Calculation of a fluctuating entropic force by phase space sampling

The entropic force generated by intrinsically disordered segments tunes protein function

Protein structures are dynamic and can explore a large conformational landscape^1,2. Only some of these structural substates are important for protein function (such as ligand binding, catalysis and regulation)^3-5. How evolution shapes the structural ensemble to optimize a specific function is poorly understood^3,4. One of the constraints on the evolution of proteins is the stability of the folded 'native' state. Despite this, 44% of the human proteome contains intrinsically disordered peptide segments greater than 30 residues in length⁶, the majority of which have no known function^7-9. Here we show that the entropic force produced by an intrinsically disordered carboxy terminus (ID-tail) shifts the conformational ensemble of human UDP-α-D-glucose-6-dehydrogenase (UGDH) towards a substate with a high affinity for an allosteric inhibitor. The function of the ID-tail does not depend on its sequence or chemical composition. Instead, the affinity enhancement can be accurately predicted based on the length of the intrinsically disordered segment, and is consistent with the entropic force generated by an unstructured peptide attached to the protein surface^10-13. Our data show that the unfolded state of the ID-tail rectifies the dynamics and structure of UGDH to favour inhibitor binding. Because this entropic rectifier does not have any sequence or structural constraints, it is an easily acquired adaptation. This model implies that evolution selects for disordered segments to tune the energy landscape of proteins, which may explain the persistence of intrinsic disorder in the proteome.

Force distribution in a semiflexible loop

Loops undergoing thermal fluctuations are prevalent in nature. Ringlike or cross-linked polymers, cyclic macromolecules, and protein-mediated DNA loops all belong to this category. Stability of these molecules are generally described in terms of free energy, an average quantity, but it may also be impacted by local fluctuating forces acting within these systems. The full distribution of these forces can thus give us insights into mechanochemistry beyond the predictive capability of thermodynamics. In this paper, we study the force exerted by an inextensible semiflexible polymer constrained in a looped state. By using a simulation method termed "phase-space sampling," we generate the equilibrium distribution of chain conformations in both position and momentum space. We compute the constraint forces between the two ends of the loop in this chain ensemble using Lagrangian mechanics, and show that the mean of these forces is equal to the thermodynamic force. By analyzing kinetic and potential contributions to the forces, we find that the mean force acts in the direction of increasing extension not because of bending stress, but in spite of it. Furthermore, we obtain a distribution of constraint forces as a function of chain length, extension, and stiffness. Notably, increasing contour length decreases the average force, but the additional freedom allows fluctuations in the constraint force to increase. The force distribution is asymmetric and falls off less sharply than a Gaussian distribution. Our work exemplifies a system where large-amplitude fluctuations occur in a way unforeseen by a purely thermodynamic framework, and offers computational tools useful for efficient, unbiased simulation of a constrained system.

The Effect of Basepair Mismatch on DNA Strand Displacement

DNA strand displacement is a key reaction in DNA homologous recombination and DNA mismatch repair and is also heavily utilized in DNA-based computation and locomotion. Despite its ubiquity in science and engineering, sequence-dependent effects of displacement kinetics have not been extensively characterized. Here, we measured toehold-mediated strand displacement kinetics using single-molecule fluorescence in the presence of a single basepair mismatch. The apparent displacement rate varied significantly when the mismatch was introduced in the invading DNA strand. The rate generally decreased as the mismatch in the invader was encountered earlier in displacement. Our data indicate that a single base pair mismatch in the invader stalls branch migration and displacement occurs via direct dissociation of the destabilized incumbent strand from the substrate strand. We combined both branch migration and direct dissociation into a model, which we term the concurrent displacement model, and used the first passage time approach to quantitatively explain the salient features of the observed relationship. We also introduce the concept of splitting probabilities to justify that the concurrent model can be simplified into a three-step sequential model in the presence of an invader mismatch. We expect our model to become a powerful tool to design DNA-based reaction schemes with broad functionality.

The Effect of Basepair Mismatch on DNA Strand Displacement

DNA strand displacement is a key reaction in DNA homologous recombination and DNA mismatch repair and is also heavily utilized in DNA-based computation and locomotion. Despite its ubiquity in science and engineering, sequence-dependent effects of displacement kinetics have not been extensively characterized. Here, we measured toehold-mediated strand displacement kinetics using single-molecule fluorescence in the presence of a single basepair mismatch. The apparent displacement rate varied significantly when the mismatch was introduced in the invading DNA strand. The rate generally decreased as the mismatch in the invader was encountered earlier in displacement. Our data indicate that a single base pair mismatch in the invader stalls branch migration and displacement occurs via direct dissociation of the destabilized incumbent strand from the substrate strand. We combined both branch migration and direct dissociation into a model, which we term the concurrent displacement model, and used the first passage time approach to quantitatively explain the salient features of the observed relationship. We also introduce the concept of splitting probabilities to justify that the concurrent model can be simplified into a three-step sequential model in the presence of an invader mismatch. We expect our model to become a powerful tool to design DNA-based reaction schemes with broad functionality.