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Problem 1 A SARS-CoV-2 virion (infectious virus particle) carries 100 so-called "spikes" on its membrane surface, whose appearance under the electron microscope is responsible for the name "Corona" virus. Each spike consists of a trimer of the viral S-protein. This protein is responsible for the infection of cells that express the angiotensin-converting enzyme 2 (ACE2) on their surface. Cells expressing this protein are prominently found in lungs, the small intestine and the brain, which leads to common early symptoms of COVID-19, the disease caused by the virus: pneumonia, diarrhea and a loss of smell. Infection is induced by binding of S-protein monomers (3 per spike) to ACE2 with a dissociation constant estimated between Kd1. A new experimental drug developed at UCSF is aerosol-based and intends to bind virion S- proteins before they can bind to ACE2. The active ingredient of the drug, a linked chain of three nanobodies, binds to S-protein trimers (spikes) with a dissociation constant of Kd2, which blocks the binding domains of all three S-protein monomers, prevents binding to ACE2 and host cell infection. A. Consider an aerosol particle (essentially an aqueous droplet) with a diameter of d1 micrometers, which contains n virions and was produced by the cough of a COVID- 19 patient. Consider a second aerosol particle with a d2 micrometer diameter containing the experimental drug. How many drug molecules per drug-containing aerosol particle are needed (on average, don't expect an integer result) to bind 99% of all virion spikes after the two aerosol particles have merged their volumes? B. What would your answer to the previous question be, if the virion-containing aerosol particle contains only 1 virion? C. What is the standard binding free energy at 25C for the complex formed by the s- protein monomer and ACE2? D. What is the standard binding free energy at 25C for the complex formed by the S- protein trimer (spike) and the experimental drug? Kd1 = 2.3x10- Kd2 = 1x10-13 d1 = 1 um n = 5 d2 = 0.8 um T = 6C V = 10.5 liter P = 210 bar Problem 1 A SARS-CoV-2 virion (infectious virus particle) carries 100 so-called "spikes" on its membrane surface, whose appearance under the electron microscope is responsible for the name "Corona" virus. Each spike consists of a trimer of the viral S-protein. This protein is responsible for the infection of cells that express the angiotensin-converting enzyme 2 (ACE2) on their surface. Cells expressing this protein are prominently found in lungs, the small intestine and the brain, which leads to common early symptoms of COVID-19, the disease caused by the virus: pneumonia, diarrhea and a loss of smell. Infection is induced by binding of S-protein monomers (3 per spike) to ACE2 with a dissociation constant estimated between Kd1. A new experimental drug developed at UCSF is aerosol-based and intends to bind virion S- proteins before they can bind to ACE2. The active ingredient of the drug, a linked chain of three nanobodies, binds to S-protein trimers (spikes) with a dissociation constant of Kd2, which blocks the binding domains of all three S-protein monomers, prevents binding to ACE2 and host cell infection. A. Consider an aerosol particle (essentially an aqueous droplet) with a diameter of d1 micrometers, which contains n virions and was produced by the cough of a COVID- 19 patient. Consider a second aerosol particle with a d2 micrometer diameter containing the experimental drug. How many drug molecules per drug-containing aerosol particle are needed (on average, don't expect an integer result) to bind 99% of all virion spikes after the two aerosol particles have merged their volumes? B. What would your answer to the previous question be, if the virion-containing aerosol particle contains only 1 virion? C. What is the standard binding free energy at 25C for the complex formed by the s- protein monomer and ACE2? D. What is the standard binding free energy at 25C for the complex formed by the S- protein trimer (spike) and the experimental drug? Kd1 = 2.3x10- Kd2 = 1x10-13 d1 = 1 um n = 5 d2 = 0.8 um T = 6C V = 10.5 liter P = 210 bar