December 26, 2011

The "nature" of materials: evolution and biomimetics

How do highly specialized biological materials evolve? An even better question is how the many different materials that make up animal bodies have come to coexist in the same organism. In this post, I will address the basics of these questions, although there is much to learn. This has applications to both basic research on biological systems and engineering methodology [1].

I will review the evolution of materials from three perspectives: the formation of biological composites in evolution, the phenomenon of layering in evolution, and the effects of evolving new structures on materials. Based on contemporary scientific findings, these are the most likely scientific mechanisms that account for the evolution of specialized materials and surfaces.

I. Biological composites
If you examine any segment of an animal body, you will find that it is composed of many different types of material. A human forearm, for example, is composed of fat layers, skeletal muscle, lamellar bone, and various other liquids and solids. This is a veritable kaleidoscope of tissue types, from a highly mineralized matrix (bone) to loosely-associated cell populations (fat layers). This diversity arises from the maintenance of two key mechanisms at the organ level: cell differentiation and tissue microenvironments. By contrast, biomechanical function acts to constrain the types of materials that can form through the forces experienced in functional contexts.

MRI image of human leg (left), highlighting the composite nature of the limb [2]. Material properties of trabecular bone (right) -- Voelcker Lab, Flinders University, Australia.

Cell differentiation. The differentiation of cells plays a role in the formation of these composites. In embryonic development, cell differentiation is partially determined its niche, or who its neighbors are. One possible organizing mechanism involves intercellular signaling molecules. This flexibility might allow for a wide range of materials to be formed in response to stresses and other cellular functions. It has been shown that cells can exhibit gene expression and protein production changes in response to the frictions induced by adhesion in vitro [3]. The stability of specific cell types might focus on the ability of these cells to absorb environmental stresses and fluctuations, which includes mechanical forces during movement and other interactions with the environment.

Tissue microenvironments. The aggregation of cells into tissues is also required for composite formation. More specifically, it is the co-existence of these cell populations in communities that allow for these composites to become well-integrated [4-6]. Cell populations residing in organs and other structures are organized in a manner analogous to an ecosystem, with energy exchange and substrate formation being prime candidates for the maintenance of homeostasis. Therefore, there is a hierarchical dependence leading from protein synthesis by individual cells to organismal context and back again that determine what materials will be formed in response to environmental and natural selective pressures.

Biomechanical function. While it seems counterintuitive, many structures that exist in nature may not be optimized for biomechanical function. Those that are “optimal” in terms of function tend to be highly specialized structures [7], and are also likely to be made from highly unique materials. Those structures that are less specialized in terms of function, or perform multiple functions simultaneously, should be made out of materials with a higher tribological diversity. Ultimately, these are testable predictions, but can also be inferred through examining the role of layering and the evolution of downstream [8] morphological structures.

II. Layering
In fields such as BioMEMS and bionanotechnology, a central issue is how very small functional devices can be fabricated. Generally, there are two methods for fabrication in very small devices: etching features into an existing surface, and deposition of materials onto an existing surface.

Examples of etching (left, courtesy London Centre for Nanotechnology) and deposition (right, courtesy ASME). Several research groups have used X-ray beams to etch patterns into very small surfaces (on the order of uM). Carbon nanotubes can be grown on a surface using a process called vapor deposition to modify very small surface function (on the order of uM).

Natural Microfabrication. In systems that are driven by natural processes, microfabrication cannot be top-down as engineering techniques generally are. A bottom-up strategy involves a mechanism called directed self-assembly [9]. In self-assembly, the configuration of a molecular system is biased by the available free energy, and the result is a highly-ordered system. The directed component comes into play in the form of "templates" or building blocks that guide further self-organization [10]. This is similar to the idea of building blocks in genetic algorithms, which appear to play a role in allowing for evolvable genotypes in silico.

One link between surfaces and materials fabricated through natural means and contemporary biomimetic engineering is the characterization of superhydrophobic surfaces. Hydrophobicity occurs when water molecules are repelled from a membrane rather than being absorbed by it. This is a feature characterized in nature by the lotus leaf, and is a design consideration in a range of BioMEMS applications.

Superhydrophobic surfaces are created by "dual-scale roughness". As the name implies, the surface exhibits a rough topology at two distinct spatial scales [11]. This further implies that hierarchical structures, with each component performing either a distinct or overlapping role, is required for evolving such surfaces. Surface stiffness is also a factor in guiding self-assembly [12], and may play the role of templates discussed in the previous section.

A picture characterizing the dual-scale roughness of a lotus leaf (courtesy, Soft Matter Interface group, Max Planck Institute).

Response to Function. While natural selection generally acts upon the entire organism, there may also be selective processes acting at multiple spatial scales within morphological structures. The structure of the Gecko's foot is an example of this. Like the lotus leaf, the Gecko's foot uses a hierarchical structure of grooves and cilia to maintain a highly specialized function [13-15]. This type of specialization is seen across plant and animal species as a diversity of biological attachment mechanisms.

While the "optimality of structure" idea presented as an outcome related to the biomechanical function of biological composites, is best exemplified by these systems, the existence of tribological diversity requires a different set of examples. To do this, we must turn to the evolution of a generalized trait, preferably one that plays a role in the biomechanics of an organism.

III. Evolution of the Jaw
In the evolution of the jaw, it appears that one change gives rise to another. The jaw evolved rather early in vertebrate phylogeny, constituting a group called Gnathostomes [16] and includes a diverse collection of forms. In mammals, the jaw allows for the mandible to articulate relative to the upper portion of the head in concert with muscle activity allows for chewing and active manipulation at the mouth opening. The range of motion in a jaw is variable, from the very large aperture of the hippopotamus to the more constrained mouth opening of a Primate.

Highly-stylized phylogenetic relationship between agnathans (e.g. lamprey, left) and gnathostomes (e.g. alligator snapping turtle and hippopotamus, center and right). Above phylogeny are the anatomical substrates of the jaw joint in non-eutherian Gnathostomes (left) and eutherian Gnathostomes (right).

Diagram showing the route from a joint (human temporomandibular joint, left) that can potentially transfer and/or dampen forces with regard to "downstream" morphological structures (right).

The evolution of a jaw has several indirect consequences, one of which is the introduction of large forces and stresses at the head. Much like in the case of vertebrate limbs, which are formed from highly durable and selective compliant [17] composite materials, the introduction of new functions requires a displacement of forces encountered during function.

A single evolutionary origin (monophyly). In the case of specialized and structurally specialized materials, such as specific instances of mineralized tissue, materials will arise once in a common ancestor and then be retained among members of a single clade. For example, vertebrates have tended to keep their skeletons made of either cartilage or hard bone. Major innovations in bone types tend to be restricted to specific clades. In cartilagenous fishes, the large-scale use of cartilage in the skeleton results in a single tissue type with the ability to endure a greater range of mechanical deformations. In mammals, hard bone comes in a number of forms (e.g. cortical, cancellous, and lamellar bone), each with their own physical properties and ability to endure and respond to various stresses and strains.

Multiple routes to refinement. The other option, observed in the origin of compounds such as chitin, is that a precursor material will evolve first and then be modified in various lineages to perform specific roles in a morphological system. For example, the basic chitin molecule may be adapted to a create a number of specialized materials in different lineages. Likewise, a basic set of molecules can be configured into different topologies through layering and/or other self-organized structures to produce highly-specialized materials. This is true of spider silk, which is used to build webs and other structures essential to their survival. Spider silk is a secreted protein that when spun into a silk strand has impressive mechanical properties. However, the performance characteristics of the resulting silk vary greatly in terms of both species of spider and gland of origin.

While the tribological profile of a given organisms is both determined by and a determiner of the evolution trajectory of a species, this can be approached from two perspectives. Reductionists will likely focus on the molecular building blocks of specific materials, answering questions such as: what are the signals that initiate the production of highly specific proteins and signaling molecules? Meanwhile, systems-level scientists will be more interested in the process of material synthesis during development, and answer questions such as: how is the self-assembly of highly specialized coordinated by generic processes? Both perspectives will be needed to fully appreciate the role specialized materials observed from across the diversity of the natural world and apply their artificial analogues to engineering technologies.

References and Notes
[1] Xia, F. and Jiang, L. (2008). Bio-inspired smart, multiscale interfacial materials. Advanced Materials, 20, 2842-2858.

[2] Courtesy: Imiaos.

[3] Mahoney, T.S. (2001). Cell adhesion regulates gene expression at translational checkpoints in human myeloid leukocytes. PNAS USA, 98(18), 10284–10289.

[4] Poole, C.A. (1997). Articular cartilage chondrons: form, function and failure. Journal of Anatomy, 191, 1-13.

[5] Jeanes, A.I. (2010). Cellular Microenvironment Influences the Ability of Mammary Epithelia to Undergo Cell Cycle. PLoS One, 6(3), e18144.

[6] Burdick, J.A. and Vunjak-Novakovic, G. (2009). Engineered Microenvironments for Controlled Stem Cell Differentiation. Tissue Engineering Part A, 15(2), 205-219.

[7] McNeill-Alexander, R. (1988). Elastic Mechanisms in Animal Movement. Cambridge University Press, Cambridge, UK.

[8] "downstream" in this case means structures whose change in function have an indirect effect on other structures.

[9] Romano, F. and Sciortino, F. (2011). Colloidal self-assembly: Patchy from the bottom up. Nature Materials 10, 171–173.

[10] Wang, D. and Mohwald, H. (2004). Template-directed colloidal self-assembly – the route to ‘top-down’ nanochemical engineering. Journal of Materials Chemistry, 14, 459-468.

[11] Shirtcliffe, N.J. (2004). Dual-scale roughness produces unusually water-repellent surfaces. Advanced Materials, 16, 1929-1932.

[12] Kima, T.W. and Bhushan, B. (2007). Effect of stiffness of multi-level hierarchical attachment system on adhesion enhancement. Ultramicroscopy, 107, 10-11, 902-912.

[13] Gorb, S. and Scherge, M. (2000). Biological microtribology: anisotropy in frictional forces of orthopteran attachment pads reflects the ultrastructure of a highly deformable material. Proceedings of the Royal Society of London B, 267, 1239-1244.

[14] Arzt, E., Gorb, S., and Spolenak, R. (2003). From micro to nano contacts in biological attachment devices. PNAS, 100(19), 10603-10606.

[15] I refer interested readers to a comprehensive online bibliography covering research on the biology and engineering of surface adhesion and attachment mechanisms (Gecko-centric) hosted by the Robotics and Intelligent Machines Lab at the University of California-Berkeley.

[16] Tree of Life, Gnathostomes.

[17] flexible and pliable in response to functional needs. For example, bone (e.g. mineralized tissue) can be both rigid and flexible, depending on how it is loaded and degree of hysteretic response. Material compliance is not directly related to plasticity, although there may be some interesting parallels between the two phenomena.

December 16, 2011

John Hodgeman Does the (Towel) Twist

I am currently reading the new John Hodgeman book "That is All". I also enjoyed his previous two books “Areas of my Expertise” and “More Information than you Require”. I’m not sure what it is about his style that I enjoy. Probably the wordiness mixed with wryness and absurdity. For example, on the book jacket, there is a quote from Neil Gaiman which reads: “If you see John Hodgeman on the road, kill him”. Great stuff. So do as the Buddhists do: transcend the illusion of John Hodgeman, and drink the Kool Aid if necessary (but not too much of it). Here is a little passage I wrote that is “Hodgeman-esque” in nature:

“Have you ever wondered what it would be like to mail a package to an enemy nation? John Hodgeman knows. He also knows how to custom write a series of non-sequiturs to be delivered orally at weddings, bar mitzvahs, and town council meetings (as the need arises -- he is versatile that way). Or better yet, what would it be like to mail a towel to the same rogue nation? In John Hodgeman’s house, there are thousands of unique-looking towels (mounted on the walls, not kept in the drawers, which would be silly) from all over the world, even enemy nations. While it might be a stretch to call him a "hoarder" (as seen on the television program 'Hoarders'), I can think of no other television program I would rather see him on. So the next time someone asks you 'can anthrax be delivered using a wet towel?' -- think of John Hodgeman”.

Figure 1. John Hodgeman (left) and the zombie muppet that dwells inside him (right). Don't believe me? Kill him and find out.

December 12, 2011

Google Doodle - Robert Noyce

Another interesting Google doodle, this time it is in honor of Robert Noyce (the honor being a posthumous birthday), the co-inventor of the integrated circuit.

December 9, 2011

Recent Adventures in Virtual Reality

About a month ago, I announced publication of the paper "Virtual reality in neuroscience research and therapy", published in Nature Neuroscience Reviews by myself and two other colleagues. The paper actually inspired the cover art for the December issue [1], which is now online. A closeup of the cover art (below) is entitled "Virtual Reality Reaches New Heights" by Kirsten Lee.

Also, I have been revisiting Second Life as a venue for scientific research [2]. I gave a lecture to the Embryo Physics course on 12/8 (Thursday). Topic: Cellular Reprogramming. Aside from some glitches [3] due to bandwidth issues, the talk went well. Pictures [4] from the venue can be seen below. The first picture is the meeting space, while the second is a picture of virtual horses (no kidding!) in a stable, and the third is a screenshot of my alternate avatar [5] presenting.

Notes and References:
[1] issue 12(12).

[2] this link is a photo-log of my forays into "virtual science".

[3] I did the entire lecture using text chat. Using a tablet PC, I was able to review the slides in the real world, and type (e.g. speak) to the slides being presented in Second Life.

[4] my avatar -- biodroid -- is in the foreground of the first two pictures.

[5] apparently, the "skins" of my robot were taking up too much bandwidth. I switched to a human form, but I still couldn't speak in-world.

December 3, 2011

Breakout Labs: another funding model

In a previous post, I discussed the potential of small-scale (e.g. peer-to-peer) science funding. One very recent development in alternative funding has been the founding of Breakout Labs, funded by PayPal founder Peter Theil.

Breakout Labs specializes in funding high-risk, early-stage science. These are project too risky for the major funding agencies (e.g. NIH, NSF) and too formative for venture capital investments. One area that could benefit from this model is so-called "entrepreneurial" science, which is not immediately profitable but may lead to innovations down the road. This is a "blind spot" in current science funding models. Due to the high degree of risk inherent in these early-stage projects, a funding model that provides support first and expects a rate of return on investment later is critical. If you are interested in applying for funding, see the Breakout Labs website for more details.

December 1, 2011

Tour of the OtherLab

While doing a recent search on up-and-coming technologies and cutting-edge science, I stumbled upon some YouTube videos of soft robots, and subsequently found the website of OtherLab. Other Lab is a collective of scientists and inventors involved in a number of projects, including proof-of-concept mechatronics that might be useful in building functionally adaptive and intelligent machines. In this post, I will review a number of videos from their YouTube channel.

Similar to a number of physiological pumping processes, here is a peristaltic pump design built by the lab. The process of peristalsis is the main actuation process in smooth and skeletal muscle systems. Peristalsis allows for symmetrical displacements of the muscular surface that occurs in waves and moves fluids through the body. The gastrointestinal tract and four- chambered heart are two examples of this. This pump design, optimized for modeling muscular output during joint flexion, is a key component of OtherLab's pneubotic machines.

This video shows the strategy OtherLab is using to design their soft robots and other creations. To fabricate motors, robots, and other mechanical things OtherLab specializes in, they use a CNC (computer numerical control) machine technique called "nesting". I have discussed rapid prototyping in earlier posts, particularly as it relates to building physical models. In this case, OtherLab is using a technique called nesting. In fabrication programming (as opposed to computational programming), nesting refers to the laying out of multiple parts, some entirely contained within others, on a single surface. This allows for dynamic nesting, which allows for the management of many part sizes and shapes simultaneously. A complex layer is then created, which is subsequently cut and incorporated into a technological design.

Pneubot stands for "pneumatic robot", or a robot that is actuated by pneumatic technology. A pneumatic technology involves the use of compressed air to drive mechanical motion. The compressed air can be moved through soft, balloon-like tubes, which allows for both rigidity (when filled) and flexibility (when decompressed or empty). In this video, an elephant-shaped pneubot is used to demonstrate the level of motor control allowed using this technology. The OtherLab is developing this technology in concert with Manu Prakash's lab at Stanford and DARPA's Maximum Mobility and Manipulation program.

In this video, a soft-bodied "crawler" robot moves across a flat tabletop and does the limbo, demonstrating the flexibility of gait and movement achievable with soft robot bodies. This "crawler" bot is another instance of the pneubot, just scaled down considerably. The idea of a soft-bodied robot is generally new, and can be applied to a number of medical and industrial problems.

Pneumatics are not only used to build selectively compliant skeletons for robots. They can also be used as braces and muscles, exhibiting rigidity when required. In this video, a knee brace is demonstrated that can force a human knee joint to full extension.

According to the embodiment school of thought, a robot's body and brain are dependent on each other, and interact accordingly. The soft robot examples do not come with an on-board brain. Fully autonomous control (or the robot's ability to control its own beahvior) is a "holy grail" of robotics, as it allows for both remote and on-the-fly operation that does not rely on human input. In this example, the OtherLab group demonstrates autonomous control in a model aircraft, which can maintain a circular heading without external commands.

This is another example of autonomous control, this time in the form of actuation. This form of autonomous actuation mimics tropic behaviors observed in many plants and animals. The mirror array shown in the picture/video moves with the sun (e.g. heliostatic), or in this case another light source that moves around the environment with respect to the stationary mirror array. This kind of actuation is currently used in very large solar panel arrays and solar furnaces.

November 25, 2011

Neutral networks: a critical review

Neutral networks are notoriously hard to map to a biological context. In this blog post, I will attempt to synthesize perspectives on neutral evolution and its consequences for evolving phenotypes using both computational and theoretical biology perspectives. I hope that this will synthesize the concept of neutral networks with existing theory on the evolutionary capacity of a given genotype and/or population, in addition to advancing some of my own thoughts on the subject. To do this, I will review past work on neutral networks, present formal definitions related to the neutral network concept, and then address overarching two hypotheses related to the concept of neutrality in evolutionary systems.

To fully appreciate what a neutral network represents, it is useful to revisit the role of neutrality in evolution. Motoo Kimura [1, also see Ohno’s contribution in 2, 3], as summarized in his book “Neutral Theory of Molecular Evolution“, was one of the first people to comprehensively explore the role of neutral mutations in evolution. Neutral mutations are those with no overall effect on the organism’s fitness or ability to survive and reproduce. According to the theory, most mutations occurring over the course of evolution have no effect with respect to fitness. One can think of this in terms of proportions. If 1000 mutations are observed in a made-up population of genotypes, 900 mutations will have no effect on fitness, while 70 will have a deleterious effect, and 30 will have a beneficial effect. The non-uniformity of this distribution means that while a few high fitness phenotypes could be produced at low frequencies, it is more likely that multiple solutions of lower but sufficient fitness is the more likely evolutionary outcome.

In parallel, neutral networks have been used by the evolutionary computation [4, 5], protein evolution [6], and complexity communities [7, 8] as a means to investigate evolvability. Inman Harvey has prepared a detailed resource summarizing the computational details of neutral networks [9] to which I refer interested readers. I have discussed evolvability before on this blog [10] and the way it has been defined in terms of phenotype. In this context, I am referring to the ability to evolve from one phenotypic state to another, which more explicitly involves changes in the genotype being both collectively and selectively expressed. In some cases, RNA phenotypes (which are technically phenotypes, but possess the discrete structure of a genotype) have been used to formalize the network structure as a hypercube.

In the last section, I defined fitness as the ability to “survive and reproduce”. This is a broadly construed ability, to be sure, but is related to how natural selection acts on a population. Let us make this more concrete. In the context of neutral networks, it is less helpful to think of natural selection as “survival of the fittest”, and more useful to consider the role of evolvability (e.g. the ability of a phenotype to adapt given a set of environmental conditions). We can use the example of word evolution in natural language to understand the role of possibilities (e.g. neutral pathways and evolvability) in evolution. The cartoon in Figure 1 shows an optimal path from one word (pinball) to another (partake). In this example, existing syntactical rules (e.g. what makes an English word such) constrain the number of possible pathways. Certain letter combinations are not allowed (which is analogous to fitness differences in biological neutral networks), and in this case only a few plausible pathways exist. Yet even in this simple example, there is room for innovation and thus the emergence of neutral pathways.

Figure 1. Example of word evolution in a strictly hierarchical directed graph (red branches highlight the "fittest" possible path).

Neutral neighborhoods consist of neighbors with the same fitness. Harvey and Thompson [11] originally defined this as a manifold in a fitness space. This manifold defines a collection of points that share the same fitness. This manifold is also structured with regard to connectivity (based on mutational distance) between genotypes. Populations do not move randomly through neutral networks. A majority of individuals congregate towards highly-connected parts of fitness space. This results in phenotypes that are robust to mutations. In one model [12], a given allele is selectively neutral if it is translated and transcribed without error. However, the noise inherent in the process of transcription and translation may provide an additional reason why neutral networks not only exist but are necessary for the evolution of complex phenotypes.

Evolvability requires a "unsupervised" component to get from one phenotype to another, as this adaptive mechanism is stochastic. To address this, Whitehead [12] tie neutrality into the "unsupervised" nature of evolving populations. Specifically, they remind us that mutations arise independently of their phenotypic consequences. To explain how genotypes can evolve to produce adaptive phenotypes in such a blinded context, they propose the "look-ahead" effect. The look-ahead effect takes advantage of neutrality, and the "diffuse" nature of phenotypes, where a small part of each phenotype is close to many genotypes. This is an example of how random, noisy phenotypes [see 13] can be guided towards adaptive ends. Whitehead [12] also suggests that a scenario can exist where traits can be acquired with a certain probability. This ability may be a distinct trait, and gets there in evolution through a mechanism called facultative adaptation. Combined with evolutionary processes, facultative adaptations may become so refined that genes can be acquired and/or co-opted over evolutionary time to encode a trait directly.

Part II: formalization

If we could reduce the concept of neutral networks to a simple dictum, it would be "the path less taken versus the paths mostly taken". The next section of this post walks through how configuration entropy (a tool from statistical physics) can be used to understand the role of neutral genotypes in an evolutionary system. The following mathematical formalisms are adapted from what can be found in any number of textbooks on evolutionary biology and physics, but will allow us to understand how neutral networks relate to fitness and ultimately selection.

Configuration entropy is an analytical tool from the study of Hamiltonian dynamics (classical mechanics) which quantifies how many different ways particles can be arranged given a basic set of constraints. This will serve to evaluate the number of plausible evolutionary pathways among all possible configurations within a population of genotypes (e.g. evolutionary context). In a system of n states occurring with probability Pn, configuration entropy is

In this equation, the values of Pn can range from ω-1 (minimal entropy) to 1.0 (maximum entropy). Excluding Boltzmann’s constant (-kB), the right hand side of the equation is also the basic form of Shannon entropy. Shannon entropy is widely used to characterize informational entropy, or the heterogeneity of an ensemble. While this might be more appropriate for our investigation, I will now reformulate the configuration entropy equation to include a constant value for fitness

Therefore, once the relative abundance of plausible networks in a given evolutionary context is known, the common formulation for absolute fitness (wabs) can be used to sample all genotypes for a given fitness value. The absolute fitness for a subset of genotypes (N) after a single generation can be defined as

In this formulation, a value for wabs above 1.0 is indicative of a more-fit phenotype. The absolute fitness can also be transformed into relative fitness, and then transformed again into a selection coefficient. The selection coefficient is an index with values closer to 1.0 representing increasingly stronger selection. It may be helpful to think of this process for determining equivalent pathways as a form of natural profiling. For any given fitness outcome, a proportion of neutral states will be occupied. For example, high fitness ensembles (profiles at a given fitness value) may result in fewer neutral paths taken, while lower fitness ensembles might result in a greater number of neutral paths taken. This strictly proportional relationship may be indicative of an optimization process. To better understand the role of optimization in evolution, the question we will now ask is: for a given fitness value (and, by extension, degree of selection), how many different paths through genotype space are taken?

Part III: two hypotheses

We can propose two hypotheses to understand the relationship between neutral pathways and a genomic diversity among individuals in a population. One is the linear hypothesis, which is predicted when an increase in the selection coefficient results in a corresponding decrease for all possible neutral networks. This relationship is linear, so that there are only one or a few neutral network topologies for very high selection coefficient values. An alternate scenario, the nonlinear hypothesis, occurs when a relatively large number of possible neutral network topologies exist for very high selection coefficient values. Likewise, the number of possible topologies for low selection coefficient values is saturated. This is demonstrated theoretically (using pseudo-data) in graphical form (Figure 2).

Figure 2. A graph showing functions associated with the linear and nonlinear hypotheses.

Table 1. A contingency table resulting from the relationship between the number of neutral pathways and selection coefficient value shown in Figure 2.

While Figure 2 shows the expected results for our two hypotheses, Table 1 takes this a step further and predicts what should be observed for particular selection coefficient/neutral pathway abundance combinations. It is predicted that for high degrees of selection, robustness plays a role in determining the neutrality of an evolutionary outcome, while the diversity of a population differentiate evolutionary responses given a common low degrees of selection.

To put these ideas about neutral networks in context, I recently gave a lecture in part based on a recent paper [14] that identified "rare" pathways from a differentiated cell to a pluripotent one. The idea behind this model was simple: it is known that there are a multitude of potential mechanisms (specific combinations of genes, epigenetic markers, etc) that mediate the differentiated cell-pluripotent cell transition [15], each contributing a different amount of variance. Some of these mechanisms explain more variance than do others. Therefore, a "rare" pathway is one that does not often result in a viable phenotype (or, rather, is responsible for the differentiated-pluripotent transition at a very low frequency). This is the other way in which neutral networks can act in evolution. A given genotype might harbor several distinct neutral networks, but each might only be responsible for large-scale phenotypic changes at a certain frequency.


[1] Kimura, M. (1983). The neutral theory of molecular evolution. Cambridge University Press, New York.

[2] Ohno S. 1970. Evolution by gene duplication. London: Allen and Unwin.

[3] Bershtein, S. and Tawfik, D.S. (2008). Ohno’s Model Revisited: Measuring the Frequency of Potentially Adaptive Mutations under Various Mutational Drifts. Molecular Biology and Evolution, 25(11), 2311–2318.

[4] Wagner, A. (2007). Robustness and evolvability in living systems. Princeton University Press, Princeton, NJ.

[5] Galvan-Lopez, E., Poli, R., Kattan, A., O’Neill, M., and Brabazon, A. (2011). Neutrality in evolutionary algorithms: what do we know? Evolving Systems, 2, 145–163.

[6] Maynard Smith, J., 1970. Natural selection and the concept of protein space. Nature 225, 563–564.

[7] Huynen, M.A., Stadler, P.F., AND Fontana, W.(1996). Smoothness within ruggedness: The role of neutrality in adaptation. PNAS, 93, 397-401.

[8] Van Nimwegen, E., Crutchfield, J.P., and Huynen, M. (1999). Neutral evolution of mutational robustness. PNAS, 96, 9716–9720.

[9] Harvey, I. (2009). Neutral Networks. Scholarpedia. Link.

[10] link 1, link 2.

[11] Harvey, I. and Thompson, A. (1996). Through the labyrinth evolution finds a way: a silicon ridge. In: T. Higuchi, M. Iwata, and W. Liu (eds) Proceedings of the first international conference on evolvable systems: from biology to hardware. Vol. 1259, pgs. 406–422. Springer, Berlin.

[12] Whitehead, D.J., Wilke, C.O., Vernazobres, D. and Bornberg-Bauer, E. (2008). The look-ahead effect of phenotypic mutations. Biology Direct, 3, 18.

[13] Borenstein, E., Meilijson, I., and Ruppin, E. (2006). The effect of phenotypic plasticity on evolution in multipeaked fitness landscapes. Journal of Evolutionary Biology, 19(5), 1555-1570.

[14] Artyomov, M.N. (2010). A Model for Genetic and Epigenetic Regulatory Networks Identifies Rare Pathways for Transcription Factor Induced Pluripotency. PLoS Computational Biology, 6(5), e1000785.