The duration of warrants from date of issuance.

No definition available.

Name:	ptgx_ClassOfWarrantOrRightTermOfWarrants
Namespace Prefix:	ptgx_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of warrants exercised for the period.

+ References

No definition available.

+ Details

Name:	ptgx_NumberOfWarrantsExercised
Namespace Prefix:	ptgx_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

The maximum amount of shares permits the offering, issuance, and sale by the entity.

+ References

No definition available.

+ Details

Name:	ptgx_SaleOfStockValueOfSharesAuthorized
Namespace Prefix:	ptgx_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The number of shares exchanged for pre-funded warrants.

+ References

No definition available.

+ Details

Name:	ptgx_StockExchangedForPreFundedWarrants
Namespace Prefix:	ptgx_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

Name:	us-gaap_ClassOfStockDisclosuresAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Date the warrants or rights are exercisable, in YYYY-MM-DD format.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 3
-URI http://asc.fasb.org/extlink&oid=123467817&loc=d3e21475-112644

+ Details

Name:	us-gaap_ClassOfWarrantOrRighstDateFromWhichWarrantsOrRightsExercisable
Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Exercise price per share or per unit of warrants or rights outstanding.

+ References

+ Details

Name:	us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of securities into which each warrant or right may be converted. For example, but not limited to, each warrant may be converted into two shares.

+ References

No definition available.

+ Details

Name:	us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of securities into which the class of warrant or right may be converted. For example, but not limited to, 500,000 warrants may be converted into 1,000,000 shares.

+ References

+ Details

Name:	us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of warrants or rights outstanding.

+ References

No definition available.

+ Details

Name:	us-gaap_ClassOfWarrantOrRightOutstanding
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Face amount or stated value per share of common stock.

+ References

+ Details

Name:	us-gaap_CommonStockParOrStatedValuePerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

The percentage of ownership of common stock or equity participation in the investee accounted for under the equity method of accounting.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 323
-SubTopic 10
-Section 50
-Paragraph 3
-Subparagraph (a)(1)
-URI http://asc.fasb.org/extlink&oid=114001798&loc=d3e33918-111571

+ Details

Name:	us-gaap_EquityMethodInvestmentOwnershipPercentage
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

The cash inflow from the additional capital contribution to the entity.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 14
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=123570139&loc=d3e3255-108585

+ Details

Name:	us-gaap_ProceedsFromIssuanceOfCommonStock
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Cash received on stock transaction after deduction of issuance costs.

+ References

No definition available.

+ Details

Name:	us-gaap_SaleOfStockConsiderationReceivedOnTransaction
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The number of shares issued or sold by the subsidiary or equity method investee per stock transaction.

+ References

No definition available.

+ Details

Name:	us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Per share amount received by subsidiary or equity investee for each share of common stock issued or sold in the stock transaction.

+ References

No definition available.

+ Details

Name:	us-gaap_SaleOfStockPricePerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Per share or per unit amount of equity securities issued.

+ References

No definition available.

+ Details

Name:	us-gaap_SharesIssuedPricePerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of new stock issued during the period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=123467817&loc=d3e21463-112644

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-URI http://asc.fasb.org/extlink&oid=120397183&loc=d3e187085-122770

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(28))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_StockIssuedDuringPeriodSharesNewIssues
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Value of outstanding derivative securities that permit the holder the right to purchase securities (usually equity) from the issuer at a specified price.

+ References

No definition available.

+ Details

Name:	us-gaap_WarrantsAndRightsOutstanding
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=ptgx_CommonStockPreferredStockDebtSecuritiesAndWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=ptgx_FinancingFacilitySalesAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=ptgx_UnderwrittenPublicOfferingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_OverAllotmentOptionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_CommonStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_PrivatePlacementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_CounterpartyNameAxis=ptgx_SecuritiesPurchaseAgreementWithAccreditedInvestorsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_TypeOfArrangementAxis=ptgx_ExchangeAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_CounterpartyNameAxis=ptgx_BiotechnologyValueFundL.pMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=ptgx_WarrantsPurchaseAmountPerSharePriceOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=ptgx_WarrantsPurchaseAmountPerSharePriceTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Stockholders' Equity (Details) - USD ($) $ / shares in Units, $ in Millions		1 Months Ended					3 Months Ended	6 Months Ended
	Nov. 27, 2019	Jan. 31, 2022	Jun. 30, 2021	Oct. 31, 2019	Dec. 31, 2018	Aug. 31, 2018	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021	Mar. 31, 2022	Dec. 31, 2021	Aug. 06, 2018
Stock transactions
Par value (per share)										$ 0.00001	$ 0.00001
2019 Form S-3
Stock transactions
Common stock available for sale								$ 79.3
Maximum aggregate offering price				$ 250.0
2019 Sales Agreement
Stock transactions
Common stock issued (in shares)		422,367
Common stock available for sale								$ 17.0
Maximum aggregate offering price	$ 250.0			$ 75.0
Proceeds from public offering of common stock, net of issuance costs		$ 14.6
Underwritten public offering
Stock transactions
Net proceeds from sale of common stock			$ 123.8
Common stock issued (in shares)			3,046,358
Common stock issued, price per share			$ 37.75				$ 37.75		$ 37.75
underwritten public offering, Additional offering
Stock transactions
Common stock issued (in shares)			456,953
Common stock issued, price per share			$ 37.75				$ 37.75		$ 37.75
Common Stock
Stock transactions
Common stock issued (in shares)							3,503,311	422,367	3,503,311
Common Stock \| Private Placement
Stock transactions
Number of warrants exercised								0
Investors \| Private Placement
Stock transactions
Aggregate shares of common stock sold						2,750,000
Common stock sold, price per share						$ 8.00
Net proceeds from sale of common stock						$ 21.7
Warrants issued to purchase common stock, number of shares												2,750,000
Warrants exercisable date						Aug. 08, 2023
Exchange Agreement \| Exchanging Stockholders
Stock transactions
Warrants issued to purchase common stock, number of shares					1,000,000
Exercise Price (per share)					$ 0.00001
Common stock exchanged for pre-funded warrants					1,000,000
Par value (per share)					$ 0.00001
Duration of warrants from date of issuance (in years)					10 years
Equity method investment, ownership percentage					9.99%
Exchange Agreement \| Exchanging Stockholders \| Common Stock
Stock transactions
Remaining number of Exchange Warrants unexercised								400,000
$10.00 per share \| Investors \| Private Placement
Stock transactions
Warrants to purchase common stock (in shares)												1,375,000
Exercise Price (per share)												$ 10.00
$15.00 per share \| Investors \| Private Placement
Stock transactions
Warrants to purchase common stock (in shares)												1,375,000
Exercise Price (per share)												$ 15.00