Historical review

1926

E. Gaviola created the first instrument for fluorescence measurement, which he called a fluorometer.

1934

F. Perrin formulated the relation between fluorescence depolarisation and Brownian rotary motion for hydrodynamic spherical molecules. In 1936 he extended his treatment to symmetric top molecules.

1952

G. Weber first applied Perrin theory to biological macromolecules. Numerous fluorescence polarisation measurements were carried out under steady-state conditions, utilising constant illumination. Most of them were performed on dye-conjugated macromolecules to determine the harmonic mean rotational relaxation time. Weber's classical review of the application of polarised fluorescence, particularly to proteins, appeared in the 1950s.

1961

A. Jublonski proposed following the rotational relaxation process directly by measuring the decay of the fluorescence polarisation as a function of time. He stressed that time-dependent anisotropy can be interpreted more directly and definitely than its time-average value observed with constant illumination.

1966

P. Wahl, and two years later L. Stryer, experimentally measured the time decay of fluorescence polarisation on dye-conjugated globular proteins.

1969

T. Tao derived relations between the time-dependent fluorescence polarisation anisotropy and the Brownian rotational diffusion coefficients of macromolecules. It was shown that in the most general case of a completely asymmetric body, five exponentials appear in anisotropy. In 1972 analogous results were obtained by other groups (G. G. Belford, R. L. Belford and G. Weber; T. J. Chuang and K. B. Eisenthal).

The ideal biophysical method would be capable of measuring atomic positions in molecules in vivo. It would also permit visualisation of the structures that form throughout the course of conformational changes or chemical reactions, regardless of the time scale involved. At present there is no single experimental technique that can yield this information.

A brief history and perspectives

Molecular biology was born with the double-helix model for DNA, which provided a superbly elegant explanation for the storage and transmission mechanisms of genetic information (Fig. 1). The model by J. D. Watson and F. H. C. Crick and supporting fibre diffraction studies by M. H. F Wilkins, A. R. Stokes, and H. R Wilson, and R. Franklin and R. G. Gosling, published in a series of papers in the 25 April, 1953 issue of Nature, marked a major triumph of the physical approach to biology.

The Watson and Crick model was based only in part on data from X-ray fibre diffraction diagrams. The patterns, which demonstrated the presence of a helical structure of constant pitch and diameter, could not provide unequivocal proof for a more precise structural model. One of the ‘genius’ aspects of the discovery was the realisation that A–T and G–C base pairs have identical dimensions; as the rungs of the double-helix ladder, they give rise to a constant diameter and pitch.

Historical overview and biological applications

The term thermodynamics is derived from the Greek therme meaning heat and dynamis meaning strength or force. Thermodynamics, as a science, has its beginnings in the nineteenth century, with the first experiments exploring the relationship between heat and work, the definitions of the concepts of temperature and energy and the clear enunciation of the first and second laws of thermodynamics. Classical thermodynamics uses a phenomenological approach based upon these laws, in contrast to statistical thermodynamics, which tries to establish a more fundamental understanding of heat in terms of the kinetics of large assemblies of atoms or molecules. The concept of work was generalised beyond mechanical work to include all forms of energy such as electric, magnetic, chemical, and radiation energy. The validity of thermodynamics was established for all types of system, from a volume of perfect gas at a given pressure to thermonuclear plasma, encompassing magnetic systems, liquid–vapour systems, macromolecular solutions, chemical reactions etc. In this chapter, we are concerned, in particular, with the applications of both classical and statistical equilibrium thermodynamics to biological macromolecules, their solutions and interactions.

Early in the seventeenth century, Galileo Galilei and his followers constructed the first thermometers, allowing reproducible measurements of temperature. Joseph Black (1728–1799) built the first calorimeter; he is considered the founder of calorimetry. His measurements led to the theory of caloric, a conserved elastic fluid that had weight and was associated with temperature. Antoine-Laurent Lavoisier (1780) performed the first calorimetric measurements in biology.

Historical review

1920s

M. Smoluchowski and E.Hückel were the first to elaborate the theory of electrophoresis for thin and thick double layers. D. C. Henry provided a theory for the electrophoresis of spherical polyions that was valid for double layers of arbitrary thickness. In the Henry model, charge distribution within the sphere is assumed to be spherically symmetric, and ion relaxation is ignored. In the 1950s a number of investigators (J. Th. G. Oberbeek, F. Booth, P. H. Wiersma) studied the effect of ion relaxation on the electrophoretic mobility of spheres containing a centrosymmetric charge distribution.

1930

A. Tiselius presented a new technique for studying the electrophoretic properties of proteins. He showed that sharp electrophoretic moving boundaries of ionised molecules could be obtained in U-shaped quartz glass tubes and that the protein boundary could be detected with UV light. A. Tiselius described moving boundaries corresponding to albumin, α-, β-, and γ-globulin in serum.

1940s

T. Wieland and E. Fischer proposed the use of filter paper as a supporting medium for electrophoresis. Simplicity of construction, relative cheapness and compactness, and the requirement of much less than 1mg of protein for analytical or diagnostic purposes popularised paper electrophoresis.

1950s

O. Smithies obtained good resolution of proteins using starch gels. Electrophoresis with molecular sieving of a gel gave a much higher resolution than electrophoresis in free solution. In this decade, many materials (like strips of cellulose acetate, agarose) were introduced as supports for electrophoresis.

Brief historical review and biological applications

1704

In OpticksIsaac Newton dealt with the formation of a spectrum by a prism, and the composition of white light and its dispersion. The Latin word, spectrum, means an appearance; a spectrum is obtained when radiation is broken up into its colour or wavelength distribution.

1800

The astronomer, William Herschel, discovered infrared (IR) radiation.

1801

The physicist Johann Wilhelm Ritter discovered ultraviolet (UV) radia-tion.

1814

Joseph von Frauenhofer showed that the Sun's spectrum contained dark lines (later named Frauenhofer lines), indicating that light of the corresponding colour was missing because of absorption.

1850–1900

August Beer stated the empirical law, which was named after him, that there is an exponential dependence between the transmision of light through a substance, the concentration of the substance and the path length of the beam through it. The law is also known as the Beer–Lambert law or the Beer–Lambert–Bouguer law, in recognition of the work of Pierre Bouguer (1729) and Johann Heinrich Lambert (1760). Gustav Kirchhoff's discovery that each pure substance has a characteristic spectrum provided the basis for analytical spectroscopy. Gustav Kirchhoff and Robert Bunsen identified the chemical elements in the Sun by analysing its spectrum. Johann Jacob Balmer identified a numerical series in the spectrum of hydrogen. Joseph John Thomson discovered the electron. Max Planck introduced the concept of quanta in the treatment of heat radiation and laid the foundation of quantum theory. He was awarded the Nobel prize in 1918.

Theory of small-angle scattering from particles in solution

Small-angle scattering (SAS) is a very useful method in biochemistry, providing information on molecular masses, shapes and interactions in solution (see Comment G2.1).

Dilute solutions of identical particles

In order to have an observable signal in X-ray or neutron SAS a solution of the order of 100 μl containing a few milligrams per millilitre of macromolecule is required – corresponding to about 1015 particles for a 50 kDa protein at 1 mg ml−1 (we note that 1 mg ml−1, the usual unit in biochemistry is in fact equal to 1 g l−1, the unit more conveniently used in equations).

We first consider solution conditions such that the particles do not influence each other, i.e. the position and orientation of each particle is totally independent of that of the others. This is the infinite dilution condition, for which we say there is no interparticle interference. In practice, it is achieved at different, low, concentrations for different macromolecules and solvents. For example, the condition may well be satisfied for a given protein at a few milligrams per millilitre, in a neutral pH buffer, but tRNA molecules, which are highly charged at pH 7 in low-salt buffer, interact with each other even at these concentrations, and it might not be possible to reach the infinite dilution condition without increasing the solvent salt concentration.

Historical review

J.-B. Biot and F. Savart collaborated on the theory of magnetism. Their eponymous law (formulated in 1820) describes the motion of a charge in a magnetic field.

Ernst Abbe in 1872 formulated his wave theory of microscopic imaging. In 1878, he was able to correlate resolution and wavelength of light mathematically. A few years later, through the company Zeiss, he commercialised the first ever lenses to have been designed based on sound optical theory and the laws of physics.

In the second half of the nineteenth century, J. C. Maxwell established the laws of electromagnetism. His equations first appeared in fully developed form in his book Electricity and Magnetism (1873).

In 1897 J. J. Thomson discovered electrons by demonstrating cathode rays were actually units of electrical current made up of negatively charged particles of subatomic size. For these investigations he won the Nobel Prize for physics in 1906.

In his doctoral thesis of 1924, de Broglie theorised that matter has the properties of both particles and waves. He received the 1929 Nobel Prize for physics. The particle–wave duality was confirmed experimentally, for the electron, a few years later by C. J. Davisson and L. H. Germer and by G. P. Thomson. Thomson and Davisson jointly shared the Nobel Prize in physics in 1937.

In 1926 H. Busch described a lens for electrons. H. Ruska subsequently built the first working electron microscope in 1930 (Nobel Prize in 1986).

Historical review

Early 1980s

G. Binning and H. Rohrer proposed the scanning tunnelling microscope (for which they were awarded the Nobel Prize). This invention has initiated an exciting series of novel experiments to image the surface of conducting as well as insulating solids with atomic resolution. The first attempts at imaging biological molecules using a scanning tunnelling microscope (STM) date back to 1983. In 1987, individual molecules of phthalocyanine, lipid bilayers and ascorbic acid were reported. One year later, H. Ohtani with collaborators imaged benzene, the molecule of Kekul′e 's blue dream, as three-lobed rings. In 1989 a spectacular view of the double-stranded Z-DNA molecule, the first biological macromolecule studied using a STM, was presented.

1986

G. Binning, C. F. Quate and C. Gerber invented the scanning force microscope (SFM). In this microscope a sensor tip carried by a flexible cantilever is used to touch and characterise a surface. This was a significant breakthrough which allows biological macromolecules to be scanned in aqueous solution and gives reproducible imaging of DNA and of membrane protein crystals.

Early 1990s

D. J. Keller, Q. Zhong and C. A. J. Putman independently proposed the so-called tapping mode of the atomic force microscope (AFM), in which the cantilever is oscillated vertically while it is scanned over the sample. In this mode the image is formed by displaying the reduction of the oscillation amplitude at every point of the sample.

Historical review

1850

T. Graham observed that egg albumin diffuses much more slowly than common compounds such as salt or sugar. In 1861 he used dialysis to separate mixtures of slowly and rapidly diffusing solutes, and made quantitative measurements of diffusion on many substances. On the basis of this work he classified matter in terms of colloids and crystalloids.

1855

A. Fick, in the equations now known as his first and second laws, defined a diffusion coefficient (D) to describe the flow of a solute down its concentration gradient. J. Stefan (1879) and L. Boltzmann (1894) developed mathematical integral forms of the second law, opening the way for the experimental determination of diffusion coefficients by various methods.

1905–1906

A. Einstein, W. Sutherland and M. von Smoluchowski determined that steady-state solutions of Fick's equations have a direct analogy in heat flow along a temperature gradient, and established mathematical relations between diffusion and frictional coefficients in Brownian motion. In 1905, W. Sutherland used a value of D calculated by J. Stefan from data collected by T. Graham, to obtain a molecular weight of 33000 for egg albumin (the true value is about 45000).

1926

L. Mandelshtam recognised that the translational diffusion coefficient of macromolecules could be obtained from the spectrum of scattered light. However, the lack of spatial coherence and the non-monochromatic nature of conventional light sources rendered such experiments impossible until 1964 when H. Cummins, N. Knable and Y. Yeh used an optical-mixing technique to resolve spectrally the light scattered from dilute suspensions of polystyrene latex spheres.

The present chapter is included in Part E with the other optical spectroscopy methods; however, the development of two-dimensional IR (2D-IR) spectroscopy is strongly based on two-dimensional NMR, and it is easier to understand after reading the relevant sections in Part J, which the reader is strongly encouraged to do first.

Historical review and introduction to biological problems

1950

O. Hann proposed coherent spectroscopy – the use of radiation fields with well-defined phase properties – to extract information about atoms and molecules. The ‘spin echo’ experiment in nuclear magnetic resonance was the first demonstration of the possibilities of coherent spectroscopy.

1957

R. P. Feynman, F. L. Vernon Jr. and R. W. Hellwarth published a landmark paper pointing out that if coherent light fields were ever created, it would be possible to use these same methods on optical transitions. The invention of the laser in 1960 was followed quickly by a demonstration of the ‘photon echo’ – the optical version of the ‘spin echo’.

1998

R. M. Hochstrasser and collaborators proposed 2D IR spectroscopy, in analogy with two-dimensional NMR, for the determination of time-evolving structures. The spins associated with the different nuclei in NMR are replaced in the IR experiments by a network of vibrational modes whose coupling can be used to determine molecular structure and dynamics. Structures of dipeptides, tripeptides and pentapeptides were determined by 2D IR spectroscopy. The most exciting aspect of 2D IR spectroscopy, however, is the combination of its sensitivity to structure with time resolution.

Historical review

In 1963 Richard Feynman traced to Pythagoras (c. 500bc) the first example, outside geometry, of the discovery of a numerical relationship in Nature. Pythagoras' discovery, which led to the foundation of a school of thought with mystic beliefs in the power of numbers, was that two strings under the same tension but of different lengths give a pleasant sound when plucked together if the ratio of their lengths is that of two small integers. We now say that a ratio of 1:2 corresponds to an octave, a ratio of 2:3 to a fifth and so on, which are all harmonic sounding chords. Feynman analysed this discovery in terms of three characteristics: its basis in experimental observation, the use of mathematics as a tool for understanding Nature, and its concern with aesthetics (the ‘pleasant’ quality of the sound). With easy hindsight (as he readily admits!) Feynman wrote that if Pythagoras had been more impressed by the first point on the importance of experimental observation the science of physics might have had an earlier start.

We discovered the existence and seek our biophysical understanding of macromolecules through experiment, and we use mathematical tools not only to set up experiments and analyse the results, but also for the description of the studied ‘objects’ themselves. The basis of aesthetics may still remain as mysterious as in Pythagoras' time, but there is no doubt that the ‘beauty’ of the DNA double helix and the satisfyingly elegant way in which it provided an explanation for how genetic information is stored and transmitted was an essential inspiration in the development of modern molecular biology.

Historical overview and introduction to biological applications

We recall from Chapter A1 that biological events occur on an immensely extended range of time scales – from the femtosecond of electronic rearrangements in the first step of vision, to the 109 years of evolution. Thermal energy is expressed as atomic fluctuations on the picosecond–nanosecond time scale that constitute the basis of molecular dynamics. These fluctuations are of particular interest in biophysics because they result from and reflect the forces that structure biological macromolecules and the atomic motions and molecular flexibility associated with biological activity.

Thermal energy propagates through solids in waves of atomic motion, such as the normal modes discussed in Chapters A3 and I1. We can estimate values for the frequencies, wavelengths and amplitudes of thermal excitation waves from an order of magnitude calculation, e.g. by considering the movement of a mass similar to the mass of an atom moving in a simple harmonic potential of energy equal to Boltzmann's constant multiplied by 300 K (ambient temperature). It turns out that the frequencies are of the order of 1012 s−1, while the wavelengths and amplitudes are on the ångström scale. We saw in Part E that the energy associated with thermal vibrations corresponds to the IR frequency range in optical spectroscopy. Similarly, neutron spectroscopy takes advantage of the fact that the energies of thermal neutron beams match vibrational energies in solids and liquids.

Historical review

1845

G. Stokes showed that the translational friction for a sphere is proportional to its radius, and to the viscosity of its surrounding solvent. In 1856 he demonstrated that for small angular velocity the rotation of the sphere may be characterised by a single parameter, which is proportional to the linear dimensions cubed.

1893

D. Edwardes calculated two frictional coefficients of the rotation for an ellipsoid of revolution: one for rotation around the axis of revolution and another for rotation around a direction normal to the first. In 1906 A. Einstein showed that rotation of the sphere in Stokes' approximation may be characterised by a single constant which has the dimensions of time. In 1928 R. Gans used the Edwardes frictional coefficients for an ellipsoid of revolution to calculate the ratios of the principal relaxation times to the relaxation time of a sphere of equal volume. In 1936 F. (Francis) Perrin presented equations that give the three rotational coefficients and three rotational relaxation times as functions of the dimensions of a three-axis ellipsoid. These equations could not be expressed in terms of elementary functions. In 1960 L. D. Favro showed that diffusion coefficients related to the rotational motion of a general particle involve five relaxation times; when two of the diffusion coefficients are equal the number of relaxation times is reduced to three. In 1977 E. Small and I. Isenberg solved Perrin's equations for the rotational diffusion of a general ellipsoid using a numerical integration procedure.

Historical review

1913

A. Dumansky proposed the use of ultracentrifugation to determine the dimensions of colloidal particles.

1923

T. Svedberg and J. B. Nichols constructed the first centrifuge with an optical system to follow particle behaviour in a centrifugal field. One year later, Svedberg noted the decrease in absorbance at the top of the cell during centrifugation of a haemoglobin solution.

1926

Svedberg made the first measurements of protein molecular weights (haemoglobin and ovalbumin) by sedimentation equilibrium and in 1927 he determined the molecular weight of haemoglobin using a combination of sedimentation and diffusion data. These pioneering studies led to the undeniable conclusion that proteins are truly macromolecules, made up of a large number of atoms linked by covalent bonds (Comment D4.1).

(Comment D4.1)

1929

O. Lamm deduced a general equation describing the behaviour of the moving boundary in the ultracentrifuge field. The exact solution of the equation is an infinite series of integrals, which can be computed only by numerical integration. In later work, the Lamm equation was solved analytically for specific limiting cases (H. Faxen, W. J. Archibald, H. Fujita).

1930s

Schlieren optical systems were designed by J. St. L. Philpot and H. Svenson, and independently by L. G. Longsworth; these allowed a representation of the concentration gradient (or, more precisely, the refractive index increment) as a function of distance in the centrifuge sample cell.

Historical review

1869

J. Tyndall performed the first experimental studies on light scattering from aerosols. He explained the blue colour of the sky by the presence of dust in the atmosphere.

1871

Lord Rayleigh presented the theory of scattering from assemblies of non-interacting particles that were sufficiently small compared with the wavelength of light. According to Rayleigh, scattering by a gas occurs because of the fluctuation of the molecules around a position of equilibrium. Rayleigh obtained the formulae that explained the blue colour of the sky as being due to preferential scattering of blue light in comparison with red light by molecules in atmosphere.

1906

L. Mandelshtam raised the question on the nature of scattered light once again. He pointed out that Raylegh's arguments do not fully explain the scattering phenomenon. According to Mandelshtam light scattering is also due to the random fluctuations of molecules near the position of equilibrium. As a result of random fluctuations of order λ3, where λ is the scattering wavelength, the number of macromolecules will vary with time. It follows from the Mandelshtam theory that the translational and rotational diffusion coefficients of macromolecules could be obtained from the spectrum of the scattered light.

1924

L. Mandelshtam described theoretically and experimentally so-called combination light scattering, which was later called Raman scattering. As early as 1926 he recognised that the translational diffusion coefficient of macromolecules can be obtained from the spectrum of the light they scatter.

EM in biology

Structural biology with EM

Electron microscopes can provide vivid details of biological macromolecules at the nanometre scale.

Recall from Chapter H1, an electron image is a two-dimensional projection of the object along the electron beam. A three-dimensional reconstruction of the object can be obtained by combining data measured at different angular projections. In single-particle reconstruction, a population of molecules is imaged. If these are identical (monodisperse) and present in sufficient quantities, the data from differently oriented molecules can be combined to produce an accurate three-dimensional reconstruction of the structure. The presence of symmetry is taken advantage of in helical reconstruction and two-dimensional crystallography. In tomography, the same object is imaged at different orientations. The different images are then combined together to recreate its structure.

Examples of electron cryo-microscopy reconstructions

In EM, the image is the result of the interaction of the incident electrons with the electrostatic distribution due to the atomic structure of the sample. The reconstruction of the structure results from the analysis of many images. Three-dimensional reconstructions at different resolutions depict the object at different levels of detail (Figure H2.1).

At atomic resolution, it is a good approximation to understand this structural density as being equivalent to the electron density obtained by X-ray diffraction, but with a larger contribution from hydrogen atoms in the electron diffraction case. It should furthermore be possible to distinguish the charge state of amino acids.

Introduction

All living things, despite their profound diversity, share a common architectural building block: the cell. Cells are the basic functional units of life, yet are themselves comprised of numerous components with distinct mechanical characteristics. To perform their various functions, cells undergo or control a host of intra-and extracellular events, many of which involve mechanical phenomena or that may be guided by the forces experienced by the cell. The subject of cell mechanics encompasses a wide range of essential cellular processes, ranging from macroscopic events like the maintenance of cell shape, cell motility, adhesion, and deformation to microscopic events such as how cells sense mechanical signals and transduce them into a cascade of biochemical signals ultimately leading to a host of biological responses. One goal of the study of cell mechanics is to describe and evaluate mechanical properties of cells and cellular structures and the mechanical interactions between cells and their environment.

The field of cell mechanics recently has undergone rapid development with particular attention to the rheology of the cytoskeleton and the reconstituted gels of some of the major cytoskeletal components – actin filaments, intermediate filaments, microtubules, and their cross-linking proteins – that collectively are responsible for the main structural properties and motilities of the cell. Another area of intense investigation is the mechanical interaction of the cell with its surroundings and how this interaction causes changes in cell morphology and biological signaling that ultimately lead to functional adaptation or pathological conditions.

A wide range of computational models exists for cytoskeletal mechanics, ranging from finite element-based continuum models for cell deformation to actin filamentbased models for cell motility.