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Research and Development Tax Incentive (Details) - Australian Taxation Office $ in Millions, $ in Millions | 3 Months Ended |  |
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Mar. 31, 2022 USD ($) | Mar. 31, 2022 AUD ($) | Mar. 31, 2021 USD ($) | Mar. 31, 2021 AUD ($) | Mar. 31, 2022 AUD ($) | Dec. 31, 2021 USD ($) | Dec. 31, 2021 AUD ($)
Reduction to research and development expenses | $ 0.0 | $ 0.0 | $ 0.8 | $ 1.0 |  |  |
Research And Development Cash Tax Incentive Receivable | $ 2.9 |  |  |  | $ 3.8 | $ 2.8 | $ 3.8

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- Definition The amount of research and development cash tax incentive receivable. + References No definition available. + Details
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Namespace Prefix: | ptgx_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
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- Definition The amount of reduction of research and development expense in connection with the research and development tax incentive. + References No definition available. + Details
Name: | ptgx_ResearchAndDevelopmentExpensesReduction
Namespace Prefix: | ptgx_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

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- Details
Name: | us-gaap_IncomeTaxAuthorityNameAxis=us-gaap_AustralianTaxationOfficeMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |