Writing
Ok... I now know how to make a cut. Sorry about that all! It just didn't occur to me that I could google for "livejournal cut howto". Duh.
I'm trying to write a book chapter at the moment; it's for the "New Encyclopedia of Neuroscience" for Elsevier press and the chapter is called "Computational and Theoretical Neuroscience: Axonal Pathfinding". The reason I'm writing about it now is because I'm finding it fricking impossible and I want to get it off my chest.
So: what's the deal? The "Instructions for authors" document states that "the (your) contribution should be prepared drawing on (your) broad knowledge of the available literature on the subject" and that "NO REFERENCES SHOULD BE MENTIONED IN THE TEXT". (Capitals theirs, not mine) Now... aside from the obvious problem that at this moment, I don't have a broad knowledge of the available literature on the subject (though admittedly, the available literature on the subject isn't all that large), this whole "no references" thing is really getting to me. The issue is that the "field" of "computational modeling of axon guidance" is essentially made up of a whole bunch of little bits, without all that much connecting them.
I'd really like to write an article which draws these little bits together into some sort of overview of the field, with aims, holes and challenges identified... the problem is that I have no idea what I'm talking about! Every word I write feels like a lie (or at the very least, something I'm unconfident about...) ... and without being able to reference, it makes it very difficult to talk about the "little bits" which currently make up the field.
My other difficulty is in expressing why anyone would care about modeling axonal pathfinding. (Bit of a worry, given that I'm doing my phd in it...). I think partially it's because I find the whole damn thing so complex, and I doubt my own ability to make any inroads into it (and because a lot of the modeling work out there is so CRAP). I have no picture in my head of what a "nice theoretical / modeling result" in axon guidance would be. I don't understand what the problems or challenges are to any deep level. So I don't know how to integrate the work that's been done into a coherent framework. (In short: my brain doesn't deal well with the mess that is biology... not that I'm trying to knock biology --- I just don't like ambiguity or enormous amounts of complexity...)
Anyway... I'm going to try to explain how I see the field working here, without caring whether I make gross mistakes, massive oversimplifications or tell downright furphies, in the hope that it makes writing the real document a bit easier. So... axon guidance: modeling thereof:
The development of the nervous system involves a series of (often simultaneously occurring) steps; after the embryo undergoes gastrulation, nerve cells begin to differentiate from their appropriate ecto- or mesodermal layer, then begin to migrate to their appropriate locations. Finally, these cells begin their morphological development, sending out processes known as "neurites" which ultimately form the axons and dendrites of the mature cells. Of course, for the nervous system to function correctly, these neurites need to find their appropriate targets: this search is known as the "wiring problem" of nervous system development.
Over the last decade or so, we've made some revolutionary advances in our understanding of how this wiring problem is solved. Sophisticated tissue culture and molecular biology techniques have allowed the identification and cloning of molecular species which exist in the embryonic environment and act as a kind of "roadmap" for the developing neurites. The task of reading this roadmap falls to the growth cone, a handlike structure which forms the tip of the developing neurite, and the site at which new cytoskeletal elements are incorporated into the developing axon. Growth cones play dual roles in axonal pathfinding. They can "move" semi-independently from the main neurite shaft, pushing through the embryonic environment ostensibly through an actin-mediated motility mechanism (though more recently it has also become apparent that microtubules extending from the main axon shaft have significant influence on growth cone movement, through their interactions with the actin cytoskeleton), and also acting as sensory apparati, probing the environment for guidance cues. The binding of guidance cue molecules to receptors on the surface of the growth cone trigger cascades of intracellular signals which modulate various aspects of (1) the actin machinery underlying growth cone motility (2) the microtubules which provide stability for the axon (3) the rate at which new cytoskeletal elements are incorporated into the axon shaft (4) the adhesion of the growth cone to the extracellular matrix: depending on the spatial pattern of this receptor binding, the axon can be made to extend in particular directions, to branch or to collapse.
However, while much experimental work aimed at characterising growth cone and axonal response to guidance cue molecules has been done, much of this work has focussed on a "one cue-one response" paradigm; molecules such as netrin were initially characterised as "attractive" guidance cues, as when they were originally discovered, they were found to induce axons to grow towards higher concentrations when presented in gradient form. Similarly, molecules such as the Slits and the Semaphorins were characterised as "repulsive". The inadequacy of this simple picture has become obvious with the observation that depending on the internal state of the growth cone (for example, the relative levels of the cyclic nucleotides), the receptors present on the growth cone's surface, the presence of other guidance molecules, the particular type of extracellular matrix molecules present and other such variables, growth cones and axons can be made to respond in many different ways to various cues --- for example, growth cones expressing the netrin receptor DCC typically exhibit an attractive response to netrin, however, neurons expressing both DCC and another netrin receptor, UNC-5, are repelled by netrin. It is known that guidance cues do not act independently in vivo: correct guidance is achieved by the concerted action of numerous guidance cues simultaneously (in the literature, this is referred to as "combinatorial control"). Thus, a bewildering complexity of possible responses presents itself. Thus, a great challenge in the field is to understand how growth cones and developing axons respond to multiple guidance cues presented simultaneously. This is obviously a daunting task. However, it is an important target to aim for: from a clinical perspective, many neurological defects are the result of failed neuronal pathfinding, so understanding how guidance cues are converted into directed growth is a crucial first step in the treatment and prevention of such conditions. Understanding neuronal guidance is also crucial to the development of therapies for nerve damage, such as regeneration of damaged spinal cord. From the point of view of pure science, we would also very much like to unravel the "rules" of axonal pathfinding in order to obtain a better picture of how complex systems such as organisms and their nervous systems are able to self-organise.
So: the current effort in the field of axon guidance is to dissect the signaling pathways underlying growth cone behaviour, and then to integrate the knowledge thus gained in order to predict the behaviour of neurons under varying conditions. This is where computational and mathematical modeling become indispensible: most extant models of the growth cone are described qualitatively (i.e. A activates B which suppresses C and D which in turn suppresses A... etc.)
Nup. I just don't get it after about here. I don't know why anyone should care. I certainly don't.
Where is the problem? I just can't seem to think clearly about this.
Ok. I'm going to skip that, and just get straight onto the modeling work. So: a summary of the modeling work that's been done (actually: that's another issue --- what exactly is "Modeling"? at the moment, I'm kind of including any sophisticated quantification):
(1) In axonal extension: Katz showed in 1984 that axonal extension can be modeled as a biased random walk, and that the growth cone acts to some degree independently of this extension process. This work was extended in the 90s by Buettner's group, who performed cross-correlation analysis between growth cone position and microtubule extension, finding that microtubule growth could lead to subsequent growth cone movement, and vice-versa, growth cone movement could lead to subsequent microtubule extension. These processes appear to act over different time-scales, with growth cone dynamics preceeding microtubule dynamics by ~2 minutes, and microtubule dynamics preceeding growth cone dynamics by ~20 seconds. A number of groups have studied transport of materials from the cell body to the tip of the growing neurites; the rate of this transport limits the rate at which the neurites can extend, in particular, if a neurite branches into two, then these compete for resources.
(2) In Growth Cone Motility: Several studies have looked into how actin polymerization, substrate adhesion, myosin contraction and actin depolymerization/diffusion can lead to motility --- most of this work has not been done on growth cones, but nonetheless applies. The coupling of the actin cytoskeleton to the microtubules complicates matters in growth cones, however.
(3) In axon guidance: Three themes here --- one is the development of mechanistic models coupling receptor binding to intracellular signals leading to directed growth cone motion; so little is known about the intracellular signalling networks in the growth cone that these approaches seem very premature.
The other themes deal with different classes of guidance --- guidance by chemical gradients, and guidance by so-called "guidepost cells". In the first case, the ability of an axon to be guided by a gradient of chemoattractant or chemorepellent is limited by the ability of the growth cone to detect the gradient and respond to it. This ties into two decades of research on chemotaxis in single-celled organisms, which demonstrate that unavoidable thermal fluctuations in receptor binding can swamp small chemical gradients, allowing the prediction of minimal gradient slopes to be made, assuming guidance of the growth cone occurs over a certain time-scale. Experimental evidence has shown that growth cones are incredibly sensitive, which suggests that they employ some sophisticated signal-processing in order increase their effective signal-to-noise ratio. Another open question is the role of "adaptational processes" in growth cone guidance --- experiment suggests that growth cones exposed to particular background concentrations of a chemical quickly desensitise to that chemical, then gradually resensitize. This kind of behaviour in other systems has been associated with an ability to adapt to increasing (or decreasing) levels of the molecule. However, there appear to be a number of issues with this interpretation in the case of growth cones.
Guidance by "guidepost cells" (or short-range guidance) has been analysed in terms of the dynamics of growth cone morphology. Growth cones are continually extending thin processes (filopodia) which probe the GC's immediate environment, and have been shown to act as sensors. Again, Buettner's group has looked at how different parameters governing the dynamics of growth cone morphology effect the rate / probability with which the growth cone encounters a local guidance cue. This has led them to suggest that the growth cone tunes parameters governing filopodial dynamics in order to sense effectively in different conditions.
(4) Finally, an area in which more modeling work could be profitable is in studying how patterns of guidance cues are set up. This ties in with several decades of work on the establishment of morphogen gradients; many, many hypotheses have been put forward for how particular patterns are established, from simple diffusion from a point source, to diffusion with binding, degradation and active transport. Variation in the sizes of embryos also has some non-trivial implications --- for example, as an embryo grows larger, growth cones typically remain the same size, which implies that their sensitivity to chemical gradients remains constant. If wiring a particular portion of the nervous system relied on guidance over long-range by a chemical gradient, this property may not be robust to changes in the size of the embryo.
The final section I wanted to talk about in the article concerns future challenges and directions to take; what would the ultimate model growth cone look like? What would we need to achieve? Where are the holes? One significant challenge is the lack of quantitative experimental data --- most experiments simply ask whether a growth cone turns towards or away from a chemical when presented in a gradient, and whether pharmacological interference with the growth cone (for instance, through the blocking of calcium induced calcium release, microtubule dynamics, the addition of constitutively active components or blocking of local protein synthesis etc. etc.) modulates the growth cone's response. This kind of work is useful in identifying important components in the underlying signaling pathways, but does not provide very strong constraints when it comes to modeling the pathways mathematically. However, the ideal experiments (i.e. measuring concentrations, interacting kinetics etc. between various important chemical species) are technically very difficult, if not impossible: what kinds of modeling can be done under the current conditions? Ultimately, the hope is that by modeling specific hypothetical pathways, we are able to identify weaknesses in those approaches, and thus predict the existence of new pathways and interactions.
Righto. That's about it for now. Bit of a brain dump. I'm just getting overwhelmed, and a bit down about the amount of stuff I just don't understand. I'd like to do *good* science, but I can't see how to go about it... everything is so wooly and vague...
I'm trying to write a book chapter at the moment; it's for the "New Encyclopedia of Neuroscience" for Elsevier press and the chapter is called "Computational and Theoretical Neuroscience: Axonal Pathfinding". The reason I'm writing about it now is because I'm finding it fricking impossible and I want to get it off my chest.
So: what's the deal? The "Instructions for authors" document states that "the (your) contribution should be prepared drawing on (your) broad knowledge of the available literature on the subject" and that "NO REFERENCES SHOULD BE MENTIONED IN THE TEXT". (Capitals theirs, not mine) Now... aside from the obvious problem that at this moment, I don't have a broad knowledge of the available literature on the subject (though admittedly, the available literature on the subject isn't all that large), this whole "no references" thing is really getting to me. The issue is that the "field" of "computational modeling of axon guidance" is essentially made up of a whole bunch of little bits, without all that much connecting them.
I'd really like to write an article which draws these little bits together into some sort of overview of the field, with aims, holes and challenges identified... the problem is that I have no idea what I'm talking about! Every word I write feels like a lie (or at the very least, something I'm unconfident about...) ... and without being able to reference, it makes it very difficult to talk about the "little bits" which currently make up the field.
My other difficulty is in expressing why anyone would care about modeling axonal pathfinding. (Bit of a worry, given that I'm doing my phd in it...). I think partially it's because I find the whole damn thing so complex, and I doubt my own ability to make any inroads into it (and because a lot of the modeling work out there is so CRAP). I have no picture in my head of what a "nice theoretical / modeling result" in axon guidance would be. I don't understand what the problems or challenges are to any deep level. So I don't know how to integrate the work that's been done into a coherent framework. (In short: my brain doesn't deal well with the mess that is biology... not that I'm trying to knock biology --- I just don't like ambiguity or enormous amounts of complexity...)
Anyway... I'm going to try to explain how I see the field working here, without caring whether I make gross mistakes, massive oversimplifications or tell downright furphies, in the hope that it makes writing the real document a bit easier. So... axon guidance: modeling thereof:
The development of the nervous system involves a series of (often simultaneously occurring) steps; after the embryo undergoes gastrulation, nerve cells begin to differentiate from their appropriate ecto- or mesodermal layer, then begin to migrate to their appropriate locations. Finally, these cells begin their morphological development, sending out processes known as "neurites" which ultimately form the axons and dendrites of the mature cells. Of course, for the nervous system to function correctly, these neurites need to find their appropriate targets: this search is known as the "wiring problem" of nervous system development.
Over the last decade or so, we've made some revolutionary advances in our understanding of how this wiring problem is solved. Sophisticated tissue culture and molecular biology techniques have allowed the identification and cloning of molecular species which exist in the embryonic environment and act as a kind of "roadmap" for the developing neurites. The task of reading this roadmap falls to the growth cone, a handlike structure which forms the tip of the developing neurite, and the site at which new cytoskeletal elements are incorporated into the developing axon. Growth cones play dual roles in axonal pathfinding. They can "move" semi-independently from the main neurite shaft, pushing through the embryonic environment ostensibly through an actin-mediated motility mechanism (though more recently it has also become apparent that microtubules extending from the main axon shaft have significant influence on growth cone movement, through their interactions with the actin cytoskeleton), and also acting as sensory apparati, probing the environment for guidance cues. The binding of guidance cue molecules to receptors on the surface of the growth cone trigger cascades of intracellular signals which modulate various aspects of (1) the actin machinery underlying growth cone motility (2) the microtubules which provide stability for the axon (3) the rate at which new cytoskeletal elements are incorporated into the axon shaft (4) the adhesion of the growth cone to the extracellular matrix: depending on the spatial pattern of this receptor binding, the axon can be made to extend in particular directions, to branch or to collapse.
However, while much experimental work aimed at characterising growth cone and axonal response to guidance cue molecules has been done, much of this work has focussed on a "one cue-one response" paradigm; molecules such as netrin were initially characterised as "attractive" guidance cues, as when they were originally discovered, they were found to induce axons to grow towards higher concentrations when presented in gradient form. Similarly, molecules such as the Slits and the Semaphorins were characterised as "repulsive". The inadequacy of this simple picture has become obvious with the observation that depending on the internal state of the growth cone (for example, the relative levels of the cyclic nucleotides), the receptors present on the growth cone's surface, the presence of other guidance molecules, the particular type of extracellular matrix molecules present and other such variables, growth cones and axons can be made to respond in many different ways to various cues --- for example, growth cones expressing the netrin receptor DCC typically exhibit an attractive response to netrin, however, neurons expressing both DCC and another netrin receptor, UNC-5, are repelled by netrin. It is known that guidance cues do not act independently in vivo: correct guidance is achieved by the concerted action of numerous guidance cues simultaneously (in the literature, this is referred to as "combinatorial control"). Thus, a bewildering complexity of possible responses presents itself. Thus, a great challenge in the field is to understand how growth cones and developing axons respond to multiple guidance cues presented simultaneously. This is obviously a daunting task. However, it is an important target to aim for: from a clinical perspective, many neurological defects are the result of failed neuronal pathfinding, so understanding how guidance cues are converted into directed growth is a crucial first step in the treatment and prevention of such conditions. Understanding neuronal guidance is also crucial to the development of therapies for nerve damage, such as regeneration of damaged spinal cord. From the point of view of pure science, we would also very much like to unravel the "rules" of axonal pathfinding in order to obtain a better picture of how complex systems such as organisms and their nervous systems are able to self-organise.
So: the current effort in the field of axon guidance is to dissect the signaling pathways underlying growth cone behaviour, and then to integrate the knowledge thus gained in order to predict the behaviour of neurons under varying conditions. This is where computational and mathematical modeling become indispensible: most extant models of the growth cone are described qualitatively (i.e. A activates B which suppresses C and D which in turn suppresses A... etc.)
Nup. I just don't get it after about here. I don't know why anyone should care. I certainly don't.
Where is the problem? I just can't seem to think clearly about this.
Ok. I'm going to skip that, and just get straight onto the modeling work. So: a summary of the modeling work that's been done (actually: that's another issue --- what exactly is "Modeling"? at the moment, I'm kind of including any sophisticated quantification):
(1) In axonal extension: Katz showed in 1984 that axonal extension can be modeled as a biased random walk, and that the growth cone acts to some degree independently of this extension process. This work was extended in the 90s by Buettner's group, who performed cross-correlation analysis between growth cone position and microtubule extension, finding that microtubule growth could lead to subsequent growth cone movement, and vice-versa, growth cone movement could lead to subsequent microtubule extension. These processes appear to act over different time-scales, with growth cone dynamics preceeding microtubule dynamics by ~2 minutes, and microtubule dynamics preceeding growth cone dynamics by ~20 seconds. A number of groups have studied transport of materials from the cell body to the tip of the growing neurites; the rate of this transport limits the rate at which the neurites can extend, in particular, if a neurite branches into two, then these compete for resources.
(2) In Growth Cone Motility: Several studies have looked into how actin polymerization, substrate adhesion, myosin contraction and actin depolymerization/diffusion can lead to motility --- most of this work has not been done on growth cones, but nonetheless applies. The coupling of the actin cytoskeleton to the microtubules complicates matters in growth cones, however.
(3) In axon guidance: Three themes here --- one is the development of mechanistic models coupling receptor binding to intracellular signals leading to directed growth cone motion; so little is known about the intracellular signalling networks in the growth cone that these approaches seem very premature.
The other themes deal with different classes of guidance --- guidance by chemical gradients, and guidance by so-called "guidepost cells". In the first case, the ability of an axon to be guided by a gradient of chemoattractant or chemorepellent is limited by the ability of the growth cone to detect the gradient and respond to it. This ties into two decades of research on chemotaxis in single-celled organisms, which demonstrate that unavoidable thermal fluctuations in receptor binding can swamp small chemical gradients, allowing the prediction of minimal gradient slopes to be made, assuming guidance of the growth cone occurs over a certain time-scale. Experimental evidence has shown that growth cones are incredibly sensitive, which suggests that they employ some sophisticated signal-processing in order increase their effective signal-to-noise ratio. Another open question is the role of "adaptational processes" in growth cone guidance --- experiment suggests that growth cones exposed to particular background concentrations of a chemical quickly desensitise to that chemical, then gradually resensitize. This kind of behaviour in other systems has been associated with an ability to adapt to increasing (or decreasing) levels of the molecule. However, there appear to be a number of issues with this interpretation in the case of growth cones.
Guidance by "guidepost cells" (or short-range guidance) has been analysed in terms of the dynamics of growth cone morphology. Growth cones are continually extending thin processes (filopodia) which probe the GC's immediate environment, and have been shown to act as sensors. Again, Buettner's group has looked at how different parameters governing the dynamics of growth cone morphology effect the rate / probability with which the growth cone encounters a local guidance cue. This has led them to suggest that the growth cone tunes parameters governing filopodial dynamics in order to sense effectively in different conditions.
(4) Finally, an area in which more modeling work could be profitable is in studying how patterns of guidance cues are set up. This ties in with several decades of work on the establishment of morphogen gradients; many, many hypotheses have been put forward for how particular patterns are established, from simple diffusion from a point source, to diffusion with binding, degradation and active transport. Variation in the sizes of embryos also has some non-trivial implications --- for example, as an embryo grows larger, growth cones typically remain the same size, which implies that their sensitivity to chemical gradients remains constant. If wiring a particular portion of the nervous system relied on guidance over long-range by a chemical gradient, this property may not be robust to changes in the size of the embryo.
The final section I wanted to talk about in the article concerns future challenges and directions to take; what would the ultimate model growth cone look like? What would we need to achieve? Where are the holes? One significant challenge is the lack of quantitative experimental data --- most experiments simply ask whether a growth cone turns towards or away from a chemical when presented in a gradient, and whether pharmacological interference with the growth cone (for instance, through the blocking of calcium induced calcium release, microtubule dynamics, the addition of constitutively active components or blocking of local protein synthesis etc. etc.) modulates the growth cone's response. This kind of work is useful in identifying important components in the underlying signaling pathways, but does not provide very strong constraints when it comes to modeling the pathways mathematically. However, the ideal experiments (i.e. measuring concentrations, interacting kinetics etc. between various important chemical species) are technically very difficult, if not impossible: what kinds of modeling can be done under the current conditions? Ultimately, the hope is that by modeling specific hypothetical pathways, we are able to identify weaknesses in those approaches, and thus predict the existence of new pathways and interactions.
Righto. That's about it for now. Bit of a brain dump. I'm just getting overwhelmed, and a bit down about the amount of stuff I just don't understand. I'd like to do *good* science, but I can't see how to go about it... everything is so wooly and vague...