Biocryst Pharmaceuticals Inc (BCRX): Baker Bros. Advisors Unloads Nearly 4 Million Shares

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, DC 20549

SCHEDULE 13D

Under the Securities Exchange Act of 1934

(Amendment No. 2)*

If the
filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D,
and is filing this schedule because of Rule 13d-1(e), 13d-1(f) or 13d-1(g), check the following box. x

(Continued on the following pages)

Note: Schedules filed in paper format shall include a signed
original and five copies of the schedule, including all exhibits. See Rule 13d-7 for other parties to whom copies are to be sent.

*The remainder of this cover page shall be filled out for a reporting
person’s initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing
information which would alter disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall
not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (“Act”) or
otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however,
see the Notes).

(1) Includes 75,000 shares of the Issuer’s common stock underlying options.

(1) Includes 75,000 shares of the Issuer’s common stock underlying options.

(1) Includes 75,000 shares of the Issuer’s common stock underlying options.

(1) Includes 75,000 shares of the Issuer’s common stock underlying options.

Amendment No. 2 to Schedule
13D

This Amendment No. 2 to Schedule 13D amends and supplements the previously filed Schedule 13D filed by
Baker Bros. Advisors LP (the “Adviser”), Baker Bros. Advisors (GP) LLC (the “Adviser GP”), Julian C. Baker
and Felix J. Baker (collectively the “Reporting Persons”). Except as supplemented herein, such statements, as heretofore
amended and supplemented, remain in full force and effect. Information given in response to each item shall be deemed incorporated
by reference in all other items, as applicable. Each capitalized term used but not defined herein has the meaning ascribed to such
term in the Schedule 13D, as amended.

Item 3. Source and Amount of Funds or Other Consideration

Item 3 of Schedule 13D is supplemented as follows:

The disclosure regarding purchases in Item 5(c) below is incorporated
herein by reference.

Item 4. Purpose of the Transaction.

Item 4 of Schedule 13D is supplemented and superseded, as the case
may be, as follows:

This Amendment No. 2 is being filed to report the sale of shares of the Common Stock of BioCryst Pharmaceuticals,
Inc. (the “Issuer”) reported in Item 5(c) that resulted in a more than 1 percent change in beneficial ownership. The
disclosure regarding the sales in Item 5(c) below is incorporated herein by reference.

The 667, L.P. (“667”) and Baker Brothers Life Sciences, L.P. (“Life Sciences”,
and together with 667, the “Funds”) hold securities of the Issuer for investment purposes. The Reporting Persons or
their affiliates may sell additional securities or purchase securities in varying amounts and at varying times depending upon the
Reporting Persons’ continuing assessments of pertinent factors, including the availability of shares of Common Stock or other
securities at particular price levels, the business prospects of the Issuer, other business investment opportunities, economic
conditions, stock market conditions, money market conditions, the attitudes and actions of the board of directors and management
of the Issuer, the availability and nature of opportunities to dispose of shares of the Issuer and other plans and requirements
of the particular entities. The Reporting Persons may discuss items of mutual interest with the Issuer, which could include items
in subparagraphs (a) through (j) of Item 4 of Schedule 13D.

Depending upon their assessments of the above factors, the Reporting
Persons or their affiliates may change their present intentions as stated above and they may assess whether to make suggestions
to the management of the Issuer regarding financing, and whether to acquire additional securities of the Issuer, including shares
of Common Stock (by means of open market purchases, privately negotiated purchases, or otherwise) or to dispose of some or all
of the securities of the Issuer, including shares of Common Stock, under their control.

Except as otherwise disclosed herein, at the present time, the Reporting
Persons do not have any plans or proposals with respect to any extraordinary corporate transaction involving the Issuer including,
without limitation, those matters described in subparagraphs (a) through (j) of Item 4 of Schedule 13D.

Item 5. Interest in Securities of the
Issuer.

Item 5 of this Schedule 13D is hereby amended
and restated in its entirety as follows:

(a) and (b) Items 7 through 11 and 13 of each of the cover pages of this Amendment No. 2 are incorporated
herein by reference. Set forth below is the aggregate number and percentage of shares of Common Stock directly held., Such percentage
figures were calculated in accordance with Rule 13d-3 under the Securities Exchange Act of 1934, as amended.

The Adviser GP, Felix J. Baker and Julian C. Baker as principals
of the Adviser GP, and the Adviser may be deemed to be beneficial owners of securities of the Issuer directly held by the Funds,
and may be deemed to have the power to vote or direct the vote of and the power to dispose or direct the disposition of such securities.

The Reporting Persons disclaim beneficial ownership of the securities of the Issuer held by each of the
Funds, and this Amendment No. 2 shall not be deemed an admission that the Reporting Persons are the beneficial owners of such securities
for purposes of Section 13(d) or for any other purpose, except to the extent that any such Reporting Persons actually exercises
voting or dispositive power with respect to such securities.

Pursuant to management agreements, as amended, among the Adviser,
the Funds, and their respective general partners, the Adviser has complete and unlimited discretion and authority with respect
to the Funds’ investments and voting power over investments.

Julian C. Baker and Felix J. Baker each directly hold and beneficially
own 23,459 shares of Common Stock of the Issuer received as part of a pro-rata distribution from 14159, L.P. for no consideration
on January 28, 2015.

Dr. Stephen R. Biggar, an employee of the Adviser, is a former
Director of the Issuer. In connection with his previous service on the Board of Directors of the Issuer (the
“Board”), Dr. Biggar holds options to purchase 75,000 shares of Common Stock (“Stock Options”) and
5,833 shares of Common Stock received from the exercise of options to purchase Common Stock of the Issuer. Mr. Biggar
previously served on the Board as a representative of the Funds. The policy of the Funds and the Adviser does not permit
employees of the Adviser to receive compensation for serving as a Director of the Issuer. Therefore, Mr. Biggar has no
pecuniary interest in any Stock Options or shares of Common Stock directly held by him. The Funds are instead entitled to the
pecuniary interest in any Stock Options and shares of Common Stock received as director compensation.

(c) The following transactions in the Issuer’s Common Stock were effected by the Funds noted below
during the 60 days preceding the filing of this statement using working capital of the applicable purchasing Fund. All sale transactions
were effected in the open market directly with a broker-dealer. Except as disclosed herein, none of the Reporting Persons or their
affiliates has effected any other transactions in securities of the Issuer during the past 60 days.

(1) The reported price is a weighted average price. These shares were traded in multiple transactions
at a prices ranging from $5.04 to $5.47. The Reporting Persons undertake to provide the Issuer, any security holder of the Issuer,
or the staff of the Securities and Exchange Commission (the “Staff”), upon request, full information regarding the
number of shares traded at each separate price within the ranges set forth in this footnote.

(2) The reported price is a weighted average price. These shares were
traded in multiple transactions at prices ranging from $4.70 to $5.12. The Reporting Persons undertake to provide the Issuer, any
security holder of the Issuer, or the Staff, upon request, full information regarding the number of shares traded at each separate
price within the ranges set forth in this footnote.

(3) The reported price is a weighted average price. These shares were traded in multiple transactions
at prices ranging from $4.20 to $4.30. The Reporting Persons undertake to provide the Issuer, any security holder of the Issuer,
or the Staff, upon request, full information regarding the number of shares traded at each separate price within the ranges set
forth in this footnote.

(d) Certain securities of the Issuer
are held directly by 667, a limited partnership the sole general partner of which is Baker Biotech Capital, L.P., a limited partnership
the sole general partner of which is Baker Biotech Capital (GP), LLC. Julian C. Baker and Felix J. Baker are the controlling members
of Baker Biotech Capital (GP), LLC.

Certain securities of the Issuer are held directly by Life Sciences,
a limited partnership the sole general partner of which is Baker Brothers Life Sciences Capital, L.P., a limited partnership the
sole general partner of which is Baker Brothers Life Sciences Capital (GP), LLC. Julian C. Baker and Felix J. Baker are the controlling
members of Baker Brothers Life Sciences Capital (GP), LLC.

(e) Not applicable.

SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief,
I certify that the information set forth in this statement is true, complete and correct.

Dated: August 16, 2016