Regarding the correlation b/w MEP and change of UCI No, read the following quote:
"In Express Entry, applicants are required to submit a complete electronic application for permanent residence (e-APR) within 60 calendar days of being issued an invitation to apply (ITA). The application and all supporting documents must be submitted electronically through the applicant’s online account.
Applications are assessed for completeness up front. An application found to be incomplete should be rejected as per section 10 of the Immigration and Refugee Protection Regulations, and all fees associated with the application should be refunded to the applicant.
The Express Entry six-month processing standard begins when an application is assessed as complete and is promoted in the Global Case Management System (GCMS). It ends when Immigration, Refugees and Citizenship Canada (IRCC) makes a final decision on the application."
From the above text, i believe there is a correlation b/w R10 and change of UCI no. After reviewing the documents submitted, if the application is complete, then the visa officer clears the R10 and promotes the application to GCMS, leading to change of UCI no.