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Robotic end-to-end fusion of microtubules powered by kinesin: MATLAB scripts

Saper, Gadiel; Tsitkov, Stanislav; Katira, Parag; Hess, Henry S.

Matlab scripts for: Robotic end-to-end fusion of microtubules powered by kinesin (to be published in Science Robotics). Paper abstract: The active assembly of molecules by nanorobots has advanced greatly since “molecular manufacturing”, that is the use of nanoscale tools to build molecular structures, was proposed. In contrast to a catalyst, which accelerates a reaction by smoothing the potential energy surface along the reaction coordinate, molecular machines expend energy to accelerate a reaction relative to the baseline provided by thermal motion and forces. Here, we design a nanorobotics system to accelerate end-to-end microtubule assembly by using kinesin motors and a circular confining chamber. We show that the mechanical interaction of kinesin-propelled microtubules gliding on a surface with the walls of the confining chamber results in a non-equilibrium distribution of microtubules, which increases the number of end-to-end microtubule fusion events twenty-fold compared to microtubules gliding on a plane. In contrast to earlier nanorobots, where a non-equilibrium distribution was built into the initial state and drives the process, our nanorobotic system creates and actively maintains the building blocks in the concentrated state responsible for accelerated assembly through the adenosine triphosphate-fueled generation of force by kinesin-1 motor proteins. This approach can be used in the future to develop biohybrid or bioinspired nanorobots that use molecular machines to access non-equilibrium states and accelerate nano-assembly.

The Matlab scripts were used for the simulation and to analyze the average velocity, velocity mean difference, angles, distance from center, persistence length and curvatures for the Microtubules using the locations and velocities measured with the Manual Tracking plugin in ImageJ.

List of files:
§ ForPub_Sim_MTs_In_Well.m- Simulation of microtubules as active Brownian particles confined in a circular chamber.
§ ForPub_GetEntropyFromExcel.m- Calculates the entropy from the simulation's results.
§ ForPub_radii_V_angle_Lp50um.csv- File with the angle and distance from the center for all the particles from the simulation.
§ Vel_md.m – Calculates the velocity for each microtubule and the average velocity, the standard deviation, and the mean absolute difference (using VMD function) of all microtubules.
§ VMD.m- Calculating the velocity mean absolute difference from a vector of the velocities.
§ rang.m - Calculates the angle relative to the circle tangent (using aglforR function) and distance from the center for a microtubule from a matrix with the position over time.
§ aglforR.m- Calculates the angle between the direction of the microtubule and the circle tangent.
§ LPall.m- Returns a matrix with the angle and cos(angle) of each step for all the microtubules measured by using function LP for each microtubule.
§ LP.m- Returns a matrix with the angle and cos(angle) (using aglforLP function) of each microtubule step calculated form a matrix of the locations.
§ aglforLP.m- Calculates the angle between two lines. This function is specifically used to calculate the change in angle for the persistence length measurement.
§ Read_Data_Fit_Spline_For_Pub.m- Calculates the curvature of a microtubule over time using a spline fit.


  • thumnail for ForPub_radii_V_angle_Lp50um.csv ForPub_radii_V_angle_Lp50um.csv text/comma-separated-values 327 KB Download File
  • thumnail for ForPub_Sim_MTs_In_Well.m ForPub_Sim_MTs_In_Well.m application/octet-stream 2.36 KB Download File
  • thumnail for ForPub_GetEntropyFromExcel.m ForPub_GetEntropyFromExcel.m application/octet-stream 1.21 KB Download File
  • thumnail for Read_Data_Fit_Spline_For_Pub.m Read_Data_Fit_Spline_For_Pub.m application/octet-stream 4.28 KB Download File

More About This Work

Academic Units
Biomedical Engineering
Published Here
August 6, 2021