Summary of Significant Accounting Policies - Concentrations of Credit Risk (Details)	Dec. 31, 2021 Institution
Summary of Significant Accounting Policies
Number of financial institutions at which cash is held	2

The number of financial institutions that hold the entity's cash.

No definition available.

Name:	ptgx_CashNumberOfFinancialInstitutions
Namespace Prefix:	ptgx_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant