Notes on "Biological Physics," Part II

I finished the review of "Biological Physics" today, which included the sections on bioenergetics, forces, and single-molecule experiments. I skipped the section on reaction theory because I am not familiar with the topic and it didn't interest me as much as the others.

There are two primary topics in bioenergetics at the biomolecular level: charge transport and light transduction. Charge transport refers to the process by which isolated charges travel amongst different sites in a complex molecule. This process is inherently quantum mechanical, since electrons and holes may actually tunnel into different sites in the molecule, depending on the molecule's conformation.

Light transduction refers to the conversion of energy in a photon to chemical or electronic energy. A paragraph is dedicated to human vision and the photo-induced isomerization that is central to its operation, but the rest of this sub-section is devoted to photosynthesis.

During photosynthesis, "antenna systems" in the chlorophyll molecules capture light energy, which is transferred to other parts of the plant cell along excited molecular states, much like in Foerster resonance energy transfer. The transfer is so fast that the quantum mechanical coherence of the excited states likely plays a role. It seems that most of the work done up to the point in time when the article was written has been performed by theorists.

The various forces in the cell are typically "effective" forces models typically neglect the fundamental electromagnetic nature of the primary forces in the cell. At the protein level, enzymes may actually pull apart the covalent bonds in "violent" events. It's also been hypothesized that mechanical vibrations in the form of solitons can propagate along the covalently-bonded protein backbone, but this is strongly debated.

The transmission of forces through a heterogeneous medium, like the cell membrane is also a topic of study.

Finally, single-molecule studies are gaining prominence as experimental techniques become more refined, but "the challenge of studying individual protein molecules is still very much in its infancy... The key is to use extreme dilution so that only a single biomolecule is in the reaction volume."

Much single-molecule work has been done on DNA because it is simple and readily obtained. Spring-like forces in DNA are both enthalpic, which means they depend on the energy change due to deformation of electronic orbitals, and entropic, which means the DNA resists changing its shape due to interaction with its thermal environment.

In the conclusion, the authors anticipate that problems relating to the brain lie ahead as major areas of work in biological physics.

It would seem that the experimental study of proteins remains a major challenge to biological physics, but also is perhaps the most worthwhile to pursue. Photosynthesis, the effects of a protein's environment on its folding and charge transport, disordered protein behavior, and the forces between parts of proteins are not very well-understood. If there are new discoveries to be made, then I think they lie in protein dynamics.

Notes on "Biological Physics," Part I

There is an article from 1999 in Reviews of Modern Physics entitled "Biological Physics." This review summarizes research during the twentieth century where "physics has influenced biology and where investigations on biological systems have led to new physical insights." The exchange of ideas between the two fields has not been of equal magnitude, the authors note. Many tools from physics have found their way into the biological sciences, though some biological systems have led to new physics, usually in the form of providing experimental testbeds for new physical theories. The article is primarily concerned with molecular biological physics.

The seven primary sections of the review are

1. The structures of biological systems
2. Complexity in biology
3. Dynamics, mostly within proteins
4. Reaction theory, where biology has provided testbeds for new physical theories
5. Bioenergetics
6. Forces
7. Single-molecule experiments.

Most of the interesting ideas I've found so far in the article are associated with the complexity and dynamics of biomolecules. Particularly, there is an idea known as the principle of minimal frustration. From the Wikipedia article,

"This principle says that nature has chosen amino acid sequences so that the folded state of the protein is very stable. In addition, the undesired interactions between amino acids along the folding pathway are reduced making the acquisition of the folded state a very fast process. Even though nature has reduced the level of frustration in proteins, some degree of it remains up to now as can be observed in the presence of local minima in the energy landscape of proteins."

This idea came from a theory of energy landscapes for proteins that was developed by Bryngelson and Wolynes. In language that I'm more familiar with, the potential energy of the molecules has some fractal-like structure, because from Section III in the article the authors state that

"The kinetic observations suggest that the energy landscape might have a hierarchical structure, arranged in a number of tiers, with different tiers having widely separated average barrier heights."

It seems like structural determination of proteins and other biomolecules has become something akin to bookkeeping. The tools exist and are refined to find static structures, like neutron scattering and NMR. Additionally, the energy landscape theory for protein folding seems to be mature at this point as well. So what open-ended questions still exist in biological physics? After reading up to section V, I've compiled the following grand problems in biological physics as I've interpreted them from this paper only:

1. "A synthesis that connects structure, energy landscape, dynamics, and function has not yet been achieved." This seems to suggest that there is some degree of incoherence between these individual fields of study, so ideas that link them together are required.
2. Biochemists can now synthesize their own proteins, but can they do this in a useful manner, for, say, molecular and microscopic engineering purposes?
3. Sensing and characterizing phase transitions, especially in glassy systems, could lead to better experimental investigations into protein folding.
4. "Understanding protein folding can improve the capability of predicting protein structure from sequence." Apparently there's a lot of DNA sequence information, but predicting what proteins come from it is nontrivial.

Does improving microscopy mean improving biology?

In my last article I began exploring the relationship between optics and biology to better determine to what extent optics is capable of solving problems in biology, particularly molecular and microbiology. I posed a set of questions, one of them asking whether "...the current trends in improving microscopies [will] lead to answers of the fundamental questions of molecular and microbiology."

Let me start this brief essay by stating my own current opinion, which is based primarily on speaking with biologists and perusing the internet. I believe that the fundamental problems in biology lay at the molecular level and at the systems level. The molecular-level problems include how certain proteins fold and are transported through organelles like the Golgi bodies [1].  The systems-level problems deal with the coherent interaction of the many elements within an organism. To illustrate this, consider how the coordinated actions of various cells (such as Schwann cells, astrocytes, and neurons) lead to an effective functionality of the nervous system.

Microscopy unfortunately is ill-suited to exploring either of these two levels. It is true that fluorescence microscopy has allowed us to specifically target some structures of interest inside a cell and that superresolving microscopies for beating the diffraction limit exist, like PALM and STORM. However, fluorescent markers--which are also used in PALM and STORM--are known to adversely affect the behaviors of live cells. PALM and STORM are furthermore very complex to implement and limited to some degree by their data acquisition times [2].

One popular line of microscopy research is label-free microscopy, whereby images are acquired without introducing any artificial contrast-generating mechanism into the sample. One example is based on stimulated Raman spectroscopy (SRS). This approach usually is a spectroscopic technique that involves inferring what collection of known substances contributed to a measured spectrum from an image. Achieving a good resolution with SRS or any other label-free technique usually means allowing for a severe increase in the measurement time. At the time of this writing, I see neither the spatial nor temporal resolution of label-free microscopies as good enough for addressing the current open-ended biological problems.

At the systems level, microscopy is simply not the tool to use. I think that computer modeling and experiments on live animals are the norm here, though I am not saying that optics cannot play any role.

Overall, I think that we optical scientists are placing too much emphasis on improving light microscopy [3]. It seems to me that the information that biologists require is not found in images but rather in some other form. This is not to say that optics is of no use to biology. Take the technique known as dual polarization interferometry, for example, which uses light to probe protein crystal and lipid bilayer growth on waveguides. As another example, consider that optical tweezers have been influential in measuring the mechanics of biopolymers like DNA.

So what should we focus our attention on? I think label-free sensing mechanisms are in the right direction because they risk minimal alteration to cell and biomolecule functionality. I also think that techniques for sensing dynamic phenomena will trump anything that looks at the structure of fixed (dead) cells. Structure at this point seems well-known to biologists, but how structure evolves in time is not. Finally, controlling biological systems with light seems incredibly promising (e.g. optogenetics), though I think it is too early to tell whether it'll be valuable in deepening our knowledge.

I will hopefully address whether optics is the best tool for fulfilling these characteristics in the future.

Some references
The Wikipedia articles on Molecular biology, the Central dogma of molecular biology, and Biophysics are worth reading.

Stanford Encyclopedia of Philosophy entry on Molecular Biology

Seven fundamental, unsolved questions in molecular biology: Cooperative storage and bi-directional transfer of biological information by nucleic acids and proteins: an alternative to “central dogma”

Notes
[1] I have personally been exposed to a problem of the mechanics of certain biopolymers in regulating the structure of mitochondria. Biopolymers may arguably lie outside the realm of molecular biology since they are made of many, many molecules and not just a few, but I believe that my experience with this problem gave me some good insight.

[2] I have heard that Nikon microscopes are now offering STORM capabilities.

[3] I should point out that I think that the work in improving microscopies IS worth doing, I'm just not so certain that so much attention should be given to it.

An optical scientist considers the question: what do biologists want from a microscope?

Optics and biology have been intertwined for hundreds of years. Robert Hooke and Antonie van Leeuwenhoek both contributed greatly to the fields of microscopy and microbiology in their infancy, advancing each field by establishing a greater understanding in the other. As optics evolved and technologies derived from it became more refined, the number of discoveries in the realm of microbiology witnessed a concomitant increase. This fact was perhaps recognized in part with the award of the Nobel Prize in Physics in 1953 to Fritz Zernike for the phase contrast microscope, a tool which rendered otherwise invisible cells visible with relatively modest modifications to an existing microscope. Much work in microbiology followed as a result of this along with other developments in optics.

The relationship seemed to change, though, starting in the mid-twentieth century with the advent of molecular biology. During this time, molecular biological technologies evolved and matured to the point where discoveries were facilitated primarily by non-optical means, with microscopes serving as more of a tool for routine lab work than as significant drivers for learning something new. After all, a traditional light microscope is limited to observing structures no smaller than about one wavelength of light across, or about half a micron (one millionth of a meter). DNA, proteins, and all the other biomolecules are just too small to see, even for the most powerful microscope objectives.

Of course one could argue that the development of the targeted fluorescent proteins that reveal the location of a molecule's existence within a cell helped to advance the field of optics, but in this case the role of enabler switched sides; molecular biology led to an increase in the number of optical technologies for imaging fluorescent markers, such as fluorescence correlation spectroscopy. From the viewpoint of a scientist, this reversal is a bit distasteful. We would like for technology to enable new discoveries about the fundamentals of life, not for new discoveries to lead to technology that tells us what we already know.

Now we are well into the twenty first century and are rooted firmly within the scientific age of molecular biology and biotechnology. (The age of physics is now past and now concerns itself primarily with the ultimate limits of space: the infinitesimal quark and the awesomely large cosmos.) Given the history between optics and biology and the recent change in their relationship, I think it's necessary to make an assessment, so to speak, of this relationship.

In the near future I will write posts that explore this topic. I hope to answer questions like

1. What do biologists want out of a measurement technique?
2. Will the current trends in improving microscopies lead to answers of the fundamental questions of molecular and microbiology, or are we moving in the wrong direction?
3. Are optical scientists misguided in the search for improved images? Are there other forms of information carried by light that are more useful than images?
4. Will it be possible to better control biological processes using light?

How does subdiffusion arise in cells and why is it important?

In this month's Physics Today there is an interesting article entitled "Strange kinetics of single molecules in living cells" that discusses recent interpretations of single-molecule tracking experiments. In these experiments, fluorescent molecules or microbead probes are attached to some organelle or other piece of cellular material in a live cell and then tracked using video tracking microscopy. The paths taken by the molecules or beads are then analyzed and their motion is interpreted through random walk models. The goal is to learn something about the intracellular environment from the complicated motions of these probes.

The diffusion of these probes is almost always subdiffusive, which means that their mean squared displacements (the second moment of their position vs. time) grows slower than linearly with time, or

where r(t) is the position of the probe at time t and 0 < a < 1. The brackets denote an ensemble average, or a second moment calculated over a large number of probe trajectories. In these experiments, there does not exist a large enough number of probes for sufficient averaging, so instead the time average of a few probes is calculated. However, this produces wildly different results from particle to particle. The reason is that ergodicity may not apply to cellular transport. Ergodicity is a well-known property from statistical mechanics of systems whose ensemble averages are equivalent to time averages as time tends to infinity.

This article presented two possible models for why the probes behave in this way. One model, the continuous time random walk (CTRW), is nonergodic and subdiffusive for heavy-tailed probability distributions of particle waiting times. The other interpretation is that the cellular environment is spatially inhomogeneous so that "the environment sampled by the molecule during its motion through the cell differs from one trajectory to another."

If my understanding of their reasoning is correct, then I don't think that these two possibilities are logically equivalent. The random environment of the cell is a real, physical thing. The CTRW model is just that: a model. I feel that presenting these as two possibilities to explain the motion of the probes is like saying the earth revolves around the sun because either there is an attractive gravitational force between the two or the orbit is roughly elliptical with the sun at one foci. The first is a statement about the physics of the phenomenon and the other is a mathematical model. Perhaps the random cellular environment is the cause for the CTRW model to be valid. This line of reasoning I can accept.

The article concludes with very interesting remarks on why subdiffusion of proteins and biomolecules should occur at all. Subdiffusion is a way to make certain reactions more efficient by preventing the reactants from diffusing too far apart from one another. Considering normal diffusion (a = 1 in the expression above) as the most efficient manner of passive transport for cellular materials, subdiffusion may be understood as an evolutionary compromise between fast transport and efficient use of cargo in a crowded environment. Cells should not be viewed as "small, well-mixed reaction flasks," since their order actually enables crucial cellular processes.

Other notes:

1. Advances in improving the experiments' temporal resolution and finding smaller and brighter light emitters are the primary challenges to optics from single-molecule tracking experiments.
2. Fractional Brownian motion (first developed by B. B. Mandelbrot) is another random walk model that leads to subdiffusion but does not break ergodicity. It may model single particles in many-body systems, such as a monomeric unit in a polymer chain.
3. A fundamental question in cell biology concerns how the chromosomes are packed inside the nucleus. Are they separated by unseen walls or does their connectedness and limited volume keep them effectively disentangled.
4. While reading this article the following thoughts came to mind: superdiffusive transport, like transport of vacuoles by molecular motors, is a characteristic of nonequilibrium systems. Subdiffusion does not require a nonequilibrium system since the cells' physical constrains are the likely limiting factor to transport. Does this make subdiffusion and superdiffusion fundamentally different things?