Filed by Glaukos Corporation

(Commission File No. 001-37463)

pursuant to Rule 425 under the Securities Act of 1933

and deemed filed pursuant to Rule 14a-12

under the Securities Exchange Act of 1934

Subject Company: Avedro, Inc.

(Commission File No. 001-38809)

The following is a transcript of a video communication sent to the employees of Avedro, Inc. by Thomas W. Burns, President and CEO of Glaukos Corporation, on August 7, 2019:

Good afternoon. My name is Tom Burns and I’m the president and CEO of Glaukos Corporation. I’m delighted to present to you today and very much wish that I could be there in person, but as you’re probably aware, I am currently conducting an earnings call, talking about the combination of our companies with the investment community. I wanted to tell you how promising I view this combined transaction between the companies and how we’ve been able to come to know you and the conclusions that we’ve come up with over the past several months. The first conclusion is that we believe, as you do, that keratoconus is a vastly underserved marketplace, very embryonic in nature and a marketplace that has significant unmet clinical needs. The second conclusion that we’ve come up with is that we believe that you’ve built a powerful platform company, with which to address progressive keratoconus and other corneal disorders in the future. You’ve just come off a very, very successful IPO under the leadership of Reza and the management team, but you’ve accomplished so much more as a company. On the commercial front, I’ve been entirely impressed with what you’ve done. You’ve changed a cash pay market into a buy and bill marketplace and been able to secure a J-code at the beginning of this year, which is going to give the opportunity to provide commercial payment for this very necessary bioactive treatment for the treatment of progressive keratoconus here in the United States. On the R and D side, with the work you’ve done in optical scanning and next generation bioactivated pharmaceuticals, you’ve created a pipeline that’s replete with opportunity to serve the progressive keratoconus, corneal ectasia, and other corneal disorder marketplaces in the future.

On the clinical and quality side, you’ve been able to meet your desired outcomes in terms of completing the “epi-on” study within the required timeframe and to begin a very promising, phase two-A study presbyopia. And on the manufacturing and quality side, you’ve delivered. You’ve been able to bring your devices and pharmaceuticals in a high quality nature with high yields into the marketplace while meeting demand with no backorders. All of these are very promising signs of an emerging company.

When we look at what we can do together as a company, this is where I get terribly excited. Glaukos started with from very modest beginnings. We’re a company that started with five people back in 2002 with high aspirations and a mission to transform glaucoma treatment. And over the past decade and a half, we have pioneered, created and now lead a very robust marketplace called MIGS— micro invasive glaucoma surgery. And one of the things we think our core competency is is to disrupt and to create new marketplaces. And we think by taking this, this embryonic marketplace and the great work that you’ve done, combining with our core ability to be able to create, to master, to pioneer and to lead new marketplaces that we can create an incredible opportunity here within the keratoconus and other corneal disorder marketplaces. In addition, when you look at just the opportunity we have in the commercial marketplace within the United States, you see it’s quite enviable. We call on many of the comprehensive ophthalmology and corneal refractive practices that you currently do so. In fact, about 700 of the designated 1,100 target practices that we both will seek in the future. And in doing so, we’re able to bring about six times the amount of mass and scale in terms of commercial representatives that will be in the field, in order to bring your great technology into practices so that we can advance the treatment of progressive keratoconus.  And finally, in terms of capital infusion, we’re a company that has cash on the balance sheet, has high aspirations to move projects forward. We think that we’ll be able to allow— give us the ability to have the cash to be able to bring your projects to marketplace in an accelerated fashion.

When we talk about the cultures of the company, I would define our culture as one of high integrity, one that has a thirst for innovation and energy, one that is a culture that seeks to win, but one that carries itself with a high degree of humility. And in meeting your senior

management team and many of the players within your organization, I would say that your culture is equally defined and very like in many of the characteristics that we share.

So as we look at this combined entity going forward, again I’m terribly excited about what we can do together. So with that, I look forward to meeting all of you. But I wanted to take this opportunity to introduce Glaukos to you. Very much look forward to getting to know you better, and to building a really, truly value-creating proposition of a combined company. Thank you very much.

Additional Information and Where to Find It

In connection with the proposed transaction between Glaukos and Avedro, Glaukos will file with the SEC a registration statement on Form S-4 that will include a document constituting a prospectus of Glaukos and will also contain a proxy statement of Avedro.  Glaukos and Avedro also plan to file other relevant documents with the SEC regarding the proposed transactions.  After the registration statement on Form S-4 is declared effective by the SEC, a definitive proxy statement/prospectus will be mailed to the stockholders of Avedro. INVESTORS AND SECURITY HOLDERS ARE URGED TO READ THE PROXY STATEMENT/PROSPECTUS AND OTHER RELEVANT DOCUMENTS FILED WITH THE SEC CAREFULLY AND IN THEIR ENTIRETY WHEN THEY BECOME AVAILABLE BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION. Investors and security holders will be able to obtain free copies of the registration statement on Form S-4 and the proxy statement/prospectus (when available) and other relevant documents filed or that will be filed by Glaukos or Avedro with the SEC through the website maintained by the SEC at http://www.sec.gov. Copies of the documents filed with the SEC by Glaukos will be available free of charge within the Investor Relations section of Glaukos’ internet website at http://investors.glaukos.com or by contacting Glaukos Investor Relations by email at investors@glaukos.com or by phone at 949-481-0510. Copies of the documents filed with the SEC by Avedro will be available free of charge within the Investor Relations section of Avedro’s internet website at https://investors.avedro.com or by contacting Avedro Investor Relations by email at investors@avedro.com or by phone at 646-924-1769.

No Offer or Solicitation

This communication does not constitute an offer to sell or the solicitation of an offer to buy any securities nor a solicitation of any vote or approval with respect to the proposed transaction or otherwise.  No offering of securities shall be made except by means of a prospectus meeting the requirements of Section 10 of the Securities Act of 1933, as amended, and otherwise in accordance with applicable law.

Participants in Solicitation

Each of Avedro and Glaukos and their respective directors and executive officers may be deemed to be participants in the solicitation of proxies from Avedro stockholders in connection with the proposed transaction. Information about Avedro’s directors and executive officers is included in Avedro’s Annual Report on Form 10-K for the year ended December 31, 2018, which was filed with the SEC on March 21, 2019, and is also included in Avedro’s Form S-1 Registration Statement

filed with the SEC on January 18, 2019, as amended by Amendment No. 1 to Avedro’s Form S-1 Registration Statement filed with the SEC on February 4, 2019. Information about Glaukos’ directors and executive officers is included in the definitive proxy statement for its 2019 annual meeting of stockholders, which was filed with the SEC on April 17, 2019. Other information regarding the participants in the solicitation of proxies in connection with the proposed transaction and a description of their direct and indirect interests, by security holdings or otherwise, will be contained in the proxy statement/prospectus and other relevant materials to be filed with the SEC regarding the proposed transaction when they become available. Investors may obtain free copies of these documents from Avedro or Glaukos as indicated above.

Use of Forward-Looking Statements

This communication contains “forward-looking statements” within the meaning of federal securities laws. Forward-looking statements may contain words such as “believes”, “anticipates”, “estimates”, “expects”, “intends”, “aims”, “potential”, “will”, “would”, “could”, “considered”, “likely” and words and terms of similar substance used in connection with any discussion of future plans, actions or events identify forward-looking statements. All statements, other than historical facts, including statements regarding the expected timing of the closing of the proposed transaction and the expected benefits of the proposed transaction, are forward-looking statements. These statements are based on management’s current expectations, assumptions, estimates and beliefs. While Avedro and Glaukos believe these expectations, assumptions, estimates and beliefs are reasonable, such forward-looking statements are only predictions, and are subject to a number of risks and uncertainties that could cause actual results to differ materially from those described in the forward-looking statements.

The following factors, among others, could cause actual results to differ materially from those described in the forward-looking statements: (i) failure of Avedro to obtain stockholder approval as required for the proposed transaction; (ii) failure to obtain governmental and regulatory approvals required for the closing of the proposed transaction; (iii) failure to satisfy the conditions to the closing of the proposed transaction; (iv) unexpected costs, liabilities or delays in connection with or with respect to the proposed transaction; (v) the effect of the announcement of the proposed transaction on the ability of Avedro or Glaukos to retain and hire key personnel and maintain business relationships with customers, suppliers and others with whom Avedro or Glaukos does business, or on Avedro’s or Glaukos’ operating results, market price of common stock, and business generally; (vi) potential legal proceedings relating to the proposed transaction and the outcome of any such legal proceeding; (vii) the inherent risks, costs and uncertainties associated with integrating the businesses successfully and risks of not achieving all or any of the anticipated benefits of the proposed transaction, or the risk that the anticipated benefits of the proposed transaction may not be fully realized or take longer to realize than expected; (viii) competitive pressures in the markets in which Avedro and Glaukos operate; (ix) the occurrence of any event, change or other circumstances that could give rise to the termination of the merger agreement; and (x) other risks to the consummation of the proposed transaction, including the risk that the proposed transaction will not be consummated within the expected time period or at all. Additional factors that may affect the future results of Avedro and Glaukos are set forth in their respective filings with the SEC, including each of Avedro’s and Glaukos’ most recently filed Annual Report on Form 10-K, subsequent Quarterly Reports on Form 10-Q, Current Reports on Form 8-K and other filings with the SEC, which are available on the SEC’s website at www.sec.gov. The risks and uncertainties described above and in Avedro’s most recent Quarterly Report on Form 10-Q and Glaukos’ most recent Quarterly Report on Form 10-Q are not exclusive and further information concerning Avedro and Glaukos and their respective businesses, including factors that potentially could materially affect their respective businesses, financial condition or operating results, may emerge from time to time. Readers are urged to consider these factors carefully in evaluating these

forward-looking statements, and not to place undue reliance on any forward-looking statements. Readers should also carefully review the risk factors described in other documents that Avedro and Glaukos file from time to time with the SEC. The forward-looking statements in these materials speak only as of the date of these materials. Except as required by law, Avedro and Glaukos assume no obligation to update or revise these forward-looking statements for any reason, even if new information becomes available in the future.