5/19/2023 0 Comments Wolfram mathematica for loop![]() Both Smc2 and Smc4, which have coiled-coil (CC) structures, are connected at the hinge domain. Condensin is a ring-shaped dimeric motor, containing a pair of SMC proteins (Smc2 and Smc4). Let us first describe the architecture of condensin, shown schematically in Fig. Of interest here is condensin, whose motor activity 8, results in active extrusion of loops in an ATP-dependent manner 9. The SMC complexes have been identified as a major component of the loop extrusion (LE) process 3, 4. Compaction is thought to occur by an active generation of a large array of loops, which are envisioned to form by extrusion of the genomic material 5, 6, 7 driven by ATP-consuming motors. In order to accomplish this herculean feat, nature has evolved a family of structural maintenance of chromosomes (SMC) complexes 3, 4 (bacterial SMC, cohesin, and condensin) to enable large scale compaction of chromosomes in both prokaryotic and eukaryotic systems. ![]() Remarkably, these information-carrying polymers in humans with more than 100 million base pairs, are densely packed in the 5−10 μm cell nucleus 1, 2. How chromosomes are structurally organized in the tight space of the nucleus is a long-standing problem in biology. Changes in the orientation of the motor domains are transmitted over ~50 nm, connecting the motor head and the hinge, thus providing an allosteric basis for LE. Simulations using a simple model confirm that the motor transitions between an open and a closed state in order to extrude loops by a scrunching mechanism, similar to that proposed in DNA bubble formation during bacterial transcription. ![]() The theory fits the available experimental data quantitatively, and suggests that condensin must undergo a large conformational change, induced by ATP binding, bringing distant parts of the motor to proximity. ![]() Motivated by real-time imaging of loop extrusion (LE), we created an analytically solvable model, predicting the LE velocity and step size distribution as a function of external load. The ATP consuming motor, condensin, interacts with chromatin segments to actively extrude loops. This process is driven by the formation of chromosome loops. Condensation of hundreds of mega-base-pair-long human chromosomes in a small nuclear volume is a spectacular biological phenomenon.
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