Supramolecular Assemblies
Introduction
The biological world is rich with ordered assemblies of molecules. Indeed, the assembly and function of supramolecular structures is central to modern biology. Examples span a range of length scales from protein dimers and multimers, to the extended polymers of actin and tubulin that constitute the cytoskeleton of the cell, to lipid bilayers which demarcate the cell and its compartments, to multi-component assemblies forming machines of extraordinary complexity. Often these biological assemblies consist not only of several components, but also of several types of materials, including proteins, nucleic acids, lipids, and polysaccharides, and a plethora of small molecules. The forces holding together these assemblies are equally diverse: van der Waals, electrostatic, and hydrophobic interactions, hydrogen bonds, all contribute to specific recognition between members of the assembly. Moreover, these supramolecular assemblies are typically dynamic, assembling and disassembling in response to cellular cues.
The challenges presented by biological supramolecular assemblies clearly go beyond any one traditional scientific discipline. The traditional biological tools of genetics and biochemistry have been invaluable in identifying the components of assemblies and some of their qualitative functions, but an integrated understanding of the dynamic function of assemblies, as well as the mechanisms and principles of self-assembly and disassembly is still largely lacking. Progress in this area is likely to require contributions from other disciplines, including physics, chemistry, mathematics, engineering, and information science. Here, we focus on the importance of physical theory, including simulations, model building, and quantitative analysis of data, in helping to meet the challenges outlined above. The contribution of theory is particularly critical in light of both the complexity of supramolecular structures, and the experimental difficulty of probing the dynamics of their function, assembly, and disassembly
Progress in understanding biological supramolecular assemblies will likely have an impact that extends far beyond biology. The modular design of biological structures, the processes and principles of complex self-assembly, and a deeper understanding of the biological materials themselves will impact materials science and technology on many fronts, and surely in ways that cannot yet be foreseen.
Past Successes
Here we describe some examples of the important role that physical theory has played in the study of supramolecular structures in biology, biological soft condensed matter physics, and biologically inspired materials.
Biology
The contributions made by scientists trained as physicists to the study of molecular assemblies are enormous. Classical examples include the studies of Max Delbruck (Nobel Prize in 1969) on viral infection pathways, of Francis Crick on DNA (Nobel prize with Jim Watson and Maurice Wilkins in 1962) and on icosahedral viruses, and of Aaron Klug (Nobel Prize in 1982) on the structure of important nucleic acid-protein complexes. Physicists have been essential in the initiation of the field of molecular biology and have continued to contribute to the underpinnings of its development. Here we list some specific examples of the success of soft-matter theoretical physics methods in a number of problems, ranging from simpler structures where analytical results can been obtained, to complex self-organized systems analyzed mainly by numerical approaches.
Statistics and Thermodynamics of DNA and Related Systems
Theoretical physics has contributed significantly to the understanding of the structure, mechanics, and thermodynamics of DNA. In accord with physics tradition, culture, and way of thinking, three basic models of DNA were formulated, and proved highly fruitful. These models are the elastic rod or elastic stripe model, the polyelectrolyte model, and the helix-coil model. It was pointed out by Max Delbruck in 1961 that long DNA filaments should have non-trivial topological properties, including entanglements and knot formation. It was also understood at about the same time that DNA replication, given the helical structure of DNA, also involves non-trivial topological problems of entanglements between the strands. The highly successful topological theory of the elastic rod/stripe (or worm-like chain) model of DNA allowed the understanding of fundamental properties of DNA such as linking number, twist, and writhe. These concepts, which are present now in many biology-oriented textbooks, are a result theoretical analysis coupled with further experimental studies. Elucidation of the properties of twist and writhe led directly to the discovery and understanding of plectonemic forms of DNA abundant under a variety of biological conditions. The next step in this direction was the theoretical analysis of knots in DNA. Quite spectacularly, this development turned out to follow the ideas of William Thomson (Lord Kelvin), and thus was a part of greater scientific flow of ideas. Theoretical study of knots in DNA proved useful both in finding more subtle properties of DNA, such as its diameter dependence on salt concentration, and in the discovery of a large new class of enzymes, called topological enzymes, including gyrase, topoI, and topoII. The study of these topological enzymes is now a growing field, which would not have been possible without the preceding theoretical work on DNA knots.
New achievements came to the field with single-molecule techniques and experiments. The most widely known are the force-extension experiments in which the worm-like chain model proved not only qualitatively correct, but also quantitatively accurate. Further experiments involving torque, stress, and several more complex molecules involved, once again, the exploitation of theoretical concepts such as linking, twist, and writhe, which proved invaluable in understanding the data.
The helix-coil model of DNA proved to be another important tool in understanding DNA properties. Although the study of temperature induced melting curves is now out of fashion, it yielded important insights which are now part of the foundation of our understanding of the DNA double helix, its stability, and the specificity of the related proteins. Combining the worm-like chain model with the helix-coil model allows one to look at a new class of experiments, in which DNA is unzipped by an external force. New exact theoretical models show that the force-extension curves during DNA unzipping are dominated by DNA heterogeneities over a large range of forces at room temperature leading to anomalous drift and diffusive phenomena. These observations motivated several experiments on DNA unzipping at constant force which showed jumps and plateaus at constant force, as predicted by the theory.
Electrostatics of Macro-ions in Aqueous Solution
The theory of the segregation of charged chains in the presence of polyions and their adsorption to oppositely charged surfaces or particles has explained the formation of important electrostatically bound biological complexes, including the assembly of DNA with polyamines into toroidal structures, and into chromosomes in the presence of histones (Figure 7). The role of electrostatics has been also established in the assembly of viral proteins and nucleic acids into viruses (Figure 8). These effects are important for the growth of other intracellular biopolymers as well, including actin filaments and microtubules. Relevant theoretical contributions in biology include the understanding of complexation among cationic and anionic polyions due to the release of mono-valent ions and the strong induced correlations among the macroions. These phenomena determine the degree of association of DNA and RNA with cationic molecules as a function of salt in the environment, which is essential for understanding the biological functions of these molecules. The theoretical understanding of the precipitation (complexation) and re-dissolution (de-complexation) transitions observed as the ionic strength of the solution increases are proving useful for understanding the assembly of more complex structures, both in controlled environments and in vivo.
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Figure 7. Complexes of DNA with multivalent cations at different concentrations of C+ and with proteins at different mono-valent salt concentrations. The electron micrograph is of Lambda bacteriophage genome condensed by multivalent particles [courtesy of J.-L. Sikorav, |
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Figure 8. Self-assembly of Tobacco Mosaic Virus from solution of capsid protein plus RNA molecules [H. Fraenkelconrat and R. C. Williams, Proc. Nat. Acad. Sci. 41, 690 (1955)]. |
Equilibrium shape of vesicles and red blood cells
Vesicles are closed structures whose surface is a bilayer membrane. The shape of a vesicle is determined by the fixed volume it encloses and minimization of the free energy of its membrane, which depends on membrane curvature and the relative area of inner and outer sheaths. The solution to this minimization problem has had major impacts. In particular, comparison between theory and experiment has shed light on the effect of disease on the elastic response of biological vesicles, which is manifested in abnormalities in their shape or topology. A red blood cell is basically a vesicle whose membrane is attached to a two-dimensional spectrin network with a non-zero shear modulus. The shapes of healthy and diseased red blood cells are well explained by models that include both the membrane and spectrin energies.
Force Generation by Polymerization of Filamentous Proteins
The polymerization of actin and other intracellular proteins is a crucial factor in the motion and shape changes of cells, and in the motion of some types of bacteria, such as Listeria, within other cells. The polymerization is often asymmetric. For example, actin filaments have "barbed" and "pointed" ends, with polymerization generally favored at the barbed end. This leads to a tread-milling behavior in which the barbed end grows while the pointed end shrinks.
A great deal of insight into the process of force generation by filament polymerization has been obtained from the Brownian ratchet model and extensions thereof. In this model, the motion of the obstacle (cell membrane or bacterium) results from fluctuations of the obstacle position or the position of the end of the filament contacting the obstacle. These fluctuations, if large enough, provide sufficient room for a free monomer to diffuse to the end of the filament and be incorporated. This model makes specific predictions about the dependence of the filament growth rate on the opposing force. Increased opposing force results in reduced position fluctuations, and thus a reduced growth rate. The functional form of the dependence is exponential. This prediction has been confirmed by in vitro experiments on microtubules. The measured exponential decay was different from the predicted one, but subsequent work has explained the observed decay rate in terms of a "subsidy" effect. The Brownian ratchet model has by now become the standard paradigm in the biology community for analyzing force generation by biopolymer growth.
Biological Soft Matter Physics
The individual components of cells and lipid membranes, such as polymers and polymer networks, are materials in their own right, with important technological applications. They deform easily in response to external forces, and are subject to important thermal fluctuations. Though flexible polymers whose length is much longer than their persistence length have long been studied, research on semi-flexible polymers whose contour length is less than their persistence length is more recent. Actin and microtubules are examples of these semi-flexible polymers that can be viewed as thin rods whose energy increases when they are bent. Thermal fluctuations excite bending modes of the rod leading to instantaneous configurations with wiggles such as those shown in Figure 9. The polymers can cross-link, leading to distinct structures and mechanical properties. The diffusive motion of biopolymers, particularly in the presence of varying external forces, is also an important area of soft-matter research that has several points of contact with biology. Some examples of successes of soft-matter physics relevant to biology are included in this section.
Intracellular Networks of Semiflexible Polymers
All eukaryotic cells contain a complex network of filamentous proteins and associated bundling and cross-linking proteins. This cytoskeleton is largely responsible for the cell's mechanical response to its environment. Over the past few years, an increasingly quantitative understanding of such systems has emerged which spans the range from the micromechanics of single protein-based filaments to the collective properties of networks of filaments. This progress has been made possible through a combination of efforts in theoretical soft condensed matter with new experimental developments in the microscopy and micromanipulation of in vitro model systems. Largely inspired by cell biology, recent studies of semi-flexible polymers have revealed new statistical mechanics and dynamics in the large class of polymers possessing bending and/or twist rigidity. From single-chain behavior, such as confinement effects and the unusual dynamics of conformation relaxation, to collective properties, such as entanglements, liquid-crystallinity and network formation, our understanding of this class of polymers has been rapidly developing to become a vital part of polymer physics. Recent measurements of the response and fluctuations of particles embedded in viscoelastic biological media have provided stimulus for the development of a theory of microrheology of these systems.
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Figure 9. Schematic of a semi-flexible polymer showing “wiggles” produced by thermal fluctuations. The external force t increases the length R of the polymer by pulling out the wiggles. [Courtesy of F. C. MacKintosh] |
DNA Translocation through Pores and Other 1D Diffusion Processes.
One-dimensional diffusion processes are ubiquitous in biology. Disorder can strongly influence the dynamics of such processes. Biological examples where one-dimensional diffusion over a correlated energy landscape influences the dynamics of a process include specific protein target location on DNA, nucleosome repositioning, and DNA translocation through a nanopore. Theoretical models based on classical work on diffusion in one-dimensional random potentials have recently been successfully applied to the dynamics of these systems. In particular, the fluctuations in the “mean first passage time” have been established to be quite large due to the disorder. It was shown by de Gennes (Nobel Prize in Physics 1991) that the average time t a particle spends in a space interval x is dominated by the atypical barriers of the potential, which grow proportionally to x. Work of others has concentrated on analyzing the distance traveled as a function of time. In the presence of a non-zero average random force, such as in DNA unzipping or in the dynamics of motor proteins, anomalous diffusion is predicted.
Biologically-Inspired Materials
Efforts to design new materials by using biological self-assembly concepts have grown rapidly in recent years. The soft and condensed matter physics communities have been very active advancing the understanding of these concepts to create materials with specific functions and structure.
Heterogeneous Macromolecules
An important extension of the sequence design paradigm for single heteropolymer molecules (see previous section on Biomolecules) is in the area of soft materials, so far most actively addressed in the area of so-called smart gels. Following the lead of theoretical approaches to heteropolymer design, experimenters were able to produce a gel catalyst capable of switching catalysis on and off in response to a weak stimulus, thus mimicking the allosteric function of biological enzymes.
The polymorphism of biological lipids has inspired an interest in the materials community in producing polymorphic block copolymers. Recently, the lipid-block copolymer analogy led to the discovery of water-soluble polymer vesicles (polymersomes) that have elastic properties significantly different from the biological ones that inspired them. By extending the concept of self-assembly to tri-block copolymers, researchers have been able to produce structures previously unknown and of great potential use in materials science. Ordered block copolymer structures are finding applications in thin film arrays, nano-composites, and photonic materials. Theoretical methodologies developed in studying block copolymers are in turn being applied to lipid bilayers and their properties.
Environmentally Controlled Self-Assembly of Cationic-Anionic Molecules
The understanding of electrostatic effects in the self-assembly of polyelectrolyte chains with oppositely charged macro-ions and short chains, developed by the soft matter physics community in the past decade, was inspired by important cationic-anionic complexes in biology, such as that of DNA with various cationic macromolecules, and the packing of RNA or DNA into viral capsids. The controlled assembly of nucleic acids with cationic proteins as a function of pH and salinity has generated new models to explain many electrostatically driven self-assembly processes important to generate new materials. Examples of such bio-inspired materials include DNA-cationic lipid complexes assembled into hexagonal and lamellar structures, which have potential application in drug delivery.
Another important example of cationic-anionic self-assembly is the formation of stable multi-component nano-aggregates. Amphiphilic molecules tend to aggregate into micelles or vesicles. But multi-component aggregates are generally unstable due to the low entropy of the macromolecules. This incompatibility, driven by the net van der Waals repulsion among the unlike constituents, leads to the formation of an interface along the surface of the vesicles. Biological membranes, however, are multi-component vesicles. Inspired by biological assembly of heterogeneous molecules, stable vesicles of multi-component surfactants have been produced in the laboratory using mixtures of positive and negative molecules. In contrast, vesicles of neutral molecules are not stable, leading to the formation of multi-lamellar aggregates over time. Other stable multi-component aggregates inspired by biology include cationic and anionic stoichiometric mixtures of peptide amphiphiles assembled in cylindrical (wormlike) micelles. These biocompatible materials generate nano-aggregates with surface patterns which are useful in inducing the growth of bio-inspired materials.
Current and Future Challenges
Biological systems provide many rich examples of complex and adaptive materials. These pose fundamental challenges for both physics and biology. For physics, these challenges, both experimental and theoretical, stem in part from the hierarchical structure and non-equilibrium behavior of biological materials. Along with the challenges of understanding and characterizing these biological structures comes the promise of inspiration for qualitatively new materials and technologies over the coming decades. We describe below some research areas chosen on the basis of new experimental data available for studying problems where the physics community can have a large impact. This list is of course far from exhaustive, but should rather be taken as simply a set of examples
Biomembranes and biopolymer materials
Biomembranes consist of a mixture of several membrane components, lipids and proteins, which determine their specific biological/chemical/physical properties. Recently it has been proposed that heterogeneity in biomembrane composition arises from a phase separation between domains comprised primarily of saturated lipids and cholesterol, denoted rafts, and those comprised primarily of mono-unsaturated lipids. These lipid rafts are thought to be involved in a diverse range of biological processes including signal transduction, lipid and protein sorting, the accumulation of viral capsid proteins, and the assembly of protein aggregates. The difference between the results of in vitro and in vivo experiments on rafts, however, is startling and not understood. In addition to the intrinsic biological interest of rafts, the physics of phase separation and domain formation within bio-membranes is an active area right now, with basic theoretical and experimental challenges.
In order for a cell to exchange material with its exterior (exocytosis) or for material to be exchanged between different vesicles within the cell, trafficking and fusion of membranes must occur. The actual mechanism of fusion has received little attention. An understanding of this process would elucidate the comparative roles of different membrane constituents, and the reasons for the tight regulation of these components in cells. It would also contribute to an understanding of the mechanisms of drug delivery and of viral infection, as well as to the basic problem of topological change in physical systems.
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As mentioned above, the cellular cytoskeleton is not a passive material, but rather a highly dynamic system, with regulated polymerization and active force generation. The properties of cytoskeletal materials can be tuned by associated cross-linking and bundling proteins, in a way not possible with conventional synthetic polymer gels and rubbers. Because of the possibility of cellular-scale measurements of their properties, these materials can provide a unique window into materials properties far from equilibrium. Important advances are thus likely to occur over the coming years in the study of active, non-equilibrium networks.
Viral capsids
Viruses exhibit nanometer-scale structures with specialized mechanical properties. Of particular importance to their function is the packaging and compartmentalization of their genetic cargo. The assembly of the proteinaceous shells of viruses constitutes a very basic puzzle of biology, as well as a challenge to our understanding of the physics of self-assembly. With a better understanding of viral shells, it might be possible to control the self-assembly of new nanometer-scale devices and technologies. Viruses are not just passive materials, however. Once formed, viral shells are often loaded with genetic material by specialized motor proteins (coded in the viral genome) that depend on the host for energy. The problem of viral packing and the similar problem of storage of DNA in the nuclei of eukaryotic cells pose significant challenges to our understanding of ordered phases and elastic properties of dense polymer materials. Interestingly, since a mature virus must infect its host without the benefit of the fuel required for molecular motors, it must rely in large part on the mechanical energy of storage to provide the driving force for injecting its genetic material into a new host (Figures 11 and 12).
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| Figure 12. DNA ejection from Bacteriophage T5 [courtesy of M. de Frutos, L. Letellier, and E. Raspaud, Orsay, France (2004)] |
Chromatin structure: molecular assembly on multiple scales
In the cell, DNA, with a chain length on the order of centimeters, must be packed into regions with length scales on the order of microns, a scale much smaller than the average size of the coiled DNA in solution (Figure 13). DNA packing in vivo has implications for the integrity of the genome during recombination while DNA packing in vitro has implications for new, monodisperse macromolecules that can form new, macroscopic “precision” materials.
The assembly of DNA and histone proteins into chromatin presents challenges to soft condensed matter theory and functional biology: progress requires new ideas, measurements, and models at each level of organization. DNA is precisely wrapped around histone octamers forming a zigzag, beads-on-a-chain structure (10nm). Though the DNA is bound to the histones tightly enough to be distorted, RNA transcription is thought to occur in the presence of the histones. Polymer dynamics and elasticity theory shed light on the viability of transcription and can help determine the detailed molecular mechanism by which polymerase proteins attach to the DNA.
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At the next level (30nm) the DNA-histone strand assembles into the chromatin fiber. Though there are a number of suggested models for the structure at this level, it is also known that when the DNA is cleaved, the nucleosome core particles made of a histone and a segment of DNA form a variety of liquid crystalline phases in vitro. Finally, at the level of the condensed chromatids (1400nm) there must be some registry between sister chromatids in the meiotic cell: without this registry, crossing-over and recombination are doomed to fail. As a result, despite the fact that the chromatids are chemically identical, they are often found in stereo conformations. From the materials theory perspective this is a puzzle – are the packing constraints strong enough to wash out the underlying molecular chirality? There are also important dynamical issues that are exacerbated by the small volume in which cell division takes place. The dynamics of polymers does not allow for the many crossings that must occur as the genetic material is copied. Isomerases are essential for cell function. For bio-inspired materials, can we borrow the cellular machinery that enables the rapid relaxation of strained polymers? More generally, can the organizational principles that the cell has evolved be used to create new, precise materials?
DNA assembly plays an active role in chromosome dynamics, which involves changes of structure between the condensed (inactive genes) and de-condensed (active genes) states. Unanswered physics questions include: how is the “open” architecture of the nucleus maintained? What is the osmotic pressure of de-condensed, active DNA sections?
Aggregation of misfolded proteins
Protein misfolding and aggregation (usually via inter-protein beta-sheet formation) has captured the attention of the broad scientific community and the public recently, primarily due to the “amyloid diseases'' such as Mad Cow Disease and its human variant Creutzfeldt Jakob Disease (CJD) studied in depth by Prusiner (Nobel Prize 1997), Alzheimer's disease, Parkinson's disease, type II diabetes, familial ALS (“Lou Gehrig disease”), and Huntington's disease. In each of these diseases, evidence has been found post mortem and in vitro for autocatalytic aggregation (Figure 14a) of proteins into structures (Figure 14b) different from their monomeric native form. The community consensus is that either these large aggregates or smaller oligomers of protein are responsible for disease toxicity.
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| Figure 14a. Autocatalysis of the prion protein (normal-PrPc, infectious-PrPSc) at the monomer level (upper picture) or via aggregation (lower). [Courtesy of D. L. Cox]. |
Figure 14b. Amyloid plaque from the human prion disease Kuru [from |
Theoretical scientists have already made substantial contributions to the understanding of prion disease. The biological community has reached general consensus that Prusiner's core proposal of protein only infection via misfolding of the prion protein (PrPc) is correct. This protein only infection concept was first emphasized by a mathematician. The observed exponential growth in vivo of infectious prion material is most likely due to fission of aggregate fragments as emphasized first by mathematical biologists. More recent model studies have plausibly linked simple statistical mechanics models for autocatalytic aggregation to incubation time distributions drawn from epidemiological and laboratory studies.
Theory can play several roles in autocatalytic aggregation. For example, the role of the shape of the single-molecule energy landscape has been studied extensively for proteins. The effects of modifications of the landscape resulting from cooperativity might well be understood within a framework similar to that used for single molecules. Understanding the basics of autocatalytic aggregation could well point to new hitherto unexplored mechanisms of materials growth.
Several of these neurodegenerative diseases are caused by mutations in the genes for various proteins. The proteins are mostly of unknown function, and their genes are unrelated to each other except in one crucial respect: an abnormal repetition of the triplet CAG in their code. Each CAG codes for the amino acid glutamine, and hence the CAG repeats code for abnormally-long strings of glutamine (polyglutamine), creating mutant proteins which prove to be toxic to neurons. What are the physical structures implied by this homopolymeric stretch? And how can physical theory differentiate between different models suggested by numerics and experiments?
Glutamine repeats aggregate into pleated antiparallel sheets held together by hydrogen bonds between both their main chain and side chain amides, the so-called “Perutz zipper” (Figure 15), and it has been suggested that this zipper leads to misfolding and protein-protein aggregation in the affected neurons.
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![Text Box: Figure 15. The Perutz zipper [C. A. Ross et al, Proc. Natl. Acad. Sciences 100, 1 (2003)]](Supramolecular_Assemblies_files/image027.gif) |
In all these cases, there exists a specific threshold of repeat length that causes disease, typically of order 40 consecutive glutamines. Numerical modeling has generated other possible structures for polyglutamine, including parallel sheets, hairpins, compact random coils and compact beta sheets. Two competing models are the “beta amyloid” model of Wetzel, consisting of two parallel beta sheets twisted around each other, and the Perutz helix model characterized by 20 residues per helical pitch.
While the “polymer physics” of alpha-helix forming homopolymers is well understood, the properties of beta-sheet homopolymers are fundamentally different. For instance, a class of natural questions in the context of the polyglutamine problem centers around polymer kinetics: how to calculate the percent of aggregated protein as a function of time (i.e. how does the nucleation rate of the quaternary structures depend on N in poor solvent conditions)?
Autocatalytic aggregation is of broad import in biology, materials science, and bioengineering. Theory can play several roles in this arena. For example, the role of the shape of the single-molecule energy landscape has been studied extensively for proteins. The effects of modifications of the landscape resulting from cooperativity might well be understood within a framework similar to that used for single molecules. Understanding the basics of autocatalytic aggregation could well point to new hitherto unexplored mechanisms of materials growth
Precision self-assembly of organelles
There is a great opportunity to apply recent advances in physical theory to the complex multi-component machinery of the cell, including motility organelles such as the bacterial flagellum and membranous organelles such as the Golgi apparatus and the endoplasmic reticulum. Furthermore, theoretical insights into the basic operational principles of these machines can lead to novel designs for new materials at the nanometer scale. In this section we describe two examples that are representative of potential future directions.
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Figure 16. Origin of the helical shape of a flagellar filament [K. Namba and F. Vonderviszt, Quart. Rev. Biophys. 30, 1 (1997)]. |
The bacterial flagellum is an exquisite example of Nature's nanotechnology. The flagellum consists of a 50-nm diameter rotary motor, a thin helical filament about 10 microns long and 20 nm in diameter, and a flexible universal joint called the hook that connects the motor to the filament. In the absence of external stress, the filaments are left-handed in wild type bacteria. When the motors turn counterclockwise, the filaments form a bundle that pushes the cell along. When one or more of the motors reverses, the corresponding filament comes out of the bundle and undergoes a polymorphic transition from the left-handed state to a right-handed state. This transition reorients the swimming direction of the cell. The polymorphic transitions arise from slight, Ångstrom-scale changes in conformation of the flagellin protein subunits that constitute the flagellum. These subunits are arranged in eleven nearly longitudinal proto-filaments; if all the subunits in a proto-filament undergo the conformational change to the smaller state, then the filament will distort so that this proto-filament lies on the inside of a helix (see Figure 16). Recent X-ray crystallography and cryoelectron microscopy experiments have revealed the structures of the subunit and proto-filaments to a resolution of a few Ångstroms; these experiments call for the development of new coarse-grained models to explain how an applied force or torque can trigger a polymorphic transition. A quantitative understanding of this transition could provide the basis for the design or control of a smart material that could act as a sensor or actuator: near the transition, small changes in external force or torque will lead to large changes in the overall length of the filament.
The Golgi apparatus and the endoplasmic reticulum together provide a second example. These structures are part of the secretory pathway in which proteins are synthesized, modified, and transported to their final destination. Membrane fission and fusion (previously discussed) are clearly important for this traffic, but there is also evidence that lipid can flow directly from one compartment to another. Furthermore, it has recently become clear that the Golgi apparatus is not simply a static stack of pancakes, but instead has a dynamic structure that also includes networks of tubular membranes. A challenge for physical theory is to generalize the models that have been so successful at predicting and explaining equilibrium shapes of vesicles to these non-equilibrium systems. Important issues which theory can clarify include the formation of the non-equilibrium networks and the transport of membrane-bound proteins.
Summary
What special role can physical theory play in meeting these challenges of supramolecular structures? An important lesson of modern theoretical physics has been the need to develop quantitative phenomenology and simplified models at appropriate length scales to guide and explain experiment. Molecular dynamics is, by now, well established as the work-horse for atomic level simulations of biological systems, and has become an indispensable tool in elucidating the structure of biomolecules. Longer length-scale quantitative modeling, when performed in close association with experiments, can also provide insights and key ideas into supramolecular complexes, their assembly and function. Many of the problems listed previously, either drawn from or inspired by living structures, provide a natural extension of existing research in soft condensed matter physics.
Research into living systems will inspire further development of physical theory, especially in dealing with phenomena, including statistical mechanics, far from equilibrium. Most of the examples discussed above, in fact, involve non-equilibrium physics. In self-assembly processes, the rate at which the final product is obtained crucially important, and very often the structure that is reached on biological time scales (such as a highly organized organelle) is not the equilibrium structure. The assembly and disassembly of intracellular biopolymer networks is a dynamic process driven by ATP-ADP conversion. In protein aggregation, the key question is the rate at which the aggregates nucleate and grow, rather than the equilibrium properties of the final product. The dynamic role of DNA in chromosome dynamics is clearly a non-equilibrium phenomenon. Developing a general framework for dealing with such non-equilibrium phenomena would be a major accomplishment, which would contribute to both physics and biology. From a physics perspective, the situation is further complicated by the existence of surface everywhere, where important interactions occur, so that the standard procedure in physics of taking the thermodynamic limit as the number of particles goes to infinity, does not apply.
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As in other areas of science, the major role of theory is to guide the experiment and shape thinking by formulating the very language used to think and work in the area. Outstanding examples of such theoretical concepts shaping our thinking in biological physics include the ideas of quasi-species to be discussed below under Systems Biology, entropic elasticity of polymers, charge inversion in systems of strongly charged ions, conformal diffusion of vesicle shapes, topology of DNA (including links, knots, writhe, twist), and heteropolymer sequence design. The most important mission of theory is to keep contributing to the crystallization of such general pictures, ideas, and concepts. As regards methods, it is vital that the widest possible spectrum of theoretical tools available be developed and exploited. This spectrum includes on the one hand analytical theoretical methods, ranging from the more qualitative ones, such as scaling and dimensional analysis, to more complete models such as field theories (for example Ginzburg-Landau), cellular automata,
Another important mission of theorists in this area is to establish fruitful exchange between analytical theory and simulations, as well as between these two and experiments. Theory can provide new ways of looking at problems and help develop deep insights between seemingly unrelated topics. There are many examples in physics, where such insights have proven extremely valuable in the development of a research field, and increasingly this is proving true in biology.
Despite the complexity of supramolecular assemblies in biology, focusing on simple but quantitatively precise questions should prove very important. There are many examples where highly complex processes result in very precise length or time scales. For example, the division of E. coli into two equal daughter cells is accurate to within 1-2%, and, in the same organism, the assembly of the hook of the bacterial flagellum stops reliably at 55nm, well outside of the cell wall, allowing transition to assembly of the filament. Focusing on such quantitative issues may well provide new insights into biology. It can also help engineer precision complex materials, where the components are large on the molecular scale, and yet identical. Indeed, a new set of materials are and will be constructed using the machinery of the cell, such as identical polypetides with specific charge distributions and helical structures (Figure 17). Understanding the self-organization of these new molecules will help in developing new materials with specific functions. For example, though all proteins necessary for a human being can easily be encoded in 30 Megabytes of storage, this information must serve as a complete blueprint for human structure and function, emphasizing the importance of self-assembly in biological systems. While this miraculous construction does not occur in typical synthetic molecules, it does occur in nature, partly because of the great regularity of the molecules built by the machinery of the cell.