On the coupled evolution of protein folding and binding

Michael Manhart and Alexandre V Morozov uploaded on bioRxiv their latest manuscript titled:

Protein folding and binding can emerge as evolutionary spandrels through structural coupling
http://dx.doi.org/10.1101/008250

where they show the consequences of evolutionary coupling of folding, aggregation and binding. Their study is based on computational simulations under different regimes that correlate to the presence of different selective pressures (including some combinations that cannot be studied in vivo).

I find the paper particularly interesting, both because the consequences of binding and folding-upon-binding are often difficult to study in vivo, and secondly (but more importantly) because the authors follow an evolutionary-oriented perspective where the success of a given conditions is determined by its fitness. This said, as an experimental biochemist with little (not to say no) mathematical and physical background, I found some bits of the paper difficult to follow, and some ‘wrong‘ *. However, aware of my conceptual limits, I dropped a line to the authors explaining my doubts. They kindly replied on bioRxiv, and our correspondence is reported below. The aim is to:

1) show how little math I understand (or how little I understand any math)
2) suggest that at times the need for accuracy of physical studies can lack the experimental-oriented detail that helps experimentalists ‘get the point’
3) remind the advantages of pre-print publication (although, admittedly, this time I, and not the authors, am the one that benefited from it)

The manuscript, already exciting at the first read, is now more so after the comments exchange with the authors. If only this was standard procedure in scientific publishing!

Enjoy the read

 

* by ‘wrong’ I mean that I I found it puzzling from an experimental point of view until clarified by the authors, not that there is actually anything wrong with the manuscript

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My comment

This manuscript touches on two topics I find particularly interesting:
1. Functional and ‘structural’ evolution
2. Induced folding upon binding

I was thus very interested in reading it, although as an experimental biochemist I don’t have the expertise to understand the math and physics behind it. So I apologise in advance for any basic mistake I might make later on…

There are a couple of things that didn’t convince me entirely. At times for the way things are phrased, in other occasions it is the conceptual approach. I suspect often I might have misunderstood things. I’ll try to list them below in the hope they might help the authors.

1. The authors say that (page 2):
“…structural coupling of folding and binding (the fact that folding is required for function) implies evolutionary coupling of folding stability and binding strength. Thus selection acting directly on only one of these traits may produce apparent, indirect selection for the other.”
Almost any protein will require folding to occur for its function to be possible, so the statement that an underlying selective pressure for either properties is (might be) present during evolution applies to any ‘function’ a protein might have. (Let’s for the moment ignore intrinsic disorder as the authors’ point applies to ‘standard’ proteins as well). It is thus not clear to me why (protein-protein) binding represents a special case in this sense. Indeed, enzymes also bind to their substrates (and the contribution of binding is to some extent included in the measure of catalytic efficiency) and the relationship between evolution, folding/stability and catalysis has been addressed before.

2. For a similar reason, I don’t understand why the authors say (page 4):
‘ The latter case also includes directed evolution experiments where only function is artificially selected for in vitro.’
when discussing the effects of misfolding. Indeed, it is impossible to experimentally test ‘only function’ as even in vitro systems will require folding to happen, and any protein variant needs to satisfy both kinetic (folding) and thermodynamic stability requirements to be active.

3. One of the most exciting part of the Results section is the ability to select for one property only. Although this might not be possible in vivo (see comments above), it is an interesting process to study in silico. However, it is not clear to me if the selection was done by ‘switching ON or OFF’ selected parameters in the equation or also by removing the binding partner from the simulation. In particular for the ‘folding only’ section (page 7), it’d be nice to see how the model protein behaves if the binding partner is excluded by the simulation (although binding doesn’t give any fitness advantage, interactions might influence the shape of the energy landscape for folding). In this sense it is interesting that most of the discussion on the ‘folding only’ experiment indeed deals with the presence, concentration and affinity of the binding partner.

4. At the end of page 7, the authors mention an implication of their analysis:
‘[the stability of a protein] may be restored not only through stabilizing mutations, but also by developing a novel binding interface.’

Although I’m not entirely convinced by the validity of the ‘novel interfaces’ argument (one might think that evolving interfaces that stick around in a cell’s cytoplasm might lead to aggregation and insolubility), this concept is extremely interesting and observable in vivo. Two cases that come to mind are the stability-driven generation of protein oligomers (see 1 and 2) and locally-destabilised cold adapted proteins (see 3 and 4)

5. Finally, a comment on the way selection was performed in silico. Experimentally, the conditions selection is performed in can dominate the outcome of an evolution campaign. Both in vivo and in vitro, parameters as temperature, crowding, expression rate and, for example, concentration of the selectable marker (an antibiotic, or a binding partner) will have considerable effects on evolution in addition to the main properties a protein is selected for directly (binding) and indirectly (folding/stability). Are the in silico conditions used able to mimic any of these properties? Different concentration of the binding partner are mentioned in the manuscript, does the landscape change if different initial concentration are used during selection? Also, could temperature be implemented? It would be particular interesting (at least to me…) to know if and how the fitness landscape of an evolving protein binder changes if selection is performed at temperatures more or less close to the protein’s unfolding temperature.

I realise that my approach is purely experimental (and lacks the required background to understand calculations) but the authors seem to address an experimental audience as well, so I believe (and secretly hope!) I won’t be the only reader with this expertise.

 

Authors’ reply

Thanks, Pietro — we greatly appreciate you taking the time to read our manuscript and share your thoughts. Here are our responses:

1. We agree that the coupling of structure-function should apply to all functions, not just protein-protein binding. Our model is not specific to protein-protein binding — rather, it encompasses any binding interaction that the protein might participate in, including enzyme-substrate interactions you mention.

2. Any protein will indeed need to fold to perform its function (structural coupling), even in vitro. However, there is a key distinction between direct selection, when the trait in question (binding or folding) confers an intrinsic fitness advantage, and indirect selection, when the trait is only apparently selected due to its coupling with another trait that *is* under direct selection. The indirectly selected trait is a “spandrel” — Refs. 1, 2 give a more general discussion of indirect selection and spandrels. For example, suppose that when a protein misfolds it has no fitness cost beyond the cost of loss of function; that is, the fitness of an unbound but folded protein is the same as that of an unbound and unfolded protein. In this sense we say there is direct selection for binding only, since folding is only apparently (indirectly) selected due to its structural coupling with function. This case is realized for any proteins with essential function (not binding is fatal, e.g., for antibiotic resistance proteins), or for which misfolding is not toxic to the cell.

3. What we refer to as the “binding energy” Eb is actually the free energy of binding minus the chemical potential of the target. Thus, changes in target concentration are accounted for by changes to Eb in our model. In particular, removing the target entirely is equivalent to taking Eb >=0, as described on page 7 (last paragraph of section “Direct selection for folding only”) and in Fig. S4C. In this case, the protein simply acquires as many stabilizing mutations as it can since the binding interaction is gone.

Moreover, the case of direct selection for folding only has actually been experimentally investigated in Ref. 3. They engineered yeast to express YFP, which is presumably not under selection pressure for any function. But when they imposed destabilizing mutations, they do observe a fitness cost, implying that, even in the absence of direct selection for function, there is a selection pressure for folding due to the toxic effects of misfolded proteins. Thus both of our scenarios in which there is direct selection for only one trait (binding or folding) appear to be experimentally accessible.

4. We agree that this is a very interesting possibility, and thanks for the additional references. The experiment in Ref. 4, which also finds stability-driven generation of oligomers, suggests that these nonfunctional-but-stabilizing interactions can play an important role. It is certainly possible that these nonfunctional binding interfaces may have deleterious side-effects that we have not considered (but which we can include into our model).

5. Our model does include the effects of changes to target concentration (by changing Eb — see item #3 above). Our fitness landscape also explicitly includes temperature (or inverse temperature, beta; see Eqs. 1 and 3), so one can certainly investigate how temperature changes affect adaptation. In general, changing temperature will alter the folding/binding energetics (via their entropic terms) as well as rescale all energies in the model. However, realistic temperature changes should be rather small in Kelvins; for example, going from 30 C to 40 C is only a 3% change. Thus, the fitness landscape is rather insensitive to such effects.

We have not yet studied the effects of crowding or changing the expression rate of the protein itself; these are definitely interesting subjects for future work.

We hope this clarifies things; please let us know if you have further questions.

[1] Gould SJ, Lewontin RC (1979) The spandrels of San Marco and the Panglossian paradigm: A critique of the adaptationist programme. Proc R Soc Lond B 205:581–598.
[2] Pigliucci M, Kaplan J (2000) The fall and rise of Dr Pangloss: adaptationism and the Spandrels paper 20 years later. Trends Ecol Evol 15:66–77.
[3] Geiler-Samerotte KA et al. (2011) Misfolded proteins impose a dosage-dependent fitness cost and trigger a cytosolic unfolded protein response in yeast. Proc Natl Acad Sci USA 108:680–685.
[4] Bershtein S, Mu W, Shakhnovich EI (2012) Soluble oligomerization provides a beneficial fitness effect on destabilizing mutations. Proc Natl Acad Sci USA 109:4857–4862.

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Interested in discussing (good) Science Lover of coffee & good films. Ideas all & only my own.

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