Open Letter to Johns Hopkins University Press, should publicly oppose the Research Works Act

Dear Ms. Keane:

I'm writing this open letter as a student of Johns Hopkins University, to urge the Johns Hopkins University Press to publicly oppose the Research Works Act (HR 3699), and to terminate your membership in the Association of American Publishers (AAP).

Other writers on the Internet make the case for this better than I could, so I'd like to refer you to a few online resources.

• For an overview of the proposed legislation, and some background, I recommend this recent op-ed in the NY Times, by Michael Eisen, "Research Bought, then Paid For"
• Michael Eisen has also written a blog post, "Our scientific societies need to quit the Association of American Publishers", in which he makes the case that we all must apply a concerted effort to communicate to the AAP that their support of this type of legislation is unacceptable,
• Here is an excellent post by Cameron Neylon, "IP Contributions to Scientific Papers by Publishers: An open letter to Rep Maloney and Issa", in which he makes the case that the AAP's relentless focus on IP, as a way to generate revenue, is misguided and counter-productive,

Recently, various other organizations have publically disavowed the RWA, and/or resigned their membership in the AAP, including

• MIT Press: "MIT Press distances itself from Research Works Act"
• ITHAKA and the CLIR: "ITHAKA becomes the second AAP member to disavow the Research Works Act"

I would like to suggest that this is an opportunity for Johns Hopkins University Press to lead, by coming out quickly and forcefully in favor of open access to scientific literature, which is so crucial to accelerating the advancement of science. I note that you've recently started a JHU Press Blog and I think that would be an ideal venue for this type of report.

Thank you for your consideration!

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Update:

Here are a few other blog posts I've seen recently urging this kind of action:

• Cameron Neylon, "Update on publishers and SOPA: Time for scholarly publishers to disavow the AAP"
• John Dupuis, "Scholarly Societies: It's time to abandon the AAP over The Research Works Act"

Letter regarding open access self-archiving at Johns Hopkins

The following is a letter that I just sent to some faculty and staff at Johns Hopkins University, regarding their policies about open access, their instititutional repository, and whether or not they have a mandate in place requiring their researchers to self-archive their work.

I debated with myself for some time about whether or not to put this letter on my blog. I finally decided in favor of openness. I think that this might serve as a test case for others who might be interested in this issue, and who might be considering advocating for such a policy at their own universities. I will post follow-ups with the results of this experiment. Feedback is very welcome.

---

Hi,

This email is to inquire about Johns Hopkins' policy with regards to open access self-archiving of author’s refereed journal articles. I am a student at Johns Hopkins (recently started as a Master's degree candidate in Bioinformatics) and a software developer by trade. I also have a strong interest in open access tools, policies, and methods. So, I am writing this email to introduce myself, and to ask some questions about Johns Hopkins' policies regarding some of these issues, and perhaps to stimulate some dialog.

I have recently found and read your "Johns Hopkins Scholarly Communications Group" site, and see that it says that you are "dedicated to fostering open access". I found (most of) your names from this site, and looked up your email addresses in the JHU system.

I see that JScholarship is the primary institutional repository for JHU -- is that right? Are there others? According to ROAR it uses the DSpace software. I browsed the site for a while, but didn't find very many journal articles. Would it be fair to say that currently, not a high percentage of the research papers produced as output by JHU researches is "self-archived" on JScholarship? If that's true, is there some other repository that they do use, that I haven't found yet?

The Scholarly Communications Group site also links to the Johns Hopkins Electronic Publishing Project. From there, I found the Mark Cyzyk's and Sayeed Choudhury's excellent paper from 2008, "A Survey and Evaluation of Open-Source Electronic Publishing Systems" (Wiki home; PDF whitepaper; on JScholarship; PowerPoint slides). It looks like the system that was most favored by that paper, "Open Journal System", was installed to this Electronic Publishing Project. But, it seems that, perhaps, it is no longer being actively maintained. Is that right?

I've recently been reading a lot of the writings of Stevan Harnad, who is a strong advocate of institutional repositories, and of policies that mandate self-archiving by authors, in order to further open access to scientific research. Below are a couple of links to resources related to this, that may be of interest. (Note that there is some redundancy in the material covered by these various links.)

Does Johns Hopkins have a mandate planned or in place requiring its researchers to self-archive the products of their JHU-funded research, along the lines of the other 130 institutional, 33 sub-institutional, and 52 funder mandates currently indexed in ROARMAP (including Harvard, MIT, Duke, Oberlin, Emory and NIH)? Has this been discussed at JHU? If not, what might be some good avenues that I and other interested students and faculty could pursue to help promote this goal?

Thank you very much for your time! Here are the links/resources:

• "What is Open Access and how to provide it?" - This is a blog post of an interview with Stevan Harnad, in which he very concisely lays out the case for how institutional repositories can further the goals of open access. 
• Self-Archiving FAQ - this is a very nice FAQ page that introduces the concepts and answers many common concerns that people have. This covers much of the same ground as the above post, but goes into more detail. 
• Enabling Open Scholarship (EOS) is a website and organization that "is both an information service and a forum for raising and discussing issues around the mission of modern universities and research institutions, particularly with regard to the creation, dissemination and preservation of research findings." There are many useful and informative resources on this site related to promoting and implementing open access policies, as well as several examples of other universities' open access policies. Is JHU a member of this organization? 
• The Immediate-Deposit/Optional-Access (ID/OA) Mandate: Rationale and Model - this is a very nice page on Stevan Harnad's blog, which gives a model for a policy that could be adopted to mandate that researchers deposit their works in JScholarship (or some other institutional repository). 
• The Right to Research Coalition - is a coalition of student groups that work to promote open access. I checked their membership page and did not see Johns Hopkins among the members. Are there any graduate student groups at JHU that would be an appropriate fit for this activity? How could I connect with such a group? I checked the list of Recognized Clubs in the GRO but didn't find any group that looked right. Would it be possible for me to start such a group? 
• OASIS - Open Access Scholarly Information Sourcebook - looks like it has a lot of useful, practical information. I haven't looked this over closely, but it looks promising. 

Again, thank you very much for reading this email, and I’ll anxiously await your reply.

Chris Maloney

Proper URL Encoding and Decoding

This is a reference post, on issues around encoding and decoding URLs. I've tried to summarize everything I know into a clear and concise set of guidelines. I hope you find them useful!

The character coding of all URLs is, as specified in RFC-3986, a subset of US-ASCII. US-ASCII is a seven-bit code, with characters in the range 0x00 to 0x7F. Here is a summary of the characters that are allowed and not allowed in URLs:

Excluded

0x00 - 0x1F, 0x7F (control characters),
0x20 (space),
these punctionation characters: " < > \ ^ ` { | }
All non-ASCII characters

General delimiters

these characters: % # / : ? @ [ ]

Sub delimiters

these characters: ! $ & ' ( ) * + , ; =

Unreserved

digits, letters, and these characters: - . _ ~

When dealing with URLs, Postel’s Law should apply: “Be conservative in what you send; be liberal in what you accept.”

Generating URLs (what you send)

When generating URLs for others’ consumption:

• Percent encoded values should use uppercase A-F for hex digits.
• Excluded characters within the US-ASCII range should be percent encoded as a single byte. So, for example, a space character should always be encoded as “%20”. When the space character appears in a query string, it can be encoded either as “%20” or as the plus sign “+”.
• Excluded characters outside the US-ASCII range must be first encoded in UTF-8, and then percent-encoded. For example, “Ä”, Unicode U+00C4, “Latin capital letter A with diaresis”, should be encoded as “%C3%84” and not as %C4, because it is first encoded as a two-byte UTF-8 sequence.
• General delimiters, when used literally (i.e. not as delimiters), must be percent-encoded, with certain exceptions described below.
• Sub delimiters should be percent encoded when their literal use would conflict with their use as delimiters. For example, in a query string, the ampersand “&” must be percent-encoded, but when in a path segment, it is okay to use it literally. When in doubt, percent-encode, because it can’t do any harm.

The two main portions of a URL that are of concern to developers are the path segments and the query string.

• Path segments can include literal characters in the sets unreserved, sub delimiters, and the two general delimiters “:” and “@”. All other characters must be percent-encoded. Note that path segments should never include a slash characters “/”, even if it is percent encoded, since user agents and servers both have problems with these.
• Query strings can include all of the same characters as path segments, and additionally the two general delimiters “/” and “?”.

So, for example, the following URL is legal and unambiguous:

http://example.com/doc@1:5/?back_uri=http://user:password@example.com/?foo%3Dbar

Note how, within the query string, the equals sign within the back_uri is percent-encoded as “%3D”.

Receiving URLs (what you accept)

When parsing a URL, applications should follow these guidelines:

• Within a query string, convert “+”, wherever it occurs, into a space character. (Note that this must be done before percent-decoding).
• Accept either upper or lowercase for hex digits within percent-encoded values
• Convert percent encoded substrings into sequences of bytes, and then interpret those as UTF-8.
  
  If the byte sequence is not valid UTF-8, then the application should either drop it completely, or throw an exception. For example, for this URL
  

  http://www.ncbi.nlm.nih.gov/pubmed?term=%C4rzteblatt

  the user incorrectly encodes Ä as %C4, but the single-byte sequence 0xC4 is not valid UTF-8. So the application should either drop this invalid value completely (interpret the term as “rzteblatt”), or throw an exception. The preferred behavior is to throw an exception.
  
• If the resultant character string contains characters outside the accepted range for the application, they should cause an exception. For example,
  

  http://www.ncbi.nlm.nih.gov/pubmed/?term=%E8%B5%B7%E5%8F%B8%E5%A0%A1

  which is valid UTF-8, but where the term decodes as “起司堡”, should either cause “no items found” or should result in an exception page.
  

Wikis in science and science education

I'm writing this blog post as an open letter to the faculty of Johns Hopkins, where I'm enrolled in the MS in Bioinformatics program. It's about wikis.

Lately I've stumbled upon a few presentations and websites, from independent directions, which highlight the growing importance of the role of wikis in science. Here are a few of my encounters.

TaxPub, ZooKeys, and Species-ID

At JATS-Con last year, one of the best talks was given by Terry Catapano, on TaxPub. TaxPub is a file format for journal articles. TaxPub is interesting and novel because it allows very domain-specific, structured data to be included in with the main article content. In this case, the domain is taxonomic information -- data related to the names and descriptions of species.

ZooKeys is a new, peer-reviewed, open-access journal from Pensoft. ZooKeys uses the TaxPub format, and it's licensed under the Creative Commons - attribution license (CC-BY). This means that anyone is allowed to copy and repurpose the content, for anything whatsoever, as long as he or she gives credit to the authors.

What's special about ZooKeys is, that at the same time an article is published in the journal, it is also used to produce a wiki page on the Species ID wiki. One of the first articles produced with this new workflow describes the process better than I could. Here is the article in ZooKeys, and here's the corresponding wiki page. This allows for the content to be updated as new information is found. At the same time, referencing the original journal article is always possible.

Note that the Species-ID wiki is powered by MediaWiki, the same software behind Wikipedia. This is important, because if a scientist learns to edit Wikipedia, then he or she could also contribute to Species-ID -- and vice-versa, of course.

Encyclopedia of original research

The next encounter was with a project proposal recently put forward by Daniel Mietchen for a wiki of scientific articles. You can read more about this idea, and the philosophy behinds it, in a couple more of his blog posts here and here.

His idea is to seed the wiki with a large set of journal articles that are either in the public domain, or have been published with a license at least as permissive as CC-BY. PMC (where I work) serves a set of such articles: the Open Access Subset. These articles can be downloaded from our FTP site in their original XML format. The piece that's still missing is a JATS-to-Mediawiki converter, which would be fairly easy to write.

Pfam, Rfam, and Wikipedia

Last week I had the pleasure of attending a seminar given by Rob Finn, hosted by the NCBI Computational Biology Branch. The seminar was about Pfam (on Wikipedia), Rfam (on Wikipedia), and Wikipedia. Pfam is a database of protein families, and Rfam is a database of RNA families.

What is super cool and and unique about these databases is that they both leverage the power of Wikipedia to enhance the value of the results delivered to their users. For example, the page in Pfam for the linker histone (histone H1) contains vast amounts of data (which I don't pretend to understand), which is accessible from the various menu options both across the top and down the left side of the page. But most prominently, on the summary page, they pull out the data from Wikipedia and display it within the Pfam site itself.

Rob Finn explained that, as part of their curation of the protein data, they also help to maintain and control the quality of the relevant Wikipedia entries. So it's a very synergistic relationship. The scientists themselves, and the database curators, collaborate to improve the quality of the Wikipedia content, and then Wikipedia enhances the site.

JHU AAP Online Bioinformatics program

These are all exciting trends, and of course they just scratch the surface of the science-wiki landscape. Now I want to contrast this with my experience so far in the Bioinformatics program at Johns Hopkins. I am sorry to say it, but they are woefully behind. I want to stress that my purpose in writing this post is not to bash Johns Hopkins. I think the program is great, and I have had very good experiences in my classes there so far. I have enormous respect for my advisor, and the courses that I've taken have been well designed. And the bottom line is that I am learning a hell of lot of biology. No, the purpose of this post is to encourage the administrators and faculty there to embrace the idea of preparing future scientists to collaborate in the wonderful medium of wikis. Pointing out current inadequacies is part of that.

Last semester, I proposed to my instructor and my advisor that it would be nice if at least one assignment for each class was to make a substantive contribution to Wikipedia. The assignments I was given were mostly writing assignments on particular topics. We had one big "presentation" assignment due at the end of the semester. Each student was given a different topic to research and describe. But, when the class ended that effort was then locked away in the class' archives, never to be read by anyone again? Isn't that a shame? Here is part of what I wrote to my advisor:

You help to run a Bioinformatics program, [which is about merging the technologies] of biology and computers. Wikis are emerging as a very powerful, rich, and important medium for collaboration and providing scientific results to the public.

So I think the classes in the Bioinformatics program should all encourage students to contribute to Wikipedia. Wouldn't it be nice if at least one assignment from each class were to make a substantive contribution?

My professor from last semester said that she was interested in the idea, and would try it out this semester. I don't know if she did or not -- I still have to follow up with her and ask.

But, of course, this semester I moved on to a different class. And the whole school moved on to a new software platform for their online courses. Perhaps you've heard of it: Blackboard. So far my impression of it is ... ahem ... not good.

There are many problems with Blackboard, but I'll only focus on the problems with the integrated wiki. They are legion. This past week, I just finished participating in our first group assignment, in which we were asked to collaborate on writing the answers to various questions about two research papers. I proposed that we use a wiki for this, and suggested that we could either use the Blackboard's integrated wiki, or we could use a site that lets you create a free wiki in the MediaWiki platform -- Wikia. I pointed out that the main advantage of using Wikia would be that it would introduce everyone to the MediaWiki format -- which could be a springboard into editing Wikipedia.

Not surprisingly, my teammates chose to use the Blackboard wiki. I don't blame them at all -- because on the face of it, it would seem that Wikia is too risky. But, the problems with the Blackboard wiki started to become apparent right away. Here is a list of a few of the problems we encountered:

1. It is impossible to compare two versions of a page, to see what has changed. This is a fundamental feature of a wiki. Especially in a long article, it is absolutely required that an author be able to compare the versions, to see at a glance what has changed, so that he or she can focus just on the changes. To be fair, BB has a very limited (see the next item) ability to do this, but JHU's installation seems to be defective. It is missing a "diff.css" file, which, presumably, adds the all-important highlighting of the changes.

2. The "limited" ability I refered to above is (please be warned that the following might cause your head to explode) that you can only compare revisions corresponding to edits that you yourself have made. In other words, if I want to see my own changes ("my contributions") that's fine -- I can do that. But if I want to see what somebody else changed on a page that I myself authored -- that's impossible.

3. The wiki uses a crap browser-based wysiwyg editor that produces absolutely nightmare-inducing markup. All of my teammates found themselves frustrated by the random bizarre formatting quirks of the editor. You could tweak things to look correct in the edit view, but as soon as you clicked "submit", the formatting would be all screwed up again. It does have a "view - source" view, but if you make changes in that view, to clean things up, and then switch back to wysiwyg view, all your work is lost.

But the biggest problem is -- that it is not MediaWiki. As I mentioned above, if we're going to spend the time to learn to use a wiki, then why not learn something that can really add to our value as scientific collaborators?

My hope is that in my current class, in future group assignments, that the group I'm in, and the others, all decide to use and collaborate with the new wiki I've just set up on Wikia, the Molecular Biology, AAP, Summer 2011 wiki. I expect there might be some resistance because it is "off-site", and not part of the JHU system. If so, those would be unjustified complaints. We're living in a deeply interconnected, collaborative world, now, and more and more businesses are moving their entire infrastructures into the cloud. I think as a general principle, we should make use of the best tools wherever we find them. If this objection is a show-stopper, then the next-best thing would be for JHU to set up an installation of MediaWiki itself. It is very easy to do!

Another recommendation I have is that all the professors who teach courses, be required to obtain a minimum Wikipedia-literacy. They should be required to register their Wikipedia usernames (mine is Klortho) so that anyone can go and see their list of contributions -- and this could become a part of their CV (as it should be). We all rely so heavily on Wikipedia these days, that it is a crime that we don't do more, as individuals and institutions, to support it.

UPDATE:
Daniel Mietchen pointed out to me that the journal RNA Biology actually requires a Wikipedia article (search for "A short guide to creating your first Wikipedia article") along with the submission of any new manuscript submissions to "RNA Families Track".

pH calculation of a very small concentration of a strong acid.

I have always felt that I didn't really "get" acid-base chemistry. Usually, when I'm presented with a chemistry problem, my mind just refuses to grasp what's being asked. I struggle to figure out which equations to use, and how to plug the numbers from the problem into the variables of the equation. Well, my experience this past week reassures me that I'm not the only one.

In my Biochemistry class, we got this problem:

Calculate the pH of a solution of the strong acid HCl at a concentration of 5x10^-8 M.

This is a little bit of a tricky question, because the concentration of the acid is so low. But before getting into it, let's simplify the discussion a bit by assuming that we're talking about one liter of water. Then, the amount of acid that we're adding is 5x10^-8 moles. To me, changing from concentrations into definite amounts makes it easier to understand.

A strong acid will dissociate more-or-less completely when added to water, so this is like adding a 5x10^-8 moles of H⁺ ions into the water. Note that the number of H⁺ ions in one liter of pure water is 10^-7 moles, so this is one-half of that. To use nice, small, round numbers, it's as we had a bottle of water (a very small bottle) that has 10 H⁺ ions, and we're adding an extra 5.

My first answer was based on this simple addition. I assumed that the number of H⁺ ions after the acid was added would be 1.5x10^-7. Then the pH would be the negative logarithm of that:

This would be like assuming that if the bottle of water initially had 10 H⁺ ions, and you add 5, then in the end it would have 15.

The problem set was presented online, and after submitting our answers, we could go back and review them. The answer key gave the correct answer to this problem as "7.3". ... Wait, what? Neutral water has a pH of 7, and anything above 7 is considered alkaline. So how do you get an alkaline solution after adding a strong acid to water?

It's pretty easy to see where the "7.3" answer comes from. The usual way to solve these problems is to assume that the H⁺ concentration, after you add the strong acid, is equal to the concentration of the acid. See, for example, the first sentence of the Calculation of pH for weak and strong acids section of the pH article on Wikipedia: "In the case of a strong acid, there is complete dissociation, so the pH is simply equal to minus the logarithm of the acid concentration." So following that strategy:

But the problem is that this completely neglects the baseline concentration of the H⁺ ions in pure water. This is like assuming that if the bottle of water has 10 ions, and you add 5, then in the end it will have 5. It doesn't make sense.

In fact both of these answers are wrong. What happens, after you add the new H⁺ ions, is that some of them will react with the OH^- ions to form neutral water molecules. The solution will be at equilibrium when the equilibrium equation for water is again satisfied:

To continue with the analogy I've been using, it's as if you have a bottle of water that has 10 H⁺ ions and 10 OH^- ions. The equilibrium equation for water says that H⁺ times OH^- must always equal 100, once equilibrium has been established. Now, you add 5 extra H⁺ ions. At this point the bottle has 15 H⁺ ions and 10 OH^- ions. But that product is 150, so the solution is not at equilibrium. What happens? Well, some of the H⁺ ions will react with the OH^- ions to form water. Each time that happens, the number of H⁺ ions and the number of OH^- ions both decrease by one. So first there will be 14 H⁺ ions and 9 OH^- ions, then 13 and 8. Now, 13 X 8 = 104, so in this simple-minded example, that's as close to equilibrium as we can get.

At each step, the difference in the number of H⁺ ions and OH^- ions is always a constant, and is equal to the number of H⁺ ions that were added:

When we apply this reasoning to the original problem, we see that the difference in the concentrations of H⁺ and OH^- is a constant, which is the amount of acid that was originally added:

We want to get rid of [OH^-], so let's solve for that:

And we also know that the equilibrium equation for water must be satisified. Here it is again:

So let's plug the value for [OH^-] into that:

And then put it into the form of a quadratic equation:

Then using the quadratic formula:

Clearly, the value must be positive, so we should pick "+", not "-":

Finally, we can calculate the pH:

At first, I wasn't very confident in this solution, so I dug around on the Internet. All of the examples I could find used very high concentrations of strong acid, and used the assumption that you could take the acid concentration as the H⁺ concentration. For example, here ("Find the pH of a 0.0025 M HCl solution.") and here ("How do you calculate pH of a 0.012M solution of HCL?").

Finally I found a good discussion in this online textbook, starting at section 3.1, "Strong acids and bases". Their procedure maps onto what I did above, almost exactly. Note that they refer to the hydronium ion H3O⁺ where I referred simply to the hydrogen ion H⁺.

Equation 17 from the book is:

which is the same as my quadratic equation above -- C_a is the concentration of the acid that was added, and K_w is the equilibrium constant of water.

At one point, the authors say:

As the acid concentration falls below about 10^-6M, however, ... [H3O⁺] approaches √K_w, or 10^-7M. The hydronium ion concentration can of course never fall below this value; no amount of dilution can make the solution
alkaline!

Which is another way of saying that you can't get a pH above 7, no matter how low the acid concentration is.

UPDATE:
You might notice that I linked to an old version of the Wikipedia article above. That's because when I was looking for resources for this post, I discovered that that section on Wikipedia not only had a lot of errors, but didn't even make much sense at all. So I rewrote it from scratch -- everything under "Calculations of pH", including "Strong acids and bases" and "Weak acids and bases".

Apparent negative cooperativity in proteins with multiple ligand binding sites for the same ligand.

Whew, that's a mouthful! This semester I'm taking Intro to Biochemistry, an online course from Johns Hopkins University. The following is something I wrote up in relation to a discussion question that was posed in our third week. I was bothered by something I read, and I started to tinker with the math, just to see if I could figure it out myself. Then I dusted off gnuplot, and started to make some simple plots. I'm really happy with the result, and so I'm posting it here. It's rare, in my experience, to get something to work out so nicely and cleanly, and have the math give extra insight into the physical phenomenon.

In chapter 5 of our textbook, "Lehninger Principles of Biochemistry", 5th edition, the authors describe the affinity of proteins for other molecules that bind to them, called ligands. They discuss allosteric binding, which is when the binding of a ligand to one site affects the ability of the ligand to bind to another site on the same protein. The classic case is hemoglobin. In hemoglobin, the binding of one oxygen molecule makes it more likely for other oxygen molecules to bind at the other three sites. This is an example of positive cooperativity. The book presents the following figure, which is called a Hill plot, which characterizes this phenomenon.

The positive cooperativity is apparent for hemoglobin (in red) because, within a certain range, the slope of this plot is greater than one.

For a protein with only one ligand-binding site, the characteristic equation is:

where L is the concentration of the ligand, K is the dissociation constant, and the term on the left is:

A note about my notation: in these equations, "L" and "P" are the concentrations of the ligand and the unbound protein, respectively. These are given in Lehninger and elsewhere as "[L]" and "[P]". I've just adopted a shorthand with [L] → L and [P] → P. But note that for the concentration of the bound protein-ligand complex, I still write "[PL]". If I wrote it as "PL", it would be ambiguous. So "[PL]" means the concentration of protein-ligand, and "PL" means "[P][L]", the product of two different concentrations.

Since , we get:

And taking the log() of both sides yields the characteristic equation above. In that equation, the log-log plot is linear with a slope of one. Again, the Hill plot for hemoglobin shown above, which has two binding sites that exhibit positive cooperativity, has, within a specific region, a slope greater than one.

The authors then describe negative cooperativity, which would be exhibited if the binding of a ligand to one site makes it harder for a ligand to bind at another site. They say that true negative cooperativity is rare.

The question that bothered me came from Lehninger, p. 180, problem 2, case (b): "The protein is a single polypeptide with two ligand-binding sites, each having a different affinity for the ligand." Our professor, Dr. Schwartz, indicated that this has "apparent negative cooperativity" as opposed to "true" negative cooperativity. In the solutions manual that accompanies our textbook, page S-54, it says, with regards to this case, "The higher affinity ligand-binding sites bind the ligand first. As the ligand concentration is increased, binding to the lower-affinity sites produces an nH < 1.0, even though binding to the two ligand-binding sites is completely independent."

Hmm... when I read that, I was a little bit skeptical. Intuitively, it seemed to me that the net result of two independent ligand sites, even if their affinities differ, should act like a single independent ligand site with some affinity in the middle. So I ventured to try to do the math on my own.

Now, if the protein has two binding sites, that are not cooperative at all (independent), then

As a check, notice that if , then this reduces to , same as above.

But what I really want is a function that depends only on L and the two Ks. P1 and P2 are also variable, and depend on L. To get expressions for those in terms of L, there is one more constraint that we can apply: that the sum of the concentrations of the bound and unbound sites, for site 1 and for site 2, is a constant, and is the same: the total concentration of the protein T:

We can use this to solve for P1 in terms of L and two constants K1 and T:

Likewise,

We can plug these into the above equation and, simplifying a bit (notice how T drops out),

To make it look prettier, we can define two new constants, the mean Km and the product Kp:

Then,

Finally,

The term inside the log() on the right of the equation is like the dissociation constant K for the whole complex – but of course it’s not constant, it varies with L. However, you can see that this term does approach a constant value as L → 0 and as L → ∞:

If K1 and K2 are very different, for example, if K1 << K2, then this term simplifies further:

So when the concentration of the ligand is very low, the influence of the binding site with the lower dissociation constant (higher affinity) predominates, and the whole protein acts like something with one binding site that has a dissociation constant twice this lower value (one-half the affinity). When the concentration of the ligand is high, the influence of the binding site with the higher dissociation constant (lower affinity) predominates, and the whole protein acts like something with one binding site that has a dissociation constant one-half the higher value (twice the affinity). In a critical range where L is roughly between 2K1 and K2/2, one line transitions into the other.

So, the following plot shows this curve in the range between -8 and -2, for values of K1 = 1μM (-6 on the x-axis) and K2 = 100μM (-4). It is the curve “Double(x)”, in blue. For comparison, I also plotted the straight-line graphs that this curve asymptotically approaches, “Single1(x)” and “Single2(x)”.

This is a two-part graph. Below the main part is another graph giving the slope of the Hill plot. You can see that within the range of interest, it dips well below one. This, then, is the apparent negative cooperativity.

Why this is important

Even though this result was described in the solutions manual of our textbook, it was not described in the main text. That text includes this statement (p. 164): "The slope of a Hill plot is ... a measure of the degree of cooperativity. If n_H equals 1, ligand binding is not cooperative." The latter part of this statement is demonstrably false. If the two ligand binding sites have different affinities, and they are not cooperative, then the slope will be less than one. If in this case the slope is measured to be 1, then that's an indication of positive cooperativity. In fact, the case where there is a slope of one and no cooperativity is the degenerate case where the two ligand binding sites have identical affinities. Except in the case (as in hemoglobin) where the protein is made up of identical subunits, I would guess that most of the time, the ligand binding sites should be expected to have different affinities. This needs to be taken into account when using the Hill plot for assessing cooperativities.

Appendix: Gnuplot script file

# Unit3-ApparentNegCoop.plt
# $Id$

set xr [-8:-2]

# Here are our constants

K1 = 1e-6
K2 = 1e-4
Km = (K1 + K2) / 2
Kp = K1 * K2


# I want a plot with log10(L) on the horizontal, so:  x = log10(L)
L(x) = 10 ** x

Factor(L) = (Km + L) / (Kp + Km * L)
Tp(x) = Factor(L(x)) * L(x)
Double(x) = log10(Tp(x))

# For comparison, we'll also plot the graph you'd get for a protein with one
# ligand binding site with value K1*2, and another for with K2/2:
Single1(x) = x - log10(K1 * 2)
Single2(x) = x - log10(K2 / 2)

set term x11 0
plot Single1(x), Single2(x), Double(x)


# Now take the derivative and plot the slope of the graph
u(x) = Km + 10 ** x
v(x) = Kp + Km * (10 ** x)
slope(x) = 1 + 0.43 * (1/u(x) - Km/v(x)) * (10 ** x)

set term x11 1
plot slope(x)

Why don't the ordinary Chinese people here in the U.S. protest their government?

Hu Jintao will visit the U.S. again very soon, and I have a few questions for my Chinese friends.

Why is it only the Falun Gong that protests? The last time Hu visited the U.S., in 2008, I went down to Washington Square, and was disappointed to find that the vast majority of protesters were Falun Gong. Why is it that ordinary Chinese citizens and immigrants living here don't also protest? Why is it that the only two choices are: to be with the Falun Gong, or to show support for the CCP?

Forget about the big, controversial issues like Falun Gong, Taiwan, and Tibet; I just want to ask all of you, are you all happy with the Chinese communist government? Happy with the fact that they have Liu Xiaobo in prison? What about their treatment of Hu Jia and a hundred other activists? Happy with the harassment and intimidation of human rights lawyers?

When was the last time you went back to China and tried to get on the Internet? Are you okay with the Great Firewall and the fact that people in China don't have the freedom to read what they want, so that they can make up their own minds about important issues? Don't you know you couldn't even have this discussion if you were in China -- that it's impossible to send any email in cleartext with the words "Falun Gong"? And forget about trying to write a blog post or a comment that's critical of the government - they are all deleted within hours (if not minutes) of being posted.

Are you happy with the one-party system in China? With the fact that it is not democratic - that people can't vote for their own representatives in government? With the fact that the state completely controls the media?

Protesting in front of Hu Jintao doesn't mean that you're betraying your country. There is a difference between China and the Chinese Communist Party. Americans protest their government all the time, and although a few right-wing extremists would call them traitors, they are not. Why should loving your country mean you're not allowed to criticize it?