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Topic: The design of robustness
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Art
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posted 05. June 2002 19:16
Jame's comments in several threads have gotten me thinking about the idea of robustness. I may be wrong, but I suspect that a commonly-held idea is that robustness (in protein structure, metabolic pathways, development, and the like) is seen as something that goes beyond what we currently know about the workings of living things - that some sort of new principle, perhaps ID-derived, is needed to fully understand the phenomenon. I would agree, but perhaps not in ways that most would think. The problem is in illustrating my ideas. I think I have come up with such a picture, which I am going to inflict on this group.
The picture takes on the form of a research project or proposal of a sort. Specifically, consider a five-step metabolic pathway
A->B->C->D->E->F
the individual steps of which are catalyzed by enzymes 1-5, respectively (e.g., A->B is catalyzed by enzyme 1, etc.). The project (or challenge ![[Smile]](smile.gif) ) is this - how does one design the system so that the production of end product - F - is unaffected by changes in the properties of the enzymes involved? How many parameters must we define for each enzyme, and how conditional (if at all) must each of these be? How do these considerations constrain the nature of the enzymes themselves? (I am sure others can think of other things to add, and I would hope that they will.)
Now, I will admit that this may be too much to put into a post (or ten) in this discussion, but I am hopeful that some others here can weigh in with ideas (that I will, admittedly, contrast with my own take on the subject). At the very least, we should come to a greater appreciation for the subtleties of the subject, and of different ways to attack the problem.
[ 05 June 2002, 22:22: Message edited by: Art ]
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James A. Barham
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posted 07. June 2002 13:22
Art:
I am very much looking forward to reading your further thoughts on how to achieve the sort of robust metabolic pathway---meaning one that is globally stable and relatively insensitive to changes in lower-level component parts---that you describe in your post.
As I understand it, there are only two ways to explain robustness naturally---via nonlinearities and via quantum coherence. But in the context of biology, even nonlinearities pose a problem, because they must be achieved either by imposing a set of boundary conditions or constraints, or else they must self-organize somehow.
Now, Darwinians see nothing wrong with appealing to boundary conditions as a way of establishing nonlinear dynamical robustness (as human engineers do in complex electrical circuitry, connectionist networks, "subsumption architecture" robotics, etc.), because they believe the theory of natural selection can provide a broader explanatory framework within which the prior existence of such boundary conditions makes sense. But I believe that this form of explanation is illusory, because in fact you already need the functional integrity of the system to be in place before "selection" can occur. And you cannot possibly hope to explain the prior existence of such complex boundary conditions by appealing to "chance."
It does no good to protest (as Darwinians always do) that they are not appealing to "chance" alone, because the selection mechanism freezes new attainments in place, so the mechanism works over time like a ratchet. In this way each step is supposedly small enough to allow "chance" to work. But this doesn't really change anything, because it still ignores the fact that each previous step of the "ratchet" is already a fully functionally integrated system. If a theory cannot explain any single step in a series of steps, it obviously cannot explain the overall series. The theory of natural selection is just a massive exercise in question begging, at least so far as the functional organization of life is concerned. So, in the final analysis, "boundary conditions" are not the answer. This concept presupposes a mechanistic view of life which already excludes naturalistic explanation, since only external intelligent design can account for machine-like boundary conditions.
If this reasoning is correct, then the problem you pose comes down to explaining the nonlinear dynamics of robust cellular function within a broader self-organizational explanatory framework---one which I believe can only ultimately be provided by extending quantum field theory to the living state (but, of course, I could be wrong).
At any rate, I will be very curious to see what your alternative proposal is.
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Janitor@MIT
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posted 07. June 2002 14:46
Food for thought:
Sengupta, Anirvan, Marko Djordjevic, & Boris I. Shraiman, “Specificity and robustness in transcription control networks,” PNAS, v.99, no.4, Feb. 19, 2002.
(Provides a workable definition of “robustness,” a model, and tests.)
Goh, K.-I., B. Khang, & D. Kim, “Universal Behavior of Load Distribution in Scale-Free Networks,” Phys. Rev. Lett., v.87, no.27, 31 December 2001.
(Scale-free or “small-world” networks are the object of active research to characterize their basic properties and emergence so the conclusions may prove to be “model-dependent.” Just a caveat.)
Since I’m interested in the application of engineering design theory to biology I’ve compiled a considerable volume of published research on the subject. These were near the top of my stack. Got lots more if anyone’s interested…
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James A. Barham
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posted 07. June 2002 17:17
Janitor:
Thanks much for the references. I am very interested in any research having to do with robustness and stability.
One question. You seem to equate the terms "scale free" and "small world." Isn't "scale free" a far more general term? I associate "small world" with the "6 degrees of separation" concept, or with investigations into the topology of networks, more generally. But isn't "scale free" related to the much broader idea of "universality," which in turn is related to such things as self-similarity, the renormalization group formalism, emergence, and order parameters (all under the general umbrella of "effective field theories")?
My understanding of the relationships among these various concepts is rudimentary at best, so any light you could throw on all of this would be much appreciated. I gather that some of these ideas are purely formal, some relate to nonlinear dynamics generally, and some relate mainly to condensed-matter physics, but it is all a little vague in my mind.
BTW, have you seen the new book by Albert-Laszlo Barabasi (Linked: The New Science of Networks, Perseus, 2002)? If so, I'd be curious to hear your response to it.
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Art
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posted 08. June 2002 09:11
Hi James,
Thanks for the response to my "invitation".You said: quote:
As I understand it, there are only two ways to explain robustness naturally---via nonlinearities and via quantum coherence. But in the context of biology, even nonlinearities pose a problem, because they must be achieved either by imposing a set of boundary conditions or constraints, or else they must self-organize somehow.
I am curious as to what you mean by "nonlinearities". Is it possible to use my pathway to illustrate the idea?
Thanks for your help.
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James A. Barham
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posted 09. June 2002 22:08
Art:
My grasp of nonlinearity is rudimentary (to put it mildly), but my understanding of its importance for coherence, robustness, and stability is based on the writings of a spectrum of authors---biologists, physicists, and mathematicians (F.Eugene Yates, Robert Rosen, Alwyn C. Scott, Bruce J. West, Rene Thom, Ian Stewart, to name a few)---who seem to be in agreement that it is absolutely fundamental.
Here is a helpful passage by West:
"The strength of the nonlinear terms in the field equations is such as to exactly balance the effect of linear dispersion. This delicate balance of linear dispersion driving the component waves apart and nonlinear interactions pulling them together provides for coherent structures such as solitons and generally inhibits the tendency of systems to separate into their incoherent linear components. Thus the physical effects of linear dispersion and nonlinear interactions can reach a dynamic balance to form a soliton . . . This dynamic balance is one kind of mechanism that is intrinsically nonlinear and could not have been predicted from any extrapolation of the linear world view." (Bruce J. West, An Essay on the Importance of Being Nonlinear, Springer Verlag, 1985, p. 80)
There is so much to say about this, I don't know where to begin. First, and perhaps most important, if we define "determinism" as a perfect one-to-one mapping of causes (initial states) onto effects (final states), with time invariance (effects can as well be mapped backwards onto causes), then clearly a world with true, intrinsic, ontological nonlinearity (as opposed to one in which we require nonlinear equations as an epistemological stopgap) is obviously not deterministic. Note that on this interpretation of nonlinearity, determinism is not defeated merely by indeterminacy, but by the very concept of robustness or stability itself. The existence of attractors which are insensitive to perturbations at the microlevel puts paid to the grand Laplacian clockwork vision inspired by the fantastic success of Newtonian mechanics.
Newtonian mechanics, while fantastically successful, nevertheless has been known for more than 100 years to be inherently limited. One sort of limitation was discovered by Planck, Bohr, et al., but another and equally important sort of inherent limitation was discovered by Henri Poincaré (see J. Barron-Green, Poincaré and the Three Body Problem, American Mathematical Society, 1997; and F. Diacu & P. Holmes, Celestial Encounters: The Origins of Chaos and Stability, Princeton UP, 1996). Poincaré proved (in the strict sense) that the equations describing the dynamics of a system as simple as even three bodies are non-integrable, meaning that they have no exact analytical solution, even though the trajectories can be proven to lie somewhere on various sorts of topological surfaces ("attractors"), hence the name "qualitative dynamics" for the area of physics that Poincaré pioneered (which has only come into flower over the past thirty years or so, thanks to computers).
So that is one very important aspect of nonlinearity---it forces us to rethink the traditional picture of a deterministic universe, with no inherent arrow of time and fully reducible to particle collisions at the lowest level, that we inherited from Newtonian mechanics. And it is crucial to realize that determinism is not defeated by "indeterminism" (which is no help for understanding teleology), but by coherence and stability. So nonlinearity frees us from determinism and reductionism and ushers in a metaphysics of ontological emergence. But there are other aspects of nonlinearity which are still problematic.
For one thing, while it is clear that nonlinearity is necessary for teleology (life and mind), it is equally clear that it is not sufficient. In inorganic systems, nonlinear phenomena arise through cooperative forces arising from special boundary conditions (examples include candle flames, hurricanes, tsunamis, the Red Spot of Jupiter, Bénard cells, the Belousov-Zhabotinsky reaction, etc.). Furthermore, they are ultimately the result of energy minimization. But living things are self-organizing, so obviously it is not possible to invoke "boundary conditions" in the same sense. And living things cannot be explained in terms of energy minimization alone. In biology, we must posit the existence of a type of physics that is somehow intrinsic and self-organizing, while yet transcending sheer energy minimization. This is a very tall order.
I assume that your metabolic pathway could indeed be modeled using nonlinear dynamics. In a sense, nonlinear dynamics is, I think, only a more concrete, more physical approach to the more abstract set of ideas known as cybernetics or control-theory (i.e., concepts like positive and negative feedback), which is, of course, the favored approach of contemporary molecular biology. But even the advance from control theory to nonlinear dynamics is not going to solve the problem of how to interpret the self-organizing aspect, all by itself. (At least, I don't think it will. I could well be wrong about this.)
Another problem has to do with the very nature of scientific explanation. If the universe cannot be fully modeled by means of the sorts of integrable equations with analytic solutions that have been so powerful in the past, and have created most of our modern understanding of the world and mastery of nature (because many processes in nature do approximate linear functions), then that raises the question whether a "science" of the rest of nature (the non-integrable part) is possible at all. Poincaré introduced a new approach via his qualitative or topological dynamics, which has in recent years begun to reap real empirical fruits. Quantum field theory represents another, perhaps complementary approach. And Stephen Wolfram and others are claiming that cellular automata provide yet another approach that may contain the key to unlocking the remaining secrets of nature. So, different approaches to science are indeed possible. And, of course, as always in science, the proof will be in the pudding.
However, I am betting that some combination of the quantum and nonlinear dynamical approaches is the correct way to go. I am repelled by any attempt to confound computation as a tool with computation as a fundamental principle of the universe itself, because computation implies an intelligence for whom structure has meaning (i.e., without meaning there can be no "information," "symbols," "representations," or "computation"). Therefore, Wolfram's approach, I am convinced, leads to idealism and solipsism. I feel it must be a dead end. But that is not to say there are not serious obstacles in the way of the other two approaches, as well.
The basic problem is that teleology goes beyond mere coherence all the way to a spontaneous goal-seeking (conation) together with an intrinsic ability to adjust means to ends (cognition), and we have no idea how to explain such phenomena in physical terms. That is precisely the challenge facing us. This challenge may be expressed by noting that life circumvents the Second Law of Thermodynamics in the same way that birds circumvent the law of gravity. So, what we require is a biological equivalent of the concept of "lift."
Nonlinearity alone is clearly not the biological equivalent of lift, but at least nonlinearity does buy us coherence and disproportionate response. So, if we can only ground it successfully in self-organization, as opposed to boundary conditions, then maybe we can eventually see a way to wring true teleology (conation + cognition) out of it. As I have said many times on Brainstorms, it seems to me that the necessary physical grounding of nonlinearity in self-organization can only be accomplished, in turn, via quantum field theory.
Even then, all of this still leaves open the nature of the ultimate relationship between mathematics and reality. In the end, there really is a sort of hermeneutic circle in which the universe gives rise to life and mind, life and mind give rise to humanity, language, and science, and science gives rise to theories that mirror the inmost workings of the universe. As Plotinus wrote, "Never did eye see the sun unless it had first become sunlike" (Enneads, I.6.9).
It will be a great accomplishment to understand one day (if we ever do) how the selfsame universe gave rise to suns, and also eyes with which to see them. But, obviously, even understanding finally how the eye became sunlike is not going to explain in and of itself the ultimate ground of either the sun or the eye---that is, the reason for the very principles that give rise to the emergent hierarchy. Or the reason why there is something rather than nothing.
There is only one thing I feel absolutely sure of. The theory of natural selection---i.e., "molecules just happened to fall together into cells, cells just happened to acquire rhodopsin proteins which gave them a competitive advantage, then rhodopsin proteins evolved into various photosystems, eyespots, and eventually camera eyes (independently in vertebrate and invertebrate lineages), and all of this was just [in the immortal words of the late Stephen Jay Gould] a 'glorious accident'"---as I say, the one thing I am sure of is that selection theory---or rather the fact that so many people once complacently and unreflectingly accepted selection theory as an adequate explanation for why the eye is sunlike---will one day come to be viewed as the most colossal embarrassment in the history of science.
[ 10 June 2002, 07:18: Message edited by: James A. Barham ]
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James A. Barham
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posted 14. June 2002 11:08
After doing just a bit of research on robust networks (BTW, thanks again for the Sengupta reference, Janitor), I think that this will be a very fruitful area for stimulating ISCID discussion.
The robust networks phenomenon is important, because it re-poses all of the classical questions involving teleology, selection theory, and intrinsic dynamics at a new level that seems closer to biological reality than the traditional mechanical analogy. A robust network is also a "machine" in some sense---it is purposefully organized, and in the case of inanimate networks, obviously designed---but it contains crucial informational and self-organizing characteristics that take us beyond classical machines like mousetraps, steam engines, automobiles, and so forth.
There is a lot to say about robust networks, and my grasp of the concepts involved is rudimentary in any case, but let me just make the following quick points for now.
First, appearances are deceiving, larger philosophical claims are contradictory, and each of the three positions---Darwinism, ID, and neo-vitalism---could plausibly claim support from recent work on robust networks. Sorting all of this out will be a large task.
The Darwinian position---being a "universal acid"---finds support in whatever scientific advance occurs, of course. So, it is not surprising that advances in the understanding of robust networks will be widely interpreted as a victory for Darwinism. However, one recent paper seems to me to be of very great interest to ID theorists. Although the authors pay the usual lip service to Darwinism, everything they say militates strongly against the random mutation/selective retention viewpoint, and in favor of the design-theoretic viewpoint.
The paper is J.M. Carlson and John Doyle, "Complexity and Robustness," PNAS, 2002, 99: 2538--2545.
In this paper, Carlson & Doyle show convincingly that biological systems and highly automated, human-designed systems (e.g., power grids, the Web, the Boeing 777) share a multitude of characteristics that both provide for robustness and differentiate them from inanimate systems. The most interesting claim they make, from my point of view, is that functionally robust systems are inherently heterogeneous, self-dissimilar (i.e., not fractal), and also fragile in the sense of being vulnerable to infrequent perturbations (a price one must pay for robustness for common perturbations). They call their theory "Highly Optimized Tolerance" (HOT) and they show that it fits the data from the study of a multitude of natural and artificial systems much better than the better-known "self-organized criticality" (SOC) theory of Per Bak and others (which posits homogenous, self-similar elements). Carlson & Doyle conclude that "HOT illustrates that design leads to fundamental characteristics missed by theories that ignore design" (p. 2545).
Where does HOT leave my neo-vitalist position? Well, it certainly adds an interesting perspective, but I still am not persuaded that biosystems operate by the same intrinsic principles as manmade robust networks. First of all, there is a good deal of evidence for self-similarity in biosystems in addition to heterogeneity. For example, in the same colloquium with the Carlson & Doyle paper, there is another paper by G.B. West et al. ("Allometric scaling of metabolic rate from molecules and mitochondria to cells and animals," PNAS, 2002, 99: 2473--2478), which demonstrates equally convincingly that power-law scaling (a so-called "universality" characteristic) does indeed obtain at all levels of living systems, spanning "an astounding 27 orders of magnitude in mass from a single molecule to the largest mammals. We know of no precedent for this observation nor any previous theory that could explain it. Its universal character clearly reflects something fundamental about the general principles of biological design and function." (p. 2473).
Now, how can Carlson & Doyle and West et al. both be right? Well, I think they can both be right if we keep in mind that living things are neither natural non-teleological systems like Bak's sandpiles (with homogeneity, power scaling, and universality) nor manmade teleological systems like Boeing 777s (with heterogeneity and self-dissimilarity). Rather, living things are NATURAL TELEOLOGICAL systems. So, it is not surprising that they should show characteristics of both self-organized criticality AND highly optimized tolerance. But, of course, the question is, How?
Here is another approach to robust networks that I like a lot, one that is less abstract, closer to the empirical phenomena, and that brings out the heart of the problem, as I see it.
The late biochemist and preeminent metabolic control theorist Paul Srere wrote a brief review piece in Trends in Biochemical Sciences shortly before his death ("Complexities of Metabolic Regulation," TIBS, 1994, 19: 519--520).
In this piece, Srere strongly criticizes the biochemistry textbooks used in colleges all across the country for perpetuating a highly oversimplified and demonstrably false view of metabolic regulation. I am tempted to quote the whole paper (it is only two pages long), but let me try to hit just the highlights:
"All the recent biochemical texts have chosen to practically ignore two important areas concerning metabolism . . . These are distributive metabolic control and supramolecular organization of the enzymes in a single metabolic sequence . . .
"The concept of distributive control causes us to rethink the classical metabolic precepts. As an example, for many years it was accepted that glycolysis was regulated at one step---6-phosphofructokinase (PFK) . . . However, a number of observations do not agree with this view. It has been demonstrated that overproduction of PFK or any one glycolytic enzyme in yeast has no effect on glycolytic flux. . . . A similar analysis can be made for other metabolic sequences . . .
[He goes on to discuss other empirical studies showing the incredible robustness of metabolic networks to a variety of challenges:]
"The analyses indicated that all the enzymes . . . had to be less than 25% rate controlling under any condition . . .
[Finally, he sums up as follows:]
"It should not come as a shock that we cannot ascribe control of a pathway at a single invariant point under all metabolic conditions, since the ratios of enzyme activities of a metabolic path are remarkably constant between cell types. This idea is supported by the observation that, when a particular metabolic path is stimulated or repressed, all the enzymes of that path are coordinately increased or decreased . . . A further reason for discarding the single-enzyme rate-limiting paradigm is that these ideas are obtained using dilute aqueous media at extremely low enzyme concentrations. In vivo the concentration of macromolecules is exceedingly high, giving the cytoplasm a gel-like consistency, where the protein-protein interactions are different from those found in dilute solution. Such interactions may well alter enzyme behavior and control characteristics. The interdependence of all metabolic reactions can, at least in part, be demonstrated by the observation that deletion of a single enzyme of a metabolic pathway causes pleiotropic changes in a variety of enzyme amounts in pathways not directly related to the one being studied . . .
"The simplistic ideas of metabolic control, which are now promulgated by textbooks, will continue to hamper our understanding of this important area of cell activity."
I submit that the main difference between the manmade HOT networks described by Carlson & Doyle and the living metabolic networks described by Srere has to do with the fact that the latter, in addition to being HOT networks, are at the same time SOC networks in the sense of Bak. That is, in a living organism, highly optimized tolerance arises somehow out of self-organized criticality. The result is that the matter out of which the living system is built is spontaneously and intrinsically striving to maintain the robust, global, dynamically stable state.
Think of it this way. One of Bak's sandpiles is clearly carried to its global, dynamically stable state by its own intrinsic dynamics. This makes it extremely robust within a given environment, but it obviously lacks the HOT form of flexibility and robustness under different conditions. There is simply no global dynamical state that the sandpile prefers over any other. It is just minimizing energy---that is all.
Now, living things are clearly carried to their global, dynamically stable state by their own intrinsic dynamics, as well. However, that state is actively preferred by the organism, which gives it HOT-like properties. While manmade networks have HOT properties, too, the latter do not arise out of the intrinsic dynamics of the matter the networks are made of, but rather are due to the fact that we have imposed a set of constraints on that matter. It is the constraints imposed by us that give rise to the global dynamically stable state of the network that WE view as a goal state. The matter the system is made out of is indifferent to this state.
The Web itself does not care whether it crashes. Nor does a Boeing 777---any more than a sandpile cares whether it is washed away by the sea. We care. And we care because we are organisms, made out of matter that spontaneously strives to achieve its goals in a flexible and intelligent way.
Thus, the intrinsic dynamics of the matter a system is made out of is the crucial thing. This means that manmade HOT networks, no matter how cleverly designed, will never be as robust as living networks. It also means that living things must operate according to fundamentally different principles of their own. It is these principles that we must now set out to discover.
[ 14 June 2002, 11:14: Message edited by: James A. Barham ]
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Art
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posted 15. June 2002 15:18
Returning to my hypothetical metabolic pathway and the matter of robustness. Recall that I was interested in ways to “design” robustness into the following:
A->B->C->D->E->F
What I want to do is examine some of the properties of the simplest scenario. For this, I need to add two things: first, that the concentration of A is constant, and second, that F is degraded, exported, or otherwise removed from the system (or cell, or whatever). This removal would constitute a terminal step of the pathway.
Now, we can assign arbitrary rate constants for each of these steps: A->B being “governed” by a first order rate constant k1, B->C by k2, C->D k3, D->E k4, E->F k5, and breakdown of F k6. Given this simplest of scenarios, we can model the steady state situation as follows (I will only show two steps, and leave the rest for others to fill in at their leisure):
d[B]/dt = k1[A] - k2[B]
At the steady state, d[B]/dt = 0, thus [B] = k1[A]/k2
d[C]/dt = k2[B] - k3[C]
d[C]/dt = 0, therefore [C] = k2[B]/k3 = k1[A]/k3
Etc. for all the steps, until we reach the final form:
[F] = k1[A]/k6
This result is remarkable in the context of this discussion, because it turns out that the very simplest model for the pathway is in fact highly robust! The steady-state concentration of [F] is completely unaffected by changes in any of the intermediate steps in the pathway. Which brings me to one point I wanted to make - robustness is not necessarily an indication of complicatedness; here, the simplest manifestation of the pathway is highly robust. Indeed, we need to “engineer” in features to reduce the robustness, not to attain the state. For me personally, I refer to examples like this to remind myself that simple models and ideas can have unexpected and dramatic consequences or outcomes. Of course, this is not to say that all robustness in living things is equally simple; rather, the lesson is that we do not necessarily have to invoke impressive new laws of nature to attain the state. (I’d add in passing that this simple model explains the seemingly paradoxical result described by Srere and related to us by James. Moreover, this simple model is one that so-called metabolic engineers need to be keenly aware of, for reasons that are hopefully obvious.)
Now we can turn to a question that I suspect is on the minds of many who are reading this - what does this have to say about evolution? Specifically, evolution in living things likely involves, not just the origination of robustness, but moving between different robust states. Given the result above, I think it is interesting to ask if this inherent simplicity in some ways limits the potential for evolutionary change to alternative robust, or even non-robust, states. I’ll return to the question later and give the board my own views in the context of this model, because there are one or more simple but profound statements that this simple model helps to illustrate. But I’d like for now to invite comments and variations of the model by others here.
[ 15 June 2002, 21:18: Message edited by: Art ]
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Janitor@MIT
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posted 16. June 2002 09:50
Art: Please define “robust.”
Also, it appears that you’ve designed (!) a “robust” model by arbitrarily limiting the number of parameters and setting them to constants. (Oh, if only the real world worked that way!)
James Barham, my apologies for not responding promptly. You’ll find an excellent background and review of recent research, that also touches upon some of the questions you have, in Reka Zsuzsanna Albert’s doctoral thesis: “Statistical Mechanics of Complex Networks.” (PDF online.)
I actually saw Barabasi’s book at a local bookstore just two weeks ago, but I resisted the temptation to buy it because the research in the field is moving so fast. The evolutionary dynamics of "small-world" networks are extremely interesting as they bear a very strong resemblance to the evolutionary dynamics (“Search-in-Power-Law”) of genomic architectures, which appear also to be [cross my fingers] “scale invariant,” sensu stricto, conserving degree distributions, diameters, correlation lengths, and cluster coefficients. (See e.g. Jeong, H., B. Tombor, R. Albert, Z.N. Oltvai, & A.-L. Barabasi, “The large-scale organization of metabolic networks,” PDF online or contact Barabasi alb@nd.edu) David Fell has been working in the field of metabolic control analysis and engineering for some years and has recently pronounced on the subject in: David A. Fell & Andreas Wagner, “The small world of metabolism,” Nature Biotechnology, v.18, November 2000, http://biotech.nature.com.
When I read Eric Davidson’s tour de force (2001. Genomic Regulatory Systems: Development and Evolution. Academic Press. San Diego, CA.) I was very disappointed that, other than the really cool-sounding cyberlingo biologists have adopted, a clear picture of the “system,” “network,” or “architecture” did not emerge from Davidson’s research. Developmental genetics and metabolics are struggling for a synthesis, and one promising direction appears to be in the class of small-world networks.
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Art
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posted 18. June 2002 22:52
Hi Janitor,
You aksed: quote:
Art: Please define “robust.”
Uummmm....
In the case of the example I gave, robust simply means that the end result - production of F - is not much affected by variation in the steps that give rise to F.
quote:
Also, it appears that you’ve designed (!) a “robust” model by arbitrarily limiting the number of parameters and setting them to constants. (Oh, if only the real world worked that way!)
Actually, my model is a pretty fair representation of metabolic pathways. We can make it more realistic, but that will only reinforce my basic point. (Note that this simple model does a decent job of explaining Srere's "paradox".)
Which is that the simplest case here is the most robust, and the state requires no invocations of unknown laws or unusual paradigms. The simplest of chemical kinetics takes us to the most robust state.
Is anyone interested in the questions I posed?
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James A. Barham
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posted 19. June 2002 07:58
Janitor:
Thanks very much for the additional references. I am tracking them down eagerly. I really appreciate your help in this area, which I am only now (belatedly) becoming acquainted with.
Art:
I am very much interested in your postings. Unfortunately, I do not have the mathematical background to follow your logic in detail. Could I just ask you one thing:
In qualitative language, what is the ultimate source of the robustness you describe? Is it the boundary conditions of the system which have to posited separately to make the overall network stable, or is it somehow intrinsic to the dynamics of the system itself? If the latter, can you explain a little bit about how that is possible? Your equations seem to be linear, and I was unaware that any system describable by linear equations could have this dynamical property intrinsically.
BTW, I agree with your definition of robustness as dynamical stability or relative insensitivity to perturbations in individual component steps or reactions. For Janitor and others interested in this question, I highly recommend Robert W. Batterman's new book, "The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence" (Oxford UP, 2002). He deals with robustness and stability in the context of effective field theory and condensed-matter physics, but I believe that this is the correct framework for thinking about biological robustness, as well.
[ 19 June 2002, 08:00: Message edited by: James A. Barham ]
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Janitor@MIT
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posted 19. June 2002 13:04
You’re more than welcome, James Barham and thank you.
Art, you’re model is not a “fair representation of metabolic pathways.” It’s not even a fair representation of the simplest models of simple metabolic pathways I’m familiar with. (See e.g., the six-step path modeled here: http://gepasi.dbs.aber.ac.uk/pedro/btk98.html).
Biologists should be very careful about adopting “intelligent design” concepts, such as “robustness.” Colloquially, “robustness” is often confused with the concept of stability. They are subtly related (along with optimization), but are not the same.
Robust design entered engineering theory (the only theory of “intelligent design” I know of) in the 1920’s as the result of the application of feedback amplification in telephony. Actually the roots of the concept can be traced back to the pioneering analyses of feedback instabilities by (independently) George Airy and James Clerk Maxwell in the mid-19th century. (See also the concurrent design theory of signal-to-noise “robustness” of the Taguchi Method.)
Where is the feedback in your model?
The only reason I have to believe that the simple linear path you’ve modeled is stable (not “robust”) is because you’ve implied that it is. This is contrary to virtually everything I’ve ever read: linear systems of cause-effect are often highly sensitive to and inherently unstable (often exponentially) to variations in the relevant parameters. Simplification in fact compounds the problem of inherent instability. This is a fundamental result of late 20th century computer engineering: a stable system (not “robust”) must satisfy a minimal size/scaling principle. As far as I know, Erwin Schrodinger was the first to apply the principle to biology with his prescient comments on a “codescript” in his influential “What Is Life?” (See William Bialek, “Stability and noise in biochemical switches,” arXive:cond-math/0005235 15 May 2000.)
You haven’t solved any “paradox,” you’ve only emphasized it.
I would suggest that your model might be made biologically relevant and subject to a robust design analysis if we turn it into an example of feedback inhibition, e.g.
In fact the definition of “robustness” provided by Sengupta, et al (above) is the one I’ve found most often in the biology literature. (See also Wagner, Andreas and Peter F. Stadler, “Viral RNA and Evolved Mutational Robustness,” Santa Fe Institute Working Papers).
And along similar lines: Little, John W., Donald P. Shepley & David W. Wert. 1999. “Robustness of a gene regulatory circuit,” The EMBO Journal, Vol. 18, No. 15, pp. 4299-4307; and references therein including: Savageau, Michael. 1971. “Parameter sensitivity as a criterion for evaluating and comparing the performance of biochemical systems,” Nature, 229, 542ff.; Barkai, N. & Leibler, S. 1997. “Robustness in simple biochemical networks,” Nature, 387, 913-917; Hartwell, L. 1997. “Theoretical biology—a robust view of biochemical pathways,” Nature, 387, 855ff.; Alon, U. et al. 1999. “Robustness in bacterial chemotaxis,” Nature, 397, 168-171.; Kirschner, M. & Gerhart, J. 1998. “Evolvability,” PNAS, 95, 8420-8427.; and in the field of metabolic control analysis and engineering: GOLDBETER, A. and KOSHLAND, D. E., Jr. (1981) "An amplified sensitivity arising from covalent modification in biological systems" Proc. Natl. Acad. Sci. USA 78, 6840—6844.; GOLDBETER, A. and KOSHLAND, D. E., Jr. (1982) "Sensitivity amplification in biochemical systems" Q. Rev. Biophys. 15, 555—591.; GOLDBETER, A. and KOSHLAND, D. E., Jr. (1984) "Ultrasensitivity in biochemical systems controlled by covalent modification. Interplay between zero-order and multisteps effects" J. Biol. Chem. 259, 14441--14447.; SZEDLACSEK, S. E., CÁRDENAS, M. L. and CORNISH-BOWDEN, A. 1992. "Response coefficients of interconvertible enzyme cascades towards effectors that act on one or both modifier enzymes" Eur. J. Biochem. 204, 807--813.; Cornish-Bowden, Athel & Cardenas, Maria Luz (eds.). 1990. Control of Metabolic Processes: Proceedings of a NATO Advanced Research Workshop on Control of Metabolic Processes. Plenum Press. NY. (Many of these are available online.)
A good basic review of the concept in engineering can be found in K.J. Astrom, “Model Uncertainty and Robust Control,” PDF online.
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James A. Barham
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posted 19. June 2002 18:44
Thanks so much for the additional references, Janitor!
I thought that you (and others) might be interested in a new anthology that I just got hold of today (if you don't know of it already).
Jan Walleczek (ed), Self-Organized Biological Dynamics and Nonlinear Control, Cambridge UP, 2000. It appears to have many articles highly relevant to our discussion of biological stability and coherence.
BTW, I'm afraid I have been using the terms "robustness" and "stability" interchangeably (and obviously, very informally) to mean any system whose macroscopic dynamical properties are relatively insensitive to perturbations at the micro-level. If this is a mistake, could you please tell me, in a nutshell, what the difference is? Thanks very much!
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Art
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posted 23. June 2002 10:01
Thanks to all for your responses.
James, you asked about the “source” of the robustness of the simple pathway I outlined. I guess I am stumped here - it just is. Is it because I set up the pathway so that there was a steady flux? Is the fact that it is a series of first-order reactions? Both of the above? I am not sure how to answer your question. The fact is that a simple linear pathway of first-order reactions, with a flow through the pathway, will inherently be highly robust. I think this says something about robustness. More importantly, it seems to me to introduce a new and interesting twist into the biological and evolutionary considerations.
Janitor, you said:
quote:
Art, you’re model is not a “fair representation of metabolic pathways.” It’s not even a fair representation of the simplest models of simple metabolic pathways I’m familiar with. (See e.g., the six-step path modeled here: http://gepasi.dbs.aber.ac.uk/pedro/btk98.html).
Well, we could join the legions of people who think their own particular representation is the best, but I’ll decline. My statement was merely to imply that all metabolic pathways must include flux and some sort of steady-state in their modeling. In this sense, my model, simple though it is, is a pretty general one, and must lie at the heart of other more specific elaborations (which is what the six-step path is). It is also closer to the work of others than you are giving me credit for (as the following indicates).
My simplified model, if amended to possess a branch similar to the one shown in the cited paper, leads one to exactly the same conclusions as Mendes and Kell, for very similar reasons. Which bolsters my own confidence in my very simple model. From the paper:
quote:
Comparing the parameter values of the "wild type" with our best solution we conclude that the optimal value of J5 was obtained by setting the concentration of all enzymes to their upper boundary value (1000) except E6 which was set to its lower boundary value (0.1). Interestingly this results in the finding that the only enzyme of the branch to P2 to have control over J8 is E6 (with a unity flux-control coefficient). However E1-E5 also control J8 but their flux-control coefficients cancel each other.
J5 is roughly equivalent to F in my model, and E6 is the enzyme that “creates” a branch at one of the intermediate steps. If we model the pathway of Mendes and Kell in the same simple terms that I have done, including a branch, we also get the same result that they do - only the branch-point enzyme affects the steady-state concentration of the end product (J8) of the branch itself. Subsequent (and preceding) enzymes are of little consequence. Moreover, the way that they optimize for J5 reflects the realities that are illustrated in my simple model. (I apologize for omitting the specifics here - I’d be glad to if needed. But it’ll be slow in coming, since reality is ever more intrusive.)
Of relevance to this thread is the last sentence I quoted - therein lies the answer to another of Janitor’s questions - “Where is the feedback in your model?”.
Janitor, you also said that “The only reason I have to believe that the simple linear path you’ve modeled is stable (not “robust”) is because you’ve implied that it is.” I disagree - I’ve implied nothing, but spelled out pretty plainly just how this linear pathway is highly robust. Anyone (even James J ) can fill in the algebraic steps and show how one can increase or decrease the constants that control each intermediate step in the pathway by many, many orders of magnitude without affecting the steady-state concentration of the end product. Nothing is implied, it’s all out there in the open. Nothing is asserted without justification. The fact is, the pathway I outlined is highly robust (perhaps even absurdly so). And I do mean robust in the sense that the stability derives largely from feedback control.
As far as the remark:
quote:
This is contrary to virtually everything I’ve ever read: linear systems of cause-effect are often highly sensitive to and inherently unstable (often exponentially) to variations in the relevant parameters. Simplification in fact compounds the problem of inherent instability. This is a fundamental result of late 20th century computer engineering: a stable system (not “robust”) must satisfy a minimal size/scaling principle.
I would suggest that my results in this thread indicate that concepts that arise from “20th century computer engineering” may not be particularly applicable to the working of living things.
Finally, to the comment:
quote:
Biologists should be very careful about adopting “intelligent design” concepts, such as “robustness.” Colloquially, “robustness” is often confused with the concept of stability. They are subtly related (along with optimization), but are not the same.
Since we are speaking about biological systems, I think we can settle for the colloquial usage. The issue in this thread is, as far as I am concerned, how robustness or stability can arise and change. Obviously, such a state can be modeled in very simple terms. What does this tell us about biology and evolution?
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James A. Barham
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posted 01. July 2002 10:06
I wanted to draw the attention of all those interested in the topic of this thread to the latest article on "highly optimized tolerance" network models by John Doyle and co-workers:
T. Zhou et al., "Mutation, Specialization, and Hypersensitivity in Highly Optimized Tolerance," PNAS, 2002, 99: 2049--2054.
This is an extremely interesting and important article, purporting to show the superiority of the authors' "HOT" model to the better-known "self-organized criticality" and "edge of chaos" models of Per Bak, Stuart Kauffman, and others. It contains a thorough and illuminating discussion of a great many issues in micro-macroevolution, rates of evolution, extinctions, etc.
From my personal point of view, the most interesting statement was the following:
"[The HOT model] further captures how intrinsic robust design tradeoffs interact with and constrain natural selection to generate highly ordered structure from randomness." (p. 2052)
It seems to me that the more successful such dynamical models are, the more "constrained' we are going to find natural selection, and the more the dynamics will come to be seen as explaining the "selection," not the other way around.
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