Analog Signaling Networks

Having just last week joined Researchblogging, I've been on the lookout for interesting open-access research reports or articles to blog about. thus, two articles caught my eye regarding cellular intelligence, a subject I've discussed before.

Dpr Acts as a Molecular Switch, Inhibiting Wnt Signaling when Unphosphorylated, but Promoting Wnt Signaling when Phosphorylated by Casein Kinase Iδ/ε

Teran, E., Branscomb, A., & Seeling, J. (2009). Dpr Acts as a Molecular Switch, Inhibiting Wnt Signaling when Unphosphorylated, but Promoting Wnt Signaling when Phosphorylated by Casein Kinase Iδ/ε PLoS ONE, 4 (5) DOI: 10.1371/journal.pone.0005522

Modulation of the β-Catenin Signaling Pathway by the Dishevelled-Associated Protein Hipk1

Louie, S., Yang, X., Conrad, W., Muster, J., Angers, S., Moon, R., & Cheyette, B. (2009). Modulation of the β-Catenin Signaling Pathway by the Dishevelled-Associated Protein Hipk1 PLoS ONE, 4 (2) DOI: 10.1371/journal.pone.0004310

These are dense papers, and I'm afraid the abstracts won't be much good if you aren't already familiar with the Wnt/β-Catenin signaling "cascade". Very briefly, Wnt is a large family of proteins that act as signaling molecules outside the cell within the developing (and adult) bodies of vertebrates, and probably many other bilaterians. They interact with several families of enzymes and other signaling proteins embedded in the cell membrane, passing along information to the enzyme signaling network within the cell, where they have a critical effect on the presence of β-Catenin, a (family of) protein(s) with wide effects on gene transcription.

My main focus here is not on the details of the Wnt/β-Catenin signaling, but on the tacit assumptions built into certain word choices involved in reporting, and probably setting up, research in this area.

Let's start with the word "cascade". The very word implies a false analogy: a cascade is a waterfall-by-steps, and each step is a downhill process that depends on the previous process(es) for its energy.


Figure 1: A linear cascade, which is what typically comes to mind with the word. (From the Council of Independent Colleges: Historic Campus Architecture Project website.)


Figure 2: A more complex cascade, showing some parallel interaction. (From the trüWATER! website.)

Phosphorylation is not like a waterfall, however, but more an electrical relay, or, better, like a transistor. Both phosphorylation and dephosphorylation are extremely "downhill" processes energetically.^A1

What passes along, rather than down, the cascade is information, which, unlike energy, is not subject to considerations of entropy^A2 or conservation. We should not speak of a "cascade" then, but a network, in which information is not constrained to go in only one direction, unlike water in a cascade. Indeed, the control mechanisms within the cell are full of loops.⁸

Keeping this fact in mind will help us make sense of research like that discussed here: it looks like a tangled spiderweb of causative (catalytic) relationships because it is a tangled spiderweb: a network.


The next word we need to question is "switch". The research reported in Teran, et al.¹ clearly shows that a pool of phosphorylated Dpr will tend to promote (or, perhaps, enhance) Wnt Signaling, while a pool of unphosphorylated Dpr will do the oppositte. But is all the Dpr in the pool usually one or the other? Perhaps, but it's equally plausible that it maintains a balance in vivo, with enough of both types to have an intermediate effect. Note that this effect need not be linear, with respect to the concentration ratios (or absolute concentration of either). Only after appropriate research can we be sure that this enzyme actually acts like a switch, rather than a knob, capable of assuming any value of concentration ratios (within some plausible range). And if it can act like a knob, further research would be needed before we can be sure that it acts in a linear fashion (if it does).

Even if Dpr does "switch" quickly, from one stat to another, at least some of the inputs to the network (not just "cascade") that includes it are analog, as are (ultimately) the influences that contribute to its phosphorylation level and the ultimate output: the combined catalytic effects of both species of Dpr.

It's important to note that such analog networks can have a number of metastable "digital" states, while other parts of the network vary continuously based on external and internal factors.

Rather than continue here, I'll refer you to my earlier discussion, as well as "Quantitative analysis ofsignaling networks" by Herbert M. Sauroa and Boris N. Kholodenko, a peer-reviewed paper, from which let me quote:

Whether evolution has fashioned digital devices on a large scale is still a matter of debate, but considering that our current technological mind set is digital, we may be inadvertently focusing too much attention on the possibility of a digitally driven biological cell. As a result, we may overlook the fact that not so long ago, analog was a critical aspect of man-made computational devices in the form of analog computers ([ref]). Given the flexibility of analog and its inherent ability to condense data handling to a far greater degree than its digital counterpart,¹ we think that the argument that evolution has selected largely for analog-based signaling networks is a strong one. Clearly, there are cases when on/off decision making is crucial, for example, the most obvious being cell division ([refs]) and bacterial sporulation ([refs]) being another example. Boolean-based digital circuits may be employed by gene regulatory networks; however, even here the case is not certain ([refs]).

1 Note that it requires a single transistor to store one bit in a digital device, whereas ifthe transistor were used as an analog storage device it could represent a value to an arbitrary high number base.

The probable analog nature of the signaling network, then, as called out in the title of this post, allows us a much better appreciation of the importance of these two papers: they are important advances in our understanding of how the various enzymes in (and out of) the cell interact, but the assumption that there is a signaling "cascade", and the assumption that two states automatically constitute a "switch" tend to limit our thoughts. It would be preferable to think of an analog signaling network, with the various enzymes and other molecules being studied as vertices in the network: transistors in an analog transistor network as described in How Smart is the Cell? Part I: Enzymes as an Analog Computer.

Finally, I must point out that knocking out an enzyme to determine its effect is about like taking a hammer to one of the transistors in the above-mentioned analog transistor network. It doesn't really tell us its "function", just helps identify a few critical things that go wrong when it's gone.

Appendices: Much as my thoughts ramble, I decided these needed to be "out-of-line" for purposes of readability. (This may seem ironic...)

Appendix 1. "Both phosphorylation and dephosphorylation are extremely "downhill" processes energetically."

This is because the phosphate group is added by taking it off an ATP molecule, and it is removed by dropping it into the pool of inorganic phosphate (P_i).

The total energy of the third phosphate of ATP relative to the P_i pool is typically around 0.57-0.62 electron volts (eV),⁶ reaching levels of 0.725 eV in the active heart muscle.⁷

ATP + H₂O ===> ADP + P_i = ~58 KJoules/mol = 0.6 eV(/molecule)

When it comes to phosphorylating an enzyme, the total energy can be divided between the two reactions, depending on the energy of hydrolysis of the specific phosphate bond in question, which will vary depending on what electrical charges are nearby. Since some amino acid residues carry a positive charge, and some carry a negative charge, you can see that by tweaking the amino acid sequence of the protein evolution can adjust the energy of hydrolysis of any protein phosphate to optimize its performance.

ATP + E ===> ADP + EP = x eV

EP + H₂O ===> E + P_i = (0.6 - x) eV

Once an enzyme is phosphorylated, its catalytic effect changes, however no energy is transferred from the catalyst to the substrates or products. Thus, phosphorylation is like setting a switch (for one molecule) or turning a knob (for a population of molecules), it affects the rate of other "downhill" reactions but the catalyst isn't "used up" or modified in any way by that reaction. (Of course, there will be other reactions that do modify the concentrations, but they are separate from the catalyzed reaction.)

Appendix 2. "[...] information, [...] unlike energy, is not subject to considerations of entropy [...]"

Technically there is a relationship between information and entropy, but it is totally different from that of energy and not really relevant to this discussion.

Links: These are not in any particular order, and not all called out in the text. Use the back key if you came here by clicking a footnote.

1. Dpr Acts as a Molecular Switch, Inhibiting Wnt Signaling when Unphosphorylated, but Promoting Wnt Signaling when Phosphorylated by Casein Kinase Iδ/ε

2. Modulation of the β-Catenin Signaling Pathway by the Dishevelled-Associated Protein Hipk1

3. Wnt/β-catenin signaling: new (and old) players and new insights

4. Post-translational palmitoylation and glycosylation of Wnt-5a are necessary for its signalling

5. Quantitative analysis ofsignaling networks

6. The Contents of Adenine Nucleotides, Phosphagens and some Glycolytic Intermediates in Resting Muscles from Vertebrates and Invertebrates

7. Roles of the creatine kinase system and myoglobin in maintaining energetic state in the working heart

8. Coupled positive and negative feedback circuits form an essential building block of cellular signaling pathways