Note: For computation or derivation problems, please present the equations, derivation and computational process to obtain full credits for each. 1. According to single energy barrier model, the most likely dissociation force Fin between thrombin and its DNA aptamer can be expressed as a function of the loading rate by as Fin = F, In F - where parameter F = AL is the thermal force, ka = 1.38x10 J/K is the Boltzmann constant, 7 = 25"C or 298 K is the room temperature, parameter xs is the thrombin- aptamer bond length, and parameter bay is the spontaneous dissociation time for the thrombin- aptamer binding complex. If we rewrite it as Fi = F, Inr, + F, In , and take In myas independent variable x, Fin as dependent variable y, parameter As as slope m, and parameter F In of as vertical intercept b, we can find the above formula can be expressed in the form of a linear function, i.e. y = ax + b. Suppose we have the following experimental data acquired from atomic force microscopy (AFM) based dynamic force spectroscopy (DFS) under different applied electrical fields: Electrical potential (mV) |Loading rate ry(pN/'s) | Most likely dissociation force Fun. (pN) 317 15 864 21 100 2132 27 5086 33 379 21 1032 28 -100 3278 36 12314 45 Note: 1 pN = 10# N a) Draw the Fan (dependent variable y) vs In zy ( independent variable x) scatterplot under 100 mV and -100 mV using Excel. Add linear trendlines to the original scatterplot corresponding to each electrical potential condition, and display the regression equations on the plot. Attach here the plot with the required axis labels, legends, trendlines and regression equations presented. b) Based on the slope m = F; =- -acquired in the above regression function, please compute the thrombin-aptamer bond length x, under 100 mV and -100 mV respectively. c) Based on the vertical intercept b = F, In acquired in the above regression function, please compute the spontaneous dissociation time may under 100 mV and -100 mV respectively