force.