The Role of Theory in
Biological Physics and Materials:
A report to the National Science Foundation
Michael F. Thorpe, Arizona State University
Anders E. Carlsson, Washington University in St. Louis
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| Figures reproduced from the UCSB/Caltech/MIT Institute for Collaborative Biotechnologies |
The workshop was supported by the National Science Foundation
under Grant DMR-0427933 and by Arizona State University
A workshop on The Role of Theory in Biological Physics and Materials was convened in
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What are the important problems in biology that can be solved with the help of theory?
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What types of theory are most useful in treating biological problems?
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What new physics and materials science can be learned by the study of biological systems?
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What types of educational opportunities and infrastructure support would be most helpful to nurture this community?
This report emerged from the discussions among the workshop participants and is also available at http://biophysics.asu.edu/workshop in both pdf and html formats. The structure of the workshop and the participant list are given in the Appendices. The main finding of the workshop was that this is a time of tremendous growth and opportunity for biological physics and materials, and the NSF should act strongly to support the role of theory in this field. On the basis of the workshop discussions, we recommend several specific ways to expand the pool of qualified individuals with a command of both the theoretical methods of the hard sciences and the language of biology. This involves catalyzing transitions into biological physics and materials at various career stages.
The NSF can recognize the rapid growth of this field, and its potential, by expanding the funding available to theorists working in biological physics and materials. In addition, we make the following specific recommendations:
- The expansion of NSF joint funding linking the NSF, especially DMR, with the NIH.
- The establishment of regional research and training centers in biological physics and materials to bring together biologists and physicists.
- The expansion of postdoctoral fellowships supporting transitions into biological physics.
- The development of more summer schools, internet resources and textbooks.
- Support for sabbatical visits to institutions with active biological physics and/or biology programs.
Although the recommendations in this report are primarily for the NSF, we note that universities can also support the growth of theory in biological physics and materials. We thus
- recommend that undergraduate and graduate courses contain more examples of physics being used in biology and vice versa.
- encourage more flexibility in graduate programs, especially in qualifying procedures in masters and doctoral programs.
The past decade has witnessed an unprecedented expansion of the involvement of theoretical physicists in biologically related problems. This has been driven by several factors, including the vast amount of new data emerging from new quantitative experimental methods, such as gene sequencing and advanced imaging methods; the increasing computational capabilities available to physicists for dealing with complex problems; and the realization that work on biological problems can have important spin-offs for problems in physics and materials science. The increased interest of physicists in biologically related problems is evidenced by the large number of theoretical condensed matter physicists and materials scientists currently migrating to these problems, as several different sub-communities have realized that their approaches have a potential impact on biology. The large number of positions in biological physics that have been advertised in recent years by
The physical science theory community is well poised to make important contributions to the study of biological problems, and biologically based materials. One of these contributions is the physics approach. This means searching for the single relation or phenomenon at the heart of a problem, rather than attempting a complete quantitative description of all the details of the problem. Physicists have traditionally sought underlying trends and unifying principles in complex systems. The physics approach can involve defining a paradigm model. It also includes the search for general results, such as the fluctuation-dissipation theorem of statistical mechanics, which cut across a broad range of systems. Or it can consist of the use of astutely chosen reduced variables in analyzing data, to more clearly establish relationships between quantities of interest. Such methods can have enormous payoffs when combined with the increasingly precise data emerging from quantitative experimental biology. The methods of condensed-matter and materials theory are particularly well suited to the study of biological and biologically-derived systems.
The major part of the workshop effort was devoted to examining examples of past successes in the interaction between theory and biological physics/materials, and examining prospects for the future. For this purpose, it was deemed necessary to divide up the field into subfields of manageable size, and the workshop participants were correspondingly divided into discussion teams. The subfields chosen (with necessarily fuzzy boundaries) were Biomolecules, Supramolecular Assemblies, and Systems Biology. An additional workgroup examined issues relating to Education and Infrastructure. The following report is also structured along these lines. The workshop included substantial amounts of time devoted to small-group discussions, as well as large-group discussions (see workshop schedule in Appendix B). Because of the breadth of biological physics and materials, it is impossible to give an exhaustive survey of either past successes or future research areas. Thus each section below gives a few examples of past successes and possible future research directions.
Some of the general areas treated by physicists moving into biological problems include protein folding, biomolecular phase transitions, membrane phases, bioinformatics, and applications of spatially-extended dynamical systems to biology. The specific examples that were discussed demonstrate numerous past successes of theory in the study of biomolecules and supra-molecular assemblies. These include the structure of double-stranded DNA, protein structure determination, evaluation of low-energy vesicle shapes, and random-walk treatments of DNA moving through pores. They have involved the use of a tremendous range of methodologies, over a very broad range of length scales. Systems biology is emerging and strengthening as a vital area. Almost all theoretical techniques that have been developed for condensed matter/materials problems appear to have potential applications in biological problems.
The involvement of theory in biological physics and materials leads to both answers to biological questions, and enrichment of the fields of condensed-matter and materials theory by the study of biological problems or biologically based materials. An example of the former is the evaluation of red blood cell shapes via minimization of an energy function including elastic terms. An example of the latter is the study of diffusion in random potentials. This was motivated in a general way by biological issues, and has subsequently enriched condensed-matter and materials theory. Biomimetic materials, which use biological components or their analogues to construct materials with unique properties, also demonstrate the spin-offs possible from the study of biological systems. The workshop participants felt that the entire spectrum of interactions between the disciplines should be strongly supported.
Two scientific themes occurred repeatedly throughout all the discussions: non-equilibrium thermodynamics, and molecular self-assembly.
Condensed matter/materials theory has generally focused on equilibrium problems, and a solid conceptual base exists for treating such problems. However, most biological phenomena are inherently non-equilibrium. Cells continuously consume the energy currency ATP, and this is the origin of much of their highly dynamic behavior. Spatiotemporal gradients of key chemical concentrations are ubiquitous in biology. The conversion of chemical energy into mechanical energy, required for several essential cell processes, is also a non-equilibrium phenomenon. The structure and properties of living organisms and ecosystems are determined not by a global-optimization procedure, but rather by the interaction of evolutionary dynamics with a changing environment. Thus the study of biology and biological materials could have a large impact on condensed-matter and materials physics by accelerating the development of an underlying conceptual structure for studying non-equilibrium phenomena.
Self-assembly is seen on an enormous range of length scales, including the reliable folding of proteins, the undirected growth of motility organelles such as flagella, viral capsid assembly, and the packaging of DNA. The self-assembly is often very accurate – as for example in the assembly of the hook in bacterial flagella which stops at a very well-defined length. In none of these cases is the dynamics or the perfection of the self-assembly well understood, and there is very little predictive methodology for establishing what structures can be formed. Understanding self-assembly would have very important ramifications for physics and materials science. Self-assembling materials may well be a major thrust in future materials development and understanding how biological systems assemble as accurately as they do would surely help spur this technology forward.
Having determined that the interaction between theory and biological physics/materials can have important benefits for both the physical-science and biology communities, the workshop participants addressed the question of how this interaction can best be encouraged. These discussions are summarized in the Education and Infrastructure section. There is a pronounced shortage of individuals who have a command of both the theoretical methods of the physical sciences, and the language of biology. This shortage is evident both in the experience of physics and materials science departments which have hired or attempted to hire in biological physics, and of investigators seeking to hire postdoctoral research associates. Measures that could alleviate this shortage include increased support for postdoctoral training in biological physics and mid-career research field transitions, the establishment of regional research and training centers, and expansion of educational programs such as summer schools. There is also a shortage of research funding for individuals working at the interface between the biological and physical sciences – there has been a tendency for this work to “slip between the cracks” at NSF, and it is important that mechanisms be found to support this emerging community.
Introduction
The fundamental building blocks of living cells are biomolecules which provide the bedrock of life and now pose a research frontier for theoretical physics. All life forms can be considered to be self-organized systems assembled from these building blocks. Even though one can subdivide life into substructures like cell organelles, the entire cell, tissues, multi-cellular organisms, and even societies, biomolecules make their basic role felt across the entire hierarchy of biological order: pheromones link male and females in disperse societies, drugs treat diseases in individuals, cells are guided in their development through hormones, and every process in cells is directly linked to biomolecules. So naturally, the quest for a theory of living systems starts with the fundamental building blocks – biomolecules. But much as the physics of innate matter has derived its successes from the recognition of scales that subdivide the innate world, e.g., quarks, nuclei, molecules, so life appears to be governed by its own system of scales that provide a staircase to the ultimate goal of understanding human life. We provide an overview of the particular role that theoretical physicists/materials scientists have played and future prospects in studying life from the biomolecular perspective.
Past Successes
Here we describe some of the manifold roles that theory has contributed in the field of biomolecules.
Doubled Stranded DNA
Fifty years ago models of both the double helix structure of DNA and also the first three dimensional protein structure were determined in the Cavendish laboratory of the Physics Department at
Protein Structure
The versatile roles of biomolecules in living cells have become known with the advent of crystallography that extended the work at the Cavendish. This was first accomplished by John Kendrew and Max Perutz (Nobel Prizes in 1962) who solved the atomic level structure of the oxygen storing proteins myoglobin and hemoglobin. The role of X-ray crystallography leading to this accomplishment is well known. Less well known is the role of physics, in particular, theoretical physics in the subsequent revolutionary development of structural biology that has produced to date over ten thousand three dimensional protein structures.
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| Figure 1. The study of biomolecules was initiated with the double stranded structure of DNA shown on the left and the original ball and stick model of myoglobin on the right ( http://nobelprize.org/chemistry/laureates/1962/kendrew-lecture.pdf); the first 3D structure of a protein to be determined |
This accomplishment was facilitated through advances in computing that permitted the extension of mathematical algorithms derived from theoretical physics of crystals and X-ray scattering to complex crystals. From the solution of the phase problem (Nobel prize in Chemistry 1985) to the application of NMR spectroscopy (Nobel Prizes 1991, 2002), to the use of refinement methods in software packages used widely by structural biologists, concepts and algorithms developed by theoretical physicists have been of fundamental and practical importance.
Molecular Dynamics
Naturally, biomolecules obey the same laws of physics as any other material system. However, the large number of degrees of freedom, and absence of symmetry, prohibits a complete quantum mechanical description of their dynamics. As a viable alternative, classical molecular dynamics (MD) simulations emerged as a standard approach for studying biomolecular systems. First used to investigate the condensed phase of simple mono-atomic systems, currently, as a result of spectacular developments in computational hardware, software and methodology, MD is routinely used to simulate biomolecular complexes composed of many thousands of atoms, for tens of nanoseconds. The resulting phase space trajectories are analyzed by advanced statistical mechanics methods contributed by many leading theoretical physicists.
Current and Future Challenges
Presently, theoretical investigations of life at the molecular level are experiencing a dramatic renewal due to the explosion in the amount of experimental data that is available at a level of precision unimaginable even few years ago. Here we provide examples from some of the most exciting research areas.
Protein Structure
With the near completion of a number of genomes, and the subsequent extraction of genes and hence protein sequences, attention has been focused on the determination of the three dimensional structure of proteins. This is the next logical step in the chain that leads up to biomolecular function and understanding of biological processes at the supra-molecular level. Proteins are important targets for drug design and this is greatly facilitated if the three dimensional structure is known. The Protein Structure Initiative (PSI – www.structuralgenomics.org/ ) funded by the NIH is due to move into the high throughput structure determination phase in 2005. The stated aim is to produce ~ five thousand representative three-dimensional structures in 5 years, out of ~ million protein structures. Simulation will play an important continuing role in structure refinement on both the X-ray crystallographic and NMR data. The still-missing structures will have to be determined by structure prediction methods, modeling, and simulation. Theory will advise crystallographers, NMR spectroscopists, and electron microscopists in the optimal selection of structures to be solved and to render the missing structures accessible to homology modeling (looking at the folding of similar sequences). But likely, ab initio approaches to protein folding will be required to supplement homology modeling for finding new folds. The ultimate goal would be to have high confidence in structures folded computationally, as it will never be possible to determine the three dimensional structures of all proteins experimentally.
Protein Folding
A still unsolved problem in molecular biology is to decipher how an ensemble of unfolded structures navigates rapidly through the rough free energy landscape to the unique folded structure of the native state. In the last ten years some progress has been made which has been spurred by theoretical ideas. Simulation approaches can describe protein folding in principle in great detail, but is restricted to time scales of microseconds at best. Experimentalists and theoreticians joined forces to identify fast folding proteins that open up the opportunity for computational modeling and experimental tests. Indeed, the interplay between theory and experiment is just beginning to produce a detailed characterization of the pathways, mechanisms, and transition states in the folding process. Currently, theoreticians and experimentalists are beginning to focus on understanding the folding mechanisms of larger proteins and also on the assembly of multi-protein units.
RNA folding
Single stranded RNA is composed of a sequence of bases which can pair up with others on the strand. Given a particular sequence and pairing energies, finding the optimal pairings (the so-called secondary structure) is an interesting and biologically important problem. Bio-statisticians had already identified a fast algorithm (polynomial in length) for finding the optimal pairing. Statistical mechanics contributions include showing that this algorithm had much in common with the summation of Hartree diagrams in many-body physics. Once more, this connection provided important insights and novel perspectives to both biology and statistical physics such as calculating force-extension curves for imputed RNA sequences.
Cellular Mechanics and Molecular Motors
The generation, transformation, and sustenance of mechanical forces are essential for the motion, energetics, internal transport, and stability of cells. The study of molecular motors and proteins designed for mechanical function is one of the most exciting fields of modern biophysics, guided by non-equilibrium statistical mechanics and modeling linked closely to the analysis of single molecule experiments like atomic force microscopy. Theoretical physics has rationalized the function and design of motors; while computer simulation and advanced analysis methods, e.g., using a new free energy - work relationship, have identified and explained the force-bearing and force-sensing parts of proteins in muscle and hearing. Theory has also explained the manifold adhesion properties of cells and is considered an important guidepost in planning and analyzing experiments that unravel the functioning of the many mechanical functions in cells.
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Figure 2. Schematic of thermal ratchets possibly related to molecular motors. The lateral bolts in frame (b) allow the ratchet to move to the right. [P. Nelson, “Biological Physics” (W. H. |
Photosynthesis
All life on earth depends on photosynthesis, the fundamental biological process by which the energy of sun light irradiating earth is converted into an electrochemical potential, ultimately resulting in the generation of ATP, the fuel of biological cells. Recently, atomic resolution structures of several photosynthetic systems have been solved, revealing a hierarchical, modular architecture of various protein complexes that hold several hundred chromophores, chlorophylls and carotenoids, in place. This opens the exciting opportunity to understand the quantum mechanics involved in the key electronic processes in photosynthetic cells. The quantum processes in the photosynthetic membrane are exemplary for the quantum processes that arise in many fundamental biological reactions, i.e., the primary process in vision, photo-activation of biochemical reactions, electron and proton transfer reactions, or the rearrangement of covalent bonds and conformational changes involved in enzymatic reactions. The challenge to theoretical physicists derives from the need to describe complex electronic systems that are subject to static and dynamic thermal disorder. Artificial photosynthetic compounds hold out the possibility of producing electrical energy in significant quantities.
The quantum processes in the photosynthetic membrane are also exemplary for quantum processes that arise in many fundamental biological processes, i.e., photoactivation of biochemical reactions, electron and proton transfer reactions. Quantum mechanical methods have been used to identify the nature of the electronic excitations and the mechanism of excitation transfer between the pigments in the photosynthetic system of purple bacteria. The resulting description has succeeded in predicting observed spectral and kinetic properties nearly quantitatively, thereby demonstrating that complex molecular machinery like the photosynthetic apparatus involving hundreds of pigments and tens of thousands of atoms can be described with accuracy through the application of the laws of physics.
Sequence Design of Biomolecules
Recently, progress has been made in incorporating evolutionary aspects into theoretical studies of biomolecules. The central idea was that of hetero-polymer sequence design, which refers to the (more or less sophisticated) computational or experimental procedure which mimics the role of evolution in selecting sequences, but does not require evolutionary time scales. This allowed theorists to start, for the first time, examining many different properties, first and foremost folding, of the selected molecules in such a way that the selection criteria and mechanisms are fully under control. This approach was recently replicated in a real biological experiment, in which a de novo foldable protein was produced, with a novel fold. The next important offspring of the sequence design idea was the concept of protein structure designability. In turn, this has led to the systematic study of the network of protein folds, which is currently yielding spectacular new insights into the history of protein evolution.
Short-time Crystallography
With the development of picosecond time-resolved X-ray crystallography, molecular dynamics simulations can now be compared to an experiment with comparable resolution in space and time. Such a comparison shows that MD simulations reproduce with remarkable fidelity the direction, amplitude, and time scale of protein motions over the nanosecond window of the simulations, together with concomitant ligand motions and changes in the hydration structure.
Biomolecular Machinery
Basic functions of cell-like energy transformation and protein synthesis utilize very large biomolecular assemblies involving ten of thousands to millions of atoms even in the most primitive organisms. Advances in crystallography and electron microscopy have succeeded in resolving the structures of essential molecular machines within cells. This poses great challenges for theory and modeling due to their size and multifaceted features from control switches, to large scale motion, to chemical synthesis, to force transmission. The machines need to be understood as a whole since their efficient design does not permit reduction in size, even conceptually. A prime example is the ribosome, a multi-million atom complex of RNA and protein molecules that reads genetic messages (m-RNA) and transcribes them into polypeptide strands (proteins) through faithful reading of the genetic message, recruitment of amino acid building blocks, and synthesis of peptide bonds in synchronous motion of all components.
Bio-nano devices
The machines and sensors of living cells are of nanometer size and, hence, it is no surprise that the emerging technology of nanodevices provides an unsurpassed opportunity for applications that intervene in cellular processes or mimic such processes. Examples of nanodevices are DNA chips that monitor the expression level of genes in a cell, nano-fluidic devices that can handle extremely small samples for testing, or sensors that can be implanted in the body. The role of theory in the development of such devices arises in various ways, not the least through computer simulations that reached such a high level of veracity that computers play the role of microscopes imaging nanoscale structures and processes, and this meeting an extremely urgent societal demand. An example of this role is the development of nanopores manufactured in advanced, nanoscale silicon technology for single molecule electrical recording with the prospect of serving for highly cost-effective DNA sequencing. Theory and modeling are guiding the design of the nanopores and are essential for the interpretation of electrical recordings. Another example is the development of so-called nano-disks of lipid bilayers stabilized through a protein belt on its periphery. Again, simulations, tested by atomic force microscopy, image the disks and assist in designing optimal protein "belts" and use of the disks for single protein measurements or for drug delivery. Further into the future are bio-nanodevices that manipulate specific structures in living cells and assist in gene therapy.
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Bio-computing
Biomolecules tend to be large compared to classical bit structures (such as silicon devices) or qubits (such as trapped ions) and as such are often overlooked when searching for the new computational substrates. However, owing to their self-assembly properties it is worth exploring whether we can use biomolecules for information storage and manipulation. After all, the DNA/RNA system is arguably the most robust naturally occurring complex information storage and transfer system, while the human brain is the most advanced information manipulation device. Much of the DNA/RNA system's success depends on self-assembly and redundancy. If we can mimic these processes in man-made devices, we can hope to exceed both the speed and capacity of the naturally occurring systems as we learn from evolution-driven design faults and successes and skip millions of years of natural selection. The case for bioqubits is more difficult to make because of the problem of short decoherence times. There is little theoretical work on this subject beyond crude order-of-magnitude estimates of the decoherence time for a protein. In addition, it is not clear that one has to use entire protein molecules as qubits. It is possible that subparts, such as the electric dipole moment vector orientation (which depends crucially on only a few electrons in proteins such as tubulin), could be used as the physical manifestation of a qubit. Other advantages in making "living" bio(quantum) computers include ready energy sources (e.g. sunlight or 'computer food' e.g. sugar water), the possibility of self-repair (healing), and the possibility of self-advancement.
Biologically Inspired Materials
The functional relevance of features present in multiple biomolecules can sometimes be elucidated through physical studies of simpler model systems. Understanding the biological role can in turn provide the insights needed for the design and development of new functional materials and nanodevices. Simulation studies of carbon nanotubes in water, for instance, helped clarify the role of the relatively nonpolar pores frequently found in proteins conducting water and protons, where water confined into narrow pores was shown to form one-dimensionally ordered chains. Under osmotic or pressure gradients, water moves with little friction through nonpolar pores, at rates similar to those simulated for water transport in aquaporin channels in biological membranes. Moreover, protons diffuse more than one order of magnitude faster along the 1D water chains in nanopores than in the bulk fluid. Together with the phase-transition like polarity-induced emptying and filling transitions observed in the simulations, these results suggest polarity-controlled proton wires, as in cytochrome P450 and bacteriorhodopsin, and diode-like unidirectional proton conduction as a key element in the mitochondrial proton pump cytochrome c oxidase. Recent experiments and simulations suggest that the emptying transitions seen in carbon nanotubes are also relevant for ion channel gating. The insights gained from the studies of water-nanotube systems go beyond biology, and are relevant, e.g., for fuel cell design, reverse osmosis, and nanofluidics devices. Further types of biologically inspired materials, obtained by self-assembly are discussed under Supramolecular Assemblies.
Biomolecular Compass
Recently, the long-standing problem of which biophysical mechanism underlies the physiological compass of birds has been solved, dramatically demonstrating that molecular level calculations can be used to predict animal behavior. Physical theory yields accurate predictions about the effects of weak magnetic fields through different possible magneto-receptor molecules, in particular that very weak oscillating fields in the radiofrequency range will disrupt a compass based on a chemical reaction, but not a compass based on magnetite particles. This prediction has been tested in an experiment, whose results indicate that a chemical mechanism first postulated by theory underlies the magnetic compass.
Interaction of Light with Biomolecules
Biological functions that involve electronic processes, e.g., light harvesting in photosynthesis or light reception in vision, are quantum mechanical in nature. Since living systems exist and function at physiological temperatures, their behavior is strongly affected by disorder (both dynamic and static) and, therefore, can not be described by ordinary (T=0) quantum mechanics. The development of novel stochastic quantum mechanics methods, capable of accounting for the effect of strong disorder in bioelectronic systems, is a major challenge in the field of biological physics. Such new methods would benefit life scientists in analyzing their experimental data and in developing a better understanding of the mechanisms underlying biological functions. For example, the effect of dynamic disorder on the absorption spectrum of chromophore aggregates can be calculated in the framework of the
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| Figure 5a. Molecular structure of the proton wire in gramicidin. [R. Pomes and B. Roux, Biophys. J. 82, 2304-2316 (2002)]. | Figure 5b. Free-energy profile of a proton moving along a proton wire [Y. Y Sham, I Muegge, and A. Warshel, Proteins 36, 484-500 (1999)] |
Free Energy of Biomolecules.
All biology takes place around room temperature and so it is essential to include entropic effects and hence monitor the free energy rather than the energy. Accurate calculation of the free energy difference between two distinct conformational states of a biomolecular system continues to represent one of the biggest challenges in computational biological physics. The standard method to determine the change of the free energy (also known as potential of mean force - PMF) along a reaction coordinate is the so-called umbrella sampling method. A recently derived equality, which relates the change in free energy to the statistical average of the irreversible work done by the external driving force in the considered transformation, has resulted in the development of an exciting new method of calculating the PMF through a series of steered MD simulations. This new method has been already successfully applied to solve several biologically relevant problems, for example, the ability of membrane channels to conduct matter in a highly selective, yet very fast fashion.
Non-equilibrium Statistical Mechanics of Small Systems
An important issue in biomolecules is the statistical mechanics of small systems. Even a very large biomolecule has relatively few atoms, from a thermodynamic perspective. Therefore, conventional techniques of statistical physics and condensed matter theory, which were developed for systems with approximately Avogadro's number of atoms, must be modified to treat such small systems. In this respect, techniques which have been developed for small particles can be adapted to deal with biomolecules. A related issue is that fluctuations about the mean are likely to be much larger in biosystems than in bulk materials. Such fluctuations, even rare fluctuations, may well have profound effects on the measured properties of biomolecules. Finally, biomolecules are often studied under non-equilibrium conditions. These departures from equilibrium may be larger in biomolecules than in bulk systems. Therefore, it is very important to develop appropriate tools for treating strongly non-equilibrium and small size effects in biomolecules.
Elastic Properties and Strain
It is clear that many biological functions are carried out by large scale structures which consist of several protein domains. It is urgent to understand the dynamics of large scale structures. This requires development of suitable coarse-grained models that capture the salient properties of large assemblies. Because the functions of these structures can be triggered by induced strain, it is important to understand their elastic properties. The characterization of the dynamics of structures requires the development of novel computational and theoretical tools that deal with the heterogeneous nature of interactions as well as with the mesoscopic scale.
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Figure 6. The ribosome where proteins are assembled using instructions from the genetic code is one of the largest structures ever determined by X-ray crystallography. [J.H.Cate, M.M Yusupov, G.Z. Yusupova, T.N. Earnest, H.F Noller, Science 1999;285:2095-104.] |
Molecular Recognition and Aggregation
Molecular recognition is ubiquitous in biology and is one of the bases of life. While the concept of molecular recognition occurs in chemistry, this phenomenon is more striking in biology, where molecular recognition can be triggered on and off by various co-factors. While some of the questions associated with molecular recognition belong to chemistry, others, which involve conformational changes, for example, clearly fall into the realm of physics. In biochemistry, molecular recognition is associated with ligand docking, of course, but also self-assembly of proteins. A better understanding of molecular recognition can lead to improved drug design and lessons learnt can lead to new engineering methods for self-assembly.
It is now believed that many proteins can aggregate into a beta-sheet structure instead of adopting their native state. The reason is that proteins can have a propensity both for formation of alpha-helices and beta-strands. Beta-strands attach to each other within a protein, but they can also be promiscuous and attach to beta-strands of other proteins, leading to aggregate formation. Often, these aggregates lead to pathologies, best known in case of nervous system diseases like Creutzfeldt-Jacob disease, but beta-strand cross bridging is also known to functionally join proteins in muscle and in the extra-cellular matrix. Many proteins and other biomolecules are also known to self-assemble through broad interfaces, rather then beta strands. A prominent protein aggregate occurs in the capsids of viruses that protect the genetic materials in viral DNA or RNA and release it when triggered during infection. At the molecular level, it is essential to understand the inter-protein interactions that lead to self-assembly. Since we are dealing with finite size systems, new questions arise similar to those found in atomic and molecular clusters: what are the possible metastable shapes for a given size oligomer, what is the oligomerisation pathway, and what controls the self-assembly, when this is a non-equilibrium process? These questions are discussed in more detail under Supramolecular Assemblies in the next section.
New Methods Development
The role of theory in biological physics of biomolecules is to provide new conceptual and methodological solutions that are needed due to the complexity of biomaterials, due to the non-equilibrium nature of living cells, due to the high degree of disorder experienced at physiological temperatures, and due to ill understood properties not yet encountered in inorganic matter. In many cases, including force generation by biomolecules or biomolecular assemblies, photosynthesis, biocomputing, and aggregation, the systems are out of equilibrium. This poses further challenges for method development.
Improved Potentials
Reliable biomolecular simulations are extremely difficult because they involve complex systems such as charged macromolecules bathed in a solvent environment, long-range electrostatic interactions, correlation effects, and a high sensitivity to both temperature and dynamical effects. During the past decade, large-scale codes such as AMBER, CHARMM, and NAMD – which are primarily based on empirical, classical MD potentials, have been the mainstay of biomolecular simulations. Much has been learned, but there is a clear understanding that such an approach has inherent limitations. For instance, biomolecular simulations often involve bond breakage, charge transfer, electronic correlation effects, excited states, etc. Clearly, a treatment of these issues necessitates a quantum mechanical description, which is computationally much more demanding than a classical approach. In turn, large-scale biomolecular simulations often involve solvation effects, whose atomistic description can consume the majority of cycles in a given MD simulation. A continuum description for distant solvent molecules can substantially diminish the cost of biomolecular simulations, thereby enabling simulations of complex processes at biologically relevant length and time scales.
Based on these general considerations, we feel that some of the challenges facing the biomolecular simulation community must include the continued development of classical force fields based on physics principles, as opposed to empirical, knowledge-based potentials. It has been noted that knowledge-based potentials have had success in modeling proteins; this success is largely confined to protein systems with homologs in the Protein Data Bank. They fail to predict structures outside of this domain, and because they are based on ad hoc statistical modeling as opposed to true physics principles, it is difficult to remedy their shortcomings. Moreover, it is impossible to calculate ensemble averages with them, so that predictions of free energy changes are precluded. Force fields that are based on true physics principles, on the other hand, offer a way out of this dilemma. Unfortunately, current potentials need improvement. Currently, it is understood that the greatest loss of accuracy in the modeling of classical potentials is in the non-bonded interactions – mainly the delicate, long-range electrostatic and dispersion interactions. We note that force-field development is often a long, arduous enterprise that needs the support of the entire simulation community. A better understanding of hydrogen bonds, which have energies around room temperature, is particularly important, as most biology takes place at room temperature, and so involves the making and breaking of hydrogen bonds.
Multiscale Approaches
There is a need for the development of efficient and accurate computational tools at every energy scale of the problem – i.e., quantum mechanical, classical molecular dynamics, and continuum, and the ability to couple them in such a way as to achieve breakthrough simulations. We believe that the community would benefit considerably through the development of “mix-and-match” type of modules, which would enable the coupling of standard quantum chemistry and density functional theory based packages with standard classical codes such as AMBER, CHARMM, and NAMD.
Hand-in-hand with the development of better force fields and a better description of biomolecules, it is also important that attention be paid to the timescale problem. Current biomolecular simulations range up to the order of 10's to 100's of nanoseconds, which is too short to model many biomolecular processes. It is clear that novel and new algorithms will be needed to overcome this problem. Most likely, these will fall into two broad categories: (a) fast dynamics whose aim is to extract the long-time dynamics as accurately as possible. The remedy here will most likely involve a coarse-graining of systems at different levels – the approach will most likely be system dependent; (b) fast dynamics whose aim is to accelerate a system or explore phase-space rapidly.
Diffuse motions of biomolecules on a scale of microseconds and longer are involved in many biological functions, like enzyme activity and the operation of the ribosome. Methods that suppress the higher frequency molecular motions are useful here, where MD cannot produce results. One promising new approach is to constrain a biomolecule by imposing constraints associated with the covalent and hydrogen bonds as well as hydrophobic tethers, and then study the subsequent large scale diffusive motions. This has the advantage that it scales roughly linearly with size, so very large biomolecular complexes with ~ million atoms and larger can be handled, and where geometric and steric effects are likely to be dominant in the formation and subsequent behavior of the complex. Such methods are faster than classical MD by orders of magnitude and can give insight by locating the rigid and flexible regions in biomolecular complexes. The flexible and rigid regions can be used to identify interfaces when smaller units dock together to form stable three dimensional scaffolds, and the biological functionality can then be related to the actual motions associated with the flexible regions.
Another approach may lie in a concise representation of the conformational space of biopolymers obtained through very extensive sampling. Such sampling can be carried out in parallel computations, rather then sequentially as needed in case of following an actual motion. Obviously, a parallel approach has great benefits since it can be carried out effectively on modern computers that furnish ever higher processor counts, but only limited speed increases. The needed concise presentation could map topology-conserving networks onto the energetically accessible domains and valleys of the conformational space and guiding through its nodes and links coarse-grained trajectories, e.g., from an unfolded to a folded state of a protein.
Summary
The characterization of biological systems at the molecular level is now slowly reaching a precision that compares well with that to which the physical sciences have been accustomed. This is particularly true at the biomolecular level that ultimately is the foundation for all of life. The new data, like numerous high resolution structures of biomolecules or single molecule recordings, pose a challenge to the life sciences that can be largely met through the conceptual and methodological approaches of theoretical physics. Condensed matter physics and materials science have successfully linked experiment and theory for inorganic matter, often of macroscopic scale; their culture of the combination of experiment and theory can likely benefit living matter when the challenge posed by the inherent finite size and complexity of living matter systems is met.
Molecular level theoretical descriptions can go far in understanding the function of complex biological systems, but only if working in concert with experiments. Funding should focus initially on model systems that are (1) complex enough to warrant a systemic description and simple enough so that one can connect the behavior of the system to the description of its biomolecular components and (2) for which we have corresponding experimental data on all necessary levels. Fundamental theoretical questions should drive studies. The non-equilibrium nature of many of the problems of interest should be kept in mind.
Understanding the mechanical properties of biomolecules is fundamental to a variety of frontier problems in biology. Historically, the area of single-molecule force measurement and theory is an important example of the successes of physics and physicists in the investigation of biomolecules such as DNA and protein. Beyond the scale of single molecules, physicists have made significant progress in understanding the materials properties of large protein complexes that make up, e.g. the cytoskeleton. These materials properties and dynamics are essential to biology since:
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understanding the nanoscale dynamics and conformational fluctuations of proteins is necessary to elucidate their biochemistry including protein/ligand binding and protein/DNA interactions,
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studying force propagation in the cytoskeleton will lead to a better understanding and perhaps control over cell adhesion, motility, and mechanosensory transduction.
One of the key functions of certain classes of biomolecules is to either induce or transfer charge carriers of various types (electrons, protons, excitons, etc). Currently the details of the mechanisms of charge separation and subsequent transport, and transduction are poorly understood. To enhance our understanding of these important classes of biomolecular problems, will require new quantum mechanical tools (e.g., advances in density functional theory, quantum chemistry, and quantum Monte Carlo techniques for understanding of charged and excited states), as well as a more detailed understanding of the coupling of the biomolecule to its immediate environment. This is an area whose implications feed back into nanotechnology. Specifically, there is considerable hope in the community for new biomolecular electronic devices and biosensors. Issues likely to be important here are the coupling of biomolecules to inorganic materials leading to new classes of Biomolecular ElectroMechanical Systems (BEMS).
The rapid advances in nano-electronics and molecular electronics opens up a new frontier for the development of biomolecular devices. Two research thrusts are immediately clear.
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We must increase our efforts to exploit the diverse form and functional properties of biomolecules to construct nano-devices. They have the capacity to perform complex functions that otherwise could not be achieved, or could only be achieved with much larger and complex architectures.
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Organic or inorganic nanodevices can interact with biomolecules or even bio-systems to function as sensors, monitors, or to interface with living systems.
The simplest molecular electronic elements are memory, switch or logic devices, but advances using biomolecules can lead to elements that mimic processes in photosynthesis or respiration. Electrical conduction, or electron transfer, through biomolecules is not as simple to understand or model as in metals and semiconductors, and this complexity presents new challenges for theoretical techniques and technique development. For short molecules, the electron transfer process often is quantum mechanical tunneling. The quantum mechanical nature of the problem can lead to new discoveries and interesting effects such as the Coulomb blockade. The strong electron-vibrational coupling leads to important vibronic effects producing polarons and electron hopping between localized sites. The effects of water, pH, and ions in solution are fundamental topics that have a large effect of the electronic properties of biomolecules, and will surely play important roles in understanding the full potential of devices in bio-environments. There are many opportunities for the further development of the quantum mechanics and many body physics occurring in these areas. The field is just emerging, and there is a need to produce clear successful examples of theory coupled to experiment which produce guideposts for further development.
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 |