Diffraction is not only for Crystals and X-rays

As should be apparent from the entries, comments and illustrations on this website, central to modern crystallography is the phenomenon of ‘diffraction’ of X-rays by crystals. It is the critical experimental observation in crystallography. Now, I would like to present a brief blog commentary to highlight the fact that the ‘diffraction’ effect is NOT only obtained from crystals and X-rays. It can be observed in other situations combining the interaction of ‘matter’ and ‘radiation’.  I will provide some brief background and I will discuss a serendipitous -common day- observation that will make you look through windows in the future in a different way.

Fig. 1a. The first diffraction patterns from cubic crystals of the mineral  Zinc blende first obtained in 1912 by Friedrich and Knipping, following a suggestion made by Max von Laue. Center the atomic structure of NaCl in cubic crystals inferred from W.H. Bragg and W.L. Bragg after studying the diffraction pattern of the structurally related Zn crystal.

The experiment was prompted by the suggestion by Max von Laue (German physicist, 1879-1960) that perhaps, if the X-rays were waves, they could be diffracted by a piece of matter that was supposed to have a regular atomic structure. This hypothesis about the internal structure of crystals had been suggested before by A. Bravais (French physicist, 1811-1863) and Abbé R. J. Haüy (French mineralogist, 1743-1822). It was the remarkable achievement of the experimental skills of Laue’s collaborators W. Friedrich and P. Knipping, that allowed to prove both things at the same time: the wave nature of the X-rays and the internal regular structure of crystals (Figs. 1a,b).

Fig. 1b. A moder Laue ‘type’ diffraction pattern obtained from a protein crystal using the intense beam from synchrotron sources

All of this seems to be far away from our regular daily life routines. However, during a casual look at a parking lot in a condominium in Norwalk, CT, visiting family, I was struck by how obvious the phenomenon of diffraction was. Having my cell phone readily available, I was able to photograph and document the observation (see accompanying images, Figs. 2-4).

The first image (Fig. 2, left),  shows the original photo from behind a balcony inside the condominium, with me taking the photo and four bright spots corresponding to the four strong lights in the parking lot. Careful observation of the bright images shows the central light spots coming from the lights and then something else (Fig.3) (right). Kind of a square cross pattern.  Aha!!!.

Fig. 2. Snapshot from the interior of a condominium of the view from a glass door.

Fig. 3. Close up of the central bright image from Fig. 2.

In addition, near the central bright spot, one can clearly see alternating bright and dark short lines along the horizontal and vertical directions. What is this? Where are these additional features coming from? Any ideas?

Finally, in the last close-up images (Fig. 4a,b, below), one can see  that there is a wire ‘screen-door’ in front of the glass through which I am seeing the image: look closely on the lower left-hand part of the two images.

Fig. 4a. Detail of Fig. 2 focusing on the far right images.

Aha!!. The alternating dark-bright lines along the horizontal-vertical directions (i.e. the cross) are the ‘diffraction pattern’ of the bright lights in the parking lot caused by the presence of the ‘screen-door’. You can convince yourself of this because if you slide off the wire ‘screen-door’,  all you see is the four lights. The alternating dark and bright bands provide information about the distances between the wires in the ‘screen-door’ and their directions (square mesh). Now you may capture the essence of modern crystallography: to unravel the structure of the ‘diffracting’ object from the ‘diffraction pattern’, without knowing what it is beforehand. In the experimental setting,  a small circular  ‘beam stop’ is placed in the center to ‘block’ the bright central spot and enhance the  visibility of the diffraction pattern.

Fig. 4b. Detail of the two right bright spots from Fig. 2, background enhanced.


From this brief discussion and daily life example, it should be apparent that ‘diffraction’ is a very different phenomenon from the ones we are all more familiar with of ‘reflection’ by a mirror surface, and ‘refraction’ by a water surface. Diffraction occurs when the wavelength of the incoming radiation is ‘commensurate’ with the internal dimensions of the diffracting object: X-rays to crystals vs. light waves to wire ‘screen-doors’. What does ‘commensurate’ mean: approximate the same internal dimensions or distances. The wavy pattern of the radiation repeats within approximately the same distances as the internal repeats of the interfering object.

I will conclude with a well-known quotation from Louis Pasteur (1822-1895): ‘Chance only favors the prepared mind’.

In the future,  please, be alert and prepared to observe the unexpected. It will enrich your life and you may discover something new.



Figure 3

Louis Vuitton’s Two Dimensional Crystal

Summary: Symmetrical motifs are used in a whimsical way by the world of fashion to convey subliminal messages.

The fashion world may not be familiar with the scientific notion of ‘symmetry’. Yet, the most dominant concept in most of their endeavor revolves around the ‘left-and-right’ repetition dominant in the human body. Each and every human being is aware of this and it is indeed the most dominant motif in the early art, sculpture and architecture. It might be related to the origin of the Greek work ‘sym-metron’: harmony of measurements or proportions. A common term to describe this symmetry is ‘mirror’ symmetry as it relates to the two mirror images, and also to the two-sided (bilateral) symmetry present in a myriad of biological forms.
From this mundane beginning the mathematical concept of symmetry evolved into the repetition of motifs around a circle or around a central point that remained fixed to generate the abstraction of ‘point symmetry’. Examples of this symmetry are prevalent in our daily experience as symmetrically decorated plates with a motif repeated around the circle (Fig.1).

Fig.1. Center ceramic plate: example of point symmetry around a central point. Lace (yellow square): plane symmetry, repetition in two dimensions. Lower right inset: schematic of 4mm symmetry on lace repeating ‘motif’.

The epitome of this symmetry in  Art is the magnificent repeated patterns in the rose windows of medieval cathedrals. They represent truly underappreciated examples of the interplay between mathematical symmetry and artistic expression, particularly when combined with the stained-glass content that was used to convey so much of the world vision of the medieval societies (Fig.2)

Fig.2. Point symmetry in Art. Examples of point symmetry in cathedral windows. Further details of this link between symmetry, artistic expression and the rose windows of cathedrals can be found in https://doi.org/10.1107/S1399004713032859

There is another type of symmetry that the fashion world is intimately connected to, although they might not realize it. This is ‘plane symmetry’, this is the symmetry used by ‘print designers’ to develop motifs, designs and patterns that fill the surface of printed fabrics. The vast majority of printed fabrics have a motif that repeats in the two dimensions of the plane that constitute the fabric. This type of symmetry is characterized by the absence of a ‘fixed point’: the design (unique) motif is displaced in the two directions of the fabric to fill the space (Fig. 1-table cloth lace). In three dimensions, this is named ‘Space symmetry’ and it is the symmetry that generates the internal regularity of crystals, where the repeating motif is an atomic arrangement of atoms. Crystal regularity, i.e. crystal symmetry, can be found in two and three dimensions.
This brings me to the title of this note. I had partially noticed before that the dominant motif in the pattern used to construct an ‘LV’ bag was a four-folded figure with several variations all having the mathematical symbol: 4mm (Fig. 1, inset). This symbol translates into a figure with four-fold repetition and mirror planes (reflection symmetry) every 45 degrees, around the circle. This ‘point symmetry’ is very common in many decorations and even in the architectural design of many courtyards from the 15th century.
A few days ago, on my daily commute to Chicago, the passenger next to me pulled an LV bag to get the train ticket and it was then that I realized that the decoration in the LV bag was in fact a two-dimensional crystal with two 4-folded motives and the ‘LV’ logo in the middle (Fig. 3)

Fig. 3. The repetition (‘crystal’) motif in the design of LV bags and other ‘high fashion’ objects of the ‘LV’ brand.

I was pleasantly surprised for two reasons. First, I was elated to recognize a crystal motif in an ‘haute couture’ object. Second, I was in awe as to the ingenuity of the designers to use a highly symmetrical motif to convey luxury, elegance and distinction. In the end, it is only a repetitive symmetrical pattern.

Passing the Torch

One of the pleasures of growing older and ‘respectable’ in the scientific community is the opportunity of discussing the history of our subjects with the younger generations.  As an enthusiastic crystallographer  and scientist, I do like very much to pass the torch to the upcoming generations of fresh  students to give them a sense of perspective of the scientific research that is now encompassed within the field of crystallography: how did the field started? where  are we are now?; where do we come from? who were the most prominent figures?; and what can we expect in the future?. But I like to do this not in a ‘straight line’ but rather showing the ‘pitfalls’, ‘wrong turns’ and ‘serendipitous moments’ in the erratic history of science. I also like to connect the scientific concepts with artistic metaphors, since to me those two facets of the human mind are related, sometimes in unexpected ways.  Crystallography certainly is a unique science in that regard because of the beauty of crystals, which has been appreciated since antiquity, and because of the richness and elegance of the biological forms that are being now unveiled.  HWC-Lecture-1

Thanks to my colleague from the Institute of Tuberculosis Research, Dr. Farah Movahed and her colleague Dr. Joydeep Mitra from the Harold Washington College in downtown Chicago, I had the opportunity to do this by presenting a couple lectures on the basic concepts of crystallography and its application to Structure-Based Drug Design. I was totally impressed by the group of students and attendees that were extremely attentive to my presentation even though occasionally I might have wondered too far ‘off track’. The lectures were presented in preparation for a fieAPS-HWC-1ld visit to the Advanced Photon Source (APS) in the  southwest suburbs of Chicago.  To commemorate these events, I have written this brief note that I would like to illustrate with a few related images, courtesy of my hosts and also of the APS communication office (Rick Fenner). I do hope that you -whoever you are- have the opportunity to visit the APS and have a glimpse of the amazing scientific adventures that go on hourly and daily in such a place. It is a wonderful and unique resource dedicated to hard work and discovery. What is being being worked on now -in whatever field related to X-rays and structural research- may change our lives tomorrow.

I would like to finish this brief posting with a little known quotation from Louis Pasteur, regarding the role of laboratories in facilitating human understanding and civic discourse:

 “I beseech you to take interest in these sacred domains so expressively called laboratories. Ask that there be more and they be adorned for these are the temples of the future, wealth and well-being. It is here that humanity will grow, strengthen and improve. Here, humanity will learn to read progress and individual harmony in the works of nature, while humanity’s own works are all too often those of barbarism, fanaticism and destruction.”

(Louis Pasteur (1822-1895). Le budget de la science. La Revue de cours sAPS-aerial-viewcientifiques (1869). pgs. 137-139.

For the casual visitor to this website site, who may never have the opportunity to visit the APS, I am appending an aerial view of the site (courtesy of Rick Fenner, Communications office of the APS at www.anl.aps.gov).

I would finally add a link and an image of a brief report that has appeared in the site of Argonne National Laboratory recently (May, 19.2106),
briefly mentioning the visit (http://today.anl.gov/2016/05/harold-washington-college-students-visit-aps-and-apcf/). I think that the image where my index finger is pointing to the ‘invisible crystal’ at the tip of the ‘mounting pin’ where the tiny crystal (about 0.1-0.2 mm or about 100th of an inch) is says it all! (see below left).

Pointing to the 'invisible crystal' at the tip of the mounting pin

Pointing to the ‘invisible crystal’ at the tip of the mounting pin

Quite amazing that from such a tiny speck of matter one can extract the atomic structure of a protein, a virus or any similar structural wonder at the atomic level. Synchrotrons are amazing resources to peek into the atomic structure of our surrounding world.






Tribute to a Friend: Antonio Castellanos Mata

La partida de un amigo entrañable

Antonio Castellanos Mata ha sido y siempre será mi amigo mas entrañable de la juventud y de los años que han seguido. Nuestra amistad nació y se cultivó en Valladolid, durante los años de carrera. El apareció de repente en segundo, calculo que en el otoño de 1965.

Catedratico de la Universidad de Sevilla, Spain

Catedratico de la Universidad de Sevilla, Spain

No hizo el selectivo con nosotros en Valladolid. Apareció en las clases de segundo, segun decía ‘de León’ y con ello se quedó el apodo cariñoso por el que todos le conoceríamos durante aquellos años: ‘León’. Tantas cosas que contar, en cierta forma ‘triviales’ momentos de entonces,  que en aquellos días fueron inolvidables por la intensidad de la amistad, pero que ahora detrás de la niebla mental de cincuenta años, son difíciles de detallar.

Algo que fue evidente desde el primer momento fue su inteligencia, completamente ‘fuera de lo normal’ y su capacidad de absorber el contenido de las clases de Mecánica, Termodinámica y las correspondientes matemáticas de segundo de Físicas con toda facilidad. Recordaré siempre su percepción de la relatividad restringida de Einstein en las clases de Mecánica de segundo: yo estaba admirado!!

Al principio de curso, de todos los cursos que yo recuerde -de segundo a quinto- compraba un único cuaderno de apuntes que consistía solo en un ‘block de espiral azul grueso’ y un bolígrafo ‘bic’ de plástico transparente, de los más baratos con tapadera azul que llevaba (el mismo cuaderno!) invariablemente a todas las clases. Eso era todo!! Allí apuntaba con toda claridad los puntos y ecuaciones más importantes de cada asignatura y con eso le bastaba. Yo me organizaba con cuadernos para cada asignatura, copiosas notas, y al final del día peleaba con las explicaciones y derivaciones de los profesores.  Antonio, con ese cuaderno y unas pocas horas de estudio para cada asignatura, sacaba siempre las notas más brillantes del curso. Su capacidad para resolver los problemas mas difíciles de Mecánica, Termodinámica, Electricidad, Optica, etc. era increible. A mi me dejaba anonadado.  Yo no le llegaba ni a la suela de su zapato.

Durante los últimos años de la carrera seguimos la rama de ‘Fundamental’ en lugar de ‘Electronica’ y deambulábamos por el departamento de Casanova. Al final de la carrera los dos pedimos una beca del gobierno francés par ir a Burdeos a hacer Física Nuclear, pero naturalmente con sus notas brillantes, él la consiguió y yo no, de lo cual me alegré muchísimo. El continuó en Valladolid y unos años más tarde los dos solicitamos una beca Fulbright para estudios en USA. Yo quería hacer mi doctorado allí; estaba muy descontento de lo que se me ofrecía en Valladolid-España, mientras que Antonio quería solo pasar un curso escolar en USA y viajar por todo el continente Americano y en particular visitar Mexico. Aquí ya nos separamos!

Yo seguí mi interés en estudiar cosas relacionadas con la biología –biofísica como yo lo llamaba entonces- y marché a Salamanca y luego a hacer el doctorado en USA después de casarme en 1970. Allí nos separamos y después ya no nos vimos por muchos años. Yo me asenté a vivir en USA, y aunque el estaba siempre en mi memoria, no nos pudimos ver mas que una vez mas –brevemente para una cena acelerada- cuando fuí a Sevilla para una conferencia creo que en 1992, como commemoración del quinto centenario del viaje de Colón. Yo creo que entonces aún no estaba casado con Elena, y nunca conocí a su primera esposa o hijos.

Entre los mejores momentos juntos, eran los que pasábamos haciendo problemas de matemáticas. Recuerdo en particular los diversos problemas de integrales del libro de Martínez Salas. Unas tardes íbamos a su modesto piso de la pensión enfrente de la Catedral de Valladolid, y otras tardes trabajabamos en mi habitación del colegio mayor La Salle. No es que mi familia fuera rica, sino que yo había conseguido una beca despues de selectivo para poder pagar los gastos. Mi padre –muy religioso- prefería para mí ese ambiente. Yo echaba de menos el ambiente libre y bohemio de la vida de Antonio, y en eso disfrutábamos mucho juntos. Paseábamos, charlábamos, mirábamos a las chicas. A ninguno de los dos nos gustaba beber.

Así nos llegamos a conocer más, aunque él no era un hombre de muchas palabras. Provenía de una familia modesta de León, su padre creo que era maestro, como el mío. Tenía un hermano que jugaba al ajedrez –mas sobre esto luego- pero no supe mucho mas. Esto a pesar de que me invitó un fin de semana a ir a su casa a León, con motivo de un festival de música ‘moderna’ (rock de aquellos tiempos) en un teatro de León. Recuerdo muy bien la imagen de Antonio bailando y contorsionándose de pie en el teatro (en las butacas de arriba) al son de ‘Con tu blanca palidez’ (‘Whiter Shade of pale’, un éxito de la banda británica de Rock Procol Harum en 1967 y el himno de la contracultura de entonces). Bueno, pues a pesar de esta visita, no recuerdo nada de su madre o padre, pero tengo un recuerdo vago de que también tenía una hermana. Durante esta visita a León, fué mi primera visita a la Catedral de León que me impresionó por su diseño elegante y armonioso, además de las espectaculares vidrieras y las esculturas de sus fachadas, como la de la Virgen Blanca. Todo un descubrimiento. Nuestra amistad se cimentó.

Sin embargo, recuerdo muy bien,  que los momentos mejores de nuestra convivencia durante todos aquellos años juntos, fueron los de las interminables partidas de ajedrez en el Café España de Valladolid, en la zona de la ‘Fuente Dorada’. Despues de comer yo caminaba hacia el café y alli nos juntábamos. Yo tomaba un cortado y pedíamos, como siempre, un tablero de ajedrez y fichas de aquellas de diseño viejo, altas y muy inestables. Nuestro café se prolongaba desde las 2:45 de la tarde, mas o menos, hasta pasadas las 4:00 o más, y jugábamos tipicamente dos partidas o a veces tres, por mis afanes de ‘revancha’. No conseguía ganarle casi nunca, rara vez. Yo acababa agotado!! Y luego yo tenía que empezar a estudiar; Antonio yo creo que no estudiaba mucho; no le hacía falta! El era mucho mejor jugador que yo. Yo aprendí muy tarde y sin nadie que me guiara. Creo que el aprendió de su padre y hermano, y tenían muchas ‘horas de práctica’ y de tácticas. Yo trataba de absorber cuanto pude. Es algo que SI que se nos ha quedado pendiente ahora!! Jugar alguna partida de ajedrez de nuevo. Seguro que tu ahora tendrás una inspiración extraterrestre, celestial (si no divina!) e invencible. Compañero del alma, compañero –que diría Miguel Hernández.

A cambio, quizás, yo le intentaba enseñar un poco a tocar la guitarra. A mi me enseñó mi abuelo, y en mi familia había mucha música por todas partes: mi padre y abuelo fueron músicos de afición y profesión. Llevé a la Universidad una guitarra vieja, que mi abuelo compró por doce pesetas cuando era joven, de clavijero de madera y es en la que yo aprendí. A Antonio le gustaba mucho la música de guitarra popular y sobre todo los ‘Corridos Mejicanos’, en particular ‘De Piedra a de ser la Cama’. Yo la cantaba para él y con cierta paciencia, creo que al final conseguí que pudiera cantarla solo y acompañarse el mismo en la guitarra. Tenia una auténtica fascinación por la música y la cultura mejicanas.

Siguieron muchos años separados y apenas sin saber el uno del otro. El, por su proximidad, pudo disfrutar de las visitas y celebraciones de los compañeros de carrera organizadas por Luis Bailón y sus colegas en Valladolid, especialmente la del veinticinco aniversario (ver foto). Perderme esas visitas ‘hacia el pasado’ siempre me fué difícil. Pero no había otro remedio.  Intenté escribir a Antonio cuando los principios del correo electrónico para saber mas de él: esposa, hijos, familia; pero Antonio era un hombre de pocas palabras ‘escritas’, en mi opinión. Tan afable y dicharachero como era en persona, el guardaba sus palabras en papel y en medios electrónicos para él sólo y para momentos muy especiales. He sabido muy poco de él durante éstos mas de cuarenta años. Sin embargo, sé muy bien –por su parte y la mía- que hemos sido amigos entrañables. Lo hemos sentido los dos día a día.

Profesionalmente, sé muy bien de su dominio de la Física en todas sus ramas y especialidades, y no me cabe la menor duda de que sus varias decenas de promociones de estudiantes de la Universidad de Sevilla, así como sus colegas, le recuerdan como un excelente profesor. Exigente, sin duda alguna, como él lo era consigo mismo, pero justo y brillante. Cogió temas de investigación muy difíciles porque su ‘mente brillante’ lo necesitaba. El no podía contentarse con hacer Física ‘fácil’. Confieso que no he leído, ni él me mandó, ninguno de sus trabajos y ciertamente lo lamento. Seguro que hubiera aprendido mucho sobre el tema de procesos nolineales, irreversibles, que siempre me han apasionado y sobre todo su aplicación a la explicación de los procesos biológicos, metabólicos y del sistema nervioso.

Antonio reapareció con mucha fuerza de nuevo, con motivo de la última reunión de compañeros de curso de Nov. 2014 a la que –una vez más- no pude asistir.  Por las fotos, allí le volví a ver, conocí a su esposa Elena y a sus hijos mas jóvenes. A los pocos meses recibí –junto con Miguel Moreno y Luis Bailón, un mensaje entrañable donde nos comunicaba las circunstancias de su salud y con ello ‘sonó la alarma’ en mi corazón.

En los últimos días, Elena –su querida esposa, me comunicó su ingreso en el hospital (Enero 20) y un torrente de recuerdos volvieron a aparecer en mi memoria. En el intercambio de mensajes que siguió, descubrí cosas que no conocía de mi entrañable amigo: le gustaba la poesía de Machado y Lorca, entre otras. Escribí unos pocos mensajes, le envié algunas fotos, y le envié tambien una poesía de Lorca que afortunadamente pudo leer y no conocía (‘Adivinanza de la guitarra’) y traté de ‘hacerles compañía’ en la distancia a él y a Elena, tratando desesperadamente de ‘recuperar el tiempo perdido’ de la vivencia de nuestra intensa amistad. Me dije a mí mismo: ‘si se recupera le veré y le visitaré con su familia en el 2016’. Tristemente no pudo ser!!  Compañero del alma, compañero. Te fuiste demasiado pronto!

Es bien conocida la anécdota de que cuando murió Michele Besso, el gran amigo de Einstein de sus tiempos de estudiante en el Politécnico de Zurich, éste le escribió a su esposa viuda (solo unas semanas antes de su propia muerte) diciendo que para los físicos la distinción entre el pasado, presente y futuro (el paso del tiempo) era solamente una ilusión ( ‘only a stubborn illusion’). El tiempo es reversible en las ecuaciones y por eso no cuenta.  Ojala!! querido Antonio. Tu partida nos ha traído tragicamente a la otra concepción del tiempo:  la dirección termodinámica, irreversible, personal –la ‘duración’ del filósofo francés Henri Bergson que en su momento (Abril 6, 1922) tuvo la histórica discusión en Paris con Einstein sobre los ‘dos tiempos’, el físico y el personal. Como seres humanos que somos, todos sabemos que ‘la flecha del tiempo’ (‘The arrow of time’) es irremisible y nos empuja hacia nuestro final temporal inevitable. Ojala que todos tengamos la gran suerte y el carácter que tú has tenido, nuestro querido y entrañable amigo Antonio, de salir por esa puerta con valentía, fuerza, buen humor y lucided hasta el último momento, como tú lo has hecho. Y además, rodeado e infinitamente querido por tu familia, tus colegas y amigos que han visto siempre en tí un ejemplo y una inspiración digna de seguir.

Antonio nuestro, descansa en paz!


Foto del grupo de Profesores y colegas de la carrera que acudieron a celebrar el 25 aniversario de las primeras promociones de la Facultad de Fisicas de Valladolid en 1994.

Incluyo dos de las pocas fotos que tengo de Antonio. En aquellos tiempos cámaras fotográficas no eran objetos de uso normal, especialmente entre nosotros los pobres estudiantes. Recuerdo, muy bien, que esta foto corresponde a la excursión que los alumnos de quinto –creo- hicimos a Madrid a escuchar a Werner Heisenberg en la Universidad Complutense, siguiendo una sugerencia e invitación de Boya, nuestro profesor de Mecánica Cuántica. Fuímos en coches particulares, y en la foto se ve el coche que condujo Victor Ordóñez. Allí se le ve a ‘León’ (derecha) en su atuendo típico, con su pantalón gris, camisa blanca, corbata, y jersey de color verde claro hasta arriba. En la foto se ven además (de izquierda a derecha): Eladio Sanz (‘Lalo’), Victor Ordóñez y Luis Alonso Romero.  Al fondo los pinos de la Ciudad Universitaria de Madrid, probablemente en la primavera de 1969.

Colegas de la carrera en una parada en la Ciudad Universitaria de Madrid, ca. 1969

Colegas de la carrera en una parada en la Ciudad Universitaria de Madrid, ca. 1969

La segunda y última foto es la ‘Orla’ de nuestra clase/promoción que preparó Javier Bustillo con tanto cariño, y que he incluído en alguno de mis ensayos como homenaje a todos nosotros, colegas y amigos de Antonio. Cuando se completó, yo recuerdo con inmenso cariño y orgullo que Antonio, mi mas entrañable amigo, estaba a mi lado.

Orla de la primeras promociones de la Facultad de Fisicas de Valladolid, 1969

Orla de la primeras promociones de la Facultad de Fisicas de Valladolid, 1969



En la redonda


seis doncellas


Tres de carne

y tres de plata.

Los sueños de ayer las buscan,

pero las tiene abrazadas

un Polifemo de oro.

!La guitarra!


Federico García Lorca (1898-1936)

Connecting Music, Literature and Architecture: A CSO concert

It is a rare opportunity to be present at the world premiere of any artistic event and particularly the interpretation of a music that has never been heard before. As part of my subscription to the Chicago Symphony Orchestra (CSO) concerts, I was treated to such a unique musical event last Thursdays, June 18 at Orchestra Hall in Michigan Avenue in Chicago.

Mason Bates has been composer in residence at the CSO for the last five years and completed his term with Anthology of Fantastic Zoology, a piece dedicated to his mentor Ricardo Muti the CSO tenth music director.  I was captivated by the sounds, the passages and resonances that this music evoked while I was listening to it. As pointed out by the program notes*, it was a mixture of Mussorgski’s Pictures from an exhibition, Saint-Saëns Carnival of the Animals, and particularly to me a showpiece for the entire orchestra reminiscent of Bartok’s Concerto for Orchestra. You can read more technical comments in the recent review. There is also an excellent image from a vantage point that is very close to where I was sitting at this memorable concert.


From the program notes, I learned the literary stimulus that inspired this amazing music created by Bates, a very young composer with interests and background in literature and music (attended the Columbia-Juilliard joint program in English literature and musical composition).  The inspiration was Borges Manual de Zoología fantástica written in 1957. This was a time when the writer’s eyesight had severely deteriorated and could no longer read what he wrote. According to a recent biography of Borges (1), this was the time of a collaboration with Margarita (Margot) Guerrero with whom he was totally infatuated. So much so that he tended to ignore the fact that Ms. Guerrero’s interest in literature were not as consuming and his. Unable to conceive any kind of relationship without a literary connection, Borges proposed to her a project in accord with Margot’s interest in the supernatural and the occult. He suggested that they prepare together a catalog of the weirdest animals created or imagined by the human mind through the ages. This imaginary bestiary was published first in 1957 (2) and later an expanded version with a different title in 1967 (3), which was translated into English as The Book of Imaginary Beings. This was the point of departure for Bates’ composition.

Creatures such as ‘The Sprite’ (an elf or fairy), ‘The A Bao A Qu’ (a serpent slithering up a tower and melting at the top to return down again) and ‘The Gryphon’ (a chimera of Eagle and Lion) among others, are presented tonally and musically in Bates’ composition with a rich orchestral sound and abundant use of various percussion  instruments (xylophone, glockenspiel, large Chinese drum, woodblocks, crash, cymbals, crotales and others).  The sound catalog of animals with their corresponding actions and motions also include the more common and melodic Nymphs and Sirens often with the use of melodious phrases in the strings. The interlacing of these various creatures is connected with what Bates called ‘forest interludes’ reminiscent of the promenades in Mussorgsky’s intermezzos between various paintings that make up his well known composition.

From this musical experience, what connected me to the world of architecture is a masterpiece of late Gothic (Flamboyant Gothic) civil architecture in Guadalajara (near Madrid, Spain) known as Palacio del Infantado built by the influential Mendoza family in 15th century Spain, a political force behind the union of the several kingdoms of Spain under Ferdinand and Isabella (of Columbus fame).

View of the upper gallery of the Palacio del Infantado en Guadalajara, Spain. The richly decorated arches and characteristic of the late Spanish Gothic and almost a trademark of its architect Juan Guas

Fig. 1. View of the upper gallery of the Palacio del Infantado in Guadalajara, Spain. The richly decorated arches are characteristic of the late Spanish Gothic and almost a trademark of its architect Juan Guas. (Author’s private collection).


Prominent in the design is an interior patio of perfect quadrangular symmetry named Patio de los Leones richly decorated with animals that at first sight appear to be lions. However, a closer inspection shows that the architect Juan Guas magnificently designed the patio, and decorated it with pairs of lions on the lower gallery and pairs of Gryphons carved in the upper gallery, with an impeccable symmetry on each arch that extents to the helical decoration of the columns framing each module (Figs. 1-3).  These images alternate symmetrically around the courtyard with the symbols of the Mendoza and Luna families. The portrayal of fiery and imaginary animals in the heraldic symbols of the Renaissance was customary to impress upon the visitor,  allies or enemies certain qualities of character such as bravery and strength.

In a magical way, the kaleidoscopic musical tapestry  that Bates has created with his Anthology of Fantastic Zoology brought me to the richly decorated galleries of the Palacio del Infantado via the literary and unparalleled ruminations and prose of Jorge Luis Borges.


Fig. 2. Patio of the Lions: Side view. General view of the two galleries on one side of the patio.

Fig. 2. Patio of the Lions: Side view. General view of the two galleries on one side of the patio (Author’s private collection).

Fig. 3. Gryphons in Architectural decorations. Detail of the two Gryphons motif in the upper gallery of the Palacio del Infantado in Guadalajar, Spain (Author's private collection).

Fig. 3. Gryphons in architectural decorations. Detail of the two Gryphons (chimera of eagle and lion) motif in the upper gallery of the Palacio del Infantado in Guadalajara, Spain (Author’s private collection).







*Program Notes by Philip Huscher program annotator for the Chicago Symphony Orchestra.

  1. Williamson, E. Borges. A Life. Viking Penguin. Printed by the Penguin Group. 2004.
  2. Borges, J.L. with Margarita Guerrero. Manual de zoología fantástica. Fondo de Cultura Económica. Mexico City. 1957.
  3. Borges, J. L. with Margarita Guerrero. Manual de zoología fantástica. Expanded edition published as El Libro de los seres imaginarios, Kier, 1967. English translation The Book of Imaginary Beings.
  4. Herrera Casado, A. El Palacio del Infantado en Guadalajara. Editorial AACHE. Colección Tierra de Guadalajara. No. 3.

The Crystallized Melon of St. Elijah

I cannot resist writing a concise  commentary and discussion of a brief article by Prof. Juan Manuel García Ruíz  (Research Professor at the CSIC in Granada, Spain) in a recent issue of the widely read Spanish Newspaper ‘El País’. His focus is a purported melon that was petrified by the Prophet Saint Elijah, in response to a cunning temptation by none other than Satan himself.  (http://elpais.com/elpais/2015/05/07/ciencia/1431017789_237800.html).  St. Elijah’s miracles and extraordinary feats are well known to scholars of the Christian tradition but the article by García Ruíz uses a revised version of one of them related by Father Manuel de San Jerónimo in his book Reforma de los Descalzos de Nuestra Señora del Carmen, published in 1706. The reformation of a wide range of religious orders was intensely pursued in Spain in the late sixteenth century to prevent what was perceived as corruption of the fundamental values of the convent life. Mystical figures such as St. Teresa de Avila (later St. Teresa de Jesus: 1515-1582; canonized in 1622) and St. Juan de la Cruz (St. John of the Cross: 1542-1591; canonized in 1726)), were prominent in these efforts.

Using a witty language, Prof. García Ruíz narrates how St. Elijah was tempted by Satan with a fresh and juicy half-melon ready to be eaten, after our prophet had been already several days fasting in the sweltering sun of the Sinai desert. Upon the realization by St. Elijah of the true intentions of Satan, he exclaimed: ‘Halt Satan, I command you to be converted into stone’ , and the salacious melon transformed itself into a stone (Fig. 1).

Image of the melon that purportedly was converted to stone by St Eliajh as seen in the chapel of the monastery of the Carmelite order in Sanlucar la Mayor (Seville, Spain).  Image courtesy of Prof. Juan Manuel Garcia Ruiz. Photograph by Hector Garrido.

Fig. 1. Image of the melon that purportedly was converted to stone by St Eliajh as seen in the chapel of the monastery of the Carmelite order in Sanlucar la Mayor (Seville, Spain). Image courtesy of Prof. Juan Manuel Garcia Ruiz. Photograph by Hector Garrido.

Whether the narration is true or not we are not going to argue. The fact is that in a reformed convent of the Discalced Carmelites in the shrine of Sanlúcar la Mayor (Seville, Spain) there is a mineral formation with the shape of an open melon, with a legend saying that this was the very same one that St. Elijah trans mutated to avoid temptation (Fig. 1).

Very elegantly, Prof. García Ruiz uses this focal point to introduce the notion that many rock/mineral formations at the macroscopic (as in the case of the melon) and microscopic level resemble biologic or organic forms. Without disturbing the community of the Discalced Carmelite sisters, he cannot fully confirm that the purported melon is a beautiful specimen of Calcedonian geode with a textured gradient going from a dark and smooth exterior to crystalline quartz in the interior.  However, it is almost certain that this is the true origin of the petrified melon, a formation quite plausible in the Sinai Peninsula or in the arid regions of Magreb. Thus, he illustrates the use of the concrete shape and form of rock or mineral formations to infer, with full confidence, an organic or biological origin, by whatever processes (miraculous or supernatural).

But as Prof. García Ruiz also notes and knows very well, since it is a major area of his research, the reverse is also often concocted: the inference that inorganic forms with suggestive curvatures and forms reminiscent of organic arrangements must be of biological origin. These types of extrapolations are particularly dangerous when the paleontologists are attempting to characterize some of the earliest ‘life forms’ or the primordial ‘micro fossils’ of ancient life.  Indeed, these extrapolations (on either side of the dichotomy) and on any metric scale (from microscopic to macroscopic) arise from confounding the substantial and the external, the inner genuine origin with the accidental resemblance.

To close this concise commentary I will only add a new idea to the observations of Prof. García Ruíz in his insightful article. Simply, we tend to underestimate the creative forces of the basic elements of matter (such as atoms and molecules) and invoke supernatural causes to explain complex but natural phenomena. We should remind ourselves constantly of the ingenious ways in which natural elements and forces, under different conditions, can create forms and entities that we could have never imagined, based on our common day-to-day experience. I will just mention two simple examples that anyone can recognize.

First, consider, the immense creativity of one of the simplest components of our world: water. It can create immense mountains of ice, rivers and exquisite and delicate snow or ice crystals as well as the transient clouds, all using a simple composition of two atoms of Hydrogen and one of Oxygen and a variety of physical parameters: atmospheric pressure, relative humidity, temperature and wind velocity among them (Figs. 2,3).

Fig.3. Ice crystals on a window pane formed overnight on a cold winter night, following slight scratches on the  window glass. (Author private colllection. Do not reproduce without permission).

Fig. 2. Ice crystals on a window pane formed overnight on a cold winter night, following the slight scratches on the window glass. (Author private collection. Do not reproduce without permission).

Fig. 2a. Ice formation upon melting and re-freezing found in a wooded area near Lake Forest, IL. (From the author private collection

Fig. 3. Ice formation upon melting and re-freezing found in a wooded area near Lake Forest, IL. (From the author private collection. Do not reproduce without permission).










Second, the ubiquitous element carbon alone can produce various types of coal, lead pencils and the exquisite diamonds as well as the subtle and elegant fullerenes, containing clusters of 60 atoms in an elegant icosahedral-like atomic soccer ball.  In addition, the combination of carbon atoms with some other light elements such as Oxygen, Nitrogen and Sulfur produces the myriad of proteins that we know and that are a key constituent of life on Earth, from sophisticated catalysts to hair and skin. Let’s just consider these simple facts before we try to invoke miracles or supernatural phenomena to explain what we see, no matter how extraordinary.


Va10 Antigua

The Rose Windows of Gothic Cathedrals: Art, Symmetry and Beyond

Gothic Rose window of the Church of Saint Pablo in Valladolid, Spain

 The meeting of the International Year of Crystallography in Montreal (IUCr2014 23rd Congress), Aug. 5-12, 2014 was an excellent opportunity to meet with friends and fellow crystallographers from all over the world. It was also an unique opportunity to be exposed to the latest developments of crystallography and crystal science in the broadest sense of the world. There were over on hundred microsymposia, plenary lectures and other technical sessions, plus exhibits and workshops. I was also invited to give one presentation in one microsymposium entitled Symmetry and its General Manifestations in Science and Art’ (MS95).

I took this opportunity to present the article recently published in Acta Cryst D 
that has been featured in previous postings in this blog (see full reference below). 
I did enjoy the opportunity to broadcast the message of this essay to a wider audience of 
crystallographers interested in the connection between symmetry/crystallography and art. 
I found it really surprising that exploring this clear manifestation of symmetry in Art had not 
occurred to anyone before, except to H. Weyl in his classic book Symmetry (1952), quoted below. 


 Here is a copy of the abstract of the presentation. More details can be found in earlier postings in the blog.

 ====== Abstract
The magnificent rose windows of the Gothic cathedrals have been the object of wonder
and fascination to architects, artists and human beings alike, since they were used 
to emphasize the splendor of Gothic architecture, its lightness of forms and luminosity of interiors. 
There is considerable amount of literature on the theme including studies on the stone tracery and 
the stained glass and a website created by a prominent author in the field (www.therosewindow.com, Cowen, 2005)
is an excellent resource. A brief reference in the classic book Symmetry by H. Weyl (Weyl, 1952) suggested that 
rose windows were indeed excellent examples of planar point group symmetry. However, a rigorous 
and systematic study of this particular facet of these masterpieces has never been done.

Preliminary results of the frequency of different symmetrical arrangements for more than five hundred windows have been recently published (Abad-Zapatero, 2014) and will be presented. In addition, detailed analysis of certain examples of rose windows and iconic macromolecular structures suggest that various symmetrical figures and entities that are part of our world can have symbolic meaning. They can be described by the rigorous framework of group theory in mathematics but they have also been used through history to convey different thoughts, insights and perceptions of the artists (and scientists) as designers and executors of the cosmological view of the times.  A project aimed at extending these studies in the future will be presented.

Abad-Zapatero, C. (2014). Acta Cryst. D70, 907-911.

Cowen, P. (2005). The Rose Window: Splendor and Symbol . Thames and Hudson, New York.

 Weyl, H. (1952). Symmetry. Princeton University Press, Princeton.
 This abstract originally published in Acta Cryst. (2014) A70, C142A.

Crystallography on Stage: Presenting the Concepts and History Dramatically

The meeting of the International Year of Crystallography in Montreal (IUCr2014 23rd Congress), Aug. 5-12, 2014
 was an excellent opportunity to meet with friends and fellow crystallographers from all over the world. 
It was also an unique opportunity to be exposed to the latest developments of crystallography and 28782D_02
crystal science in the broadest sense of the world. There were over on hundred microsymposia, 
plenary lectures and other technical sessions, plus exhibits and workshops. 
I was invited to give one presentation in a micro-symposium entitled 
'Spreading the Word. Introducing Crystallography to the Public' (MS68).
 I took this opportunity to present the work on the play 'Picasso Meets Crystallography'
 and also on its most dramatic adaptation 'Bernals' Picasso', in collaboration with 
my colleagues Jill Campbell and Greg Gerhard.
Here is a copy of the abstract of the presentation. 
You can read more details on this webpage, on the 'Science Communication' (Drama) tab.

From Christopher Marlowe’s Doctor Faust (1604) to Oxygen (2000) by Carl Djerassi and Roald Hoffmann, there is a long tradition of

dramatic work related to scien ce and scientist. More recently, the enormously successful Copenhagen (1998) by Michael Frayn’s and

a wave of new plays about scientific themes such as Arcadia, Wit, After Darwin and others have created new dramatic phenomenon.

These works are not the conventional documentary-dramas about scientific discovery but engaging plays. A recent book entitled

Science on Stage (1) reviews more than a hundred plays presenting scientific themes on stage.

Beginning in 2005, a play was developed with the objective of conveying the concepts and history of crystallography to large audiences in

a dramatic setting. The script centers on the mural drawn by Picasso in 1950 at the flat of the iconic crystallographer J.D. Bernal, during

his historical meeting with the world-famous artist. The main characters discuss the concepts of crystallography and explore t

he interconnections between Science and Art. The script has had several readings in academic settings (University of Illinois at Chicago, 2007;

Barcelona, Zaragoza, Spain, 2008). The première staged reading of the play was produced at Argonne National Laboratory on May 4th2008.

Details can be found at http://www.aps.anl.gov/Users/Meeting/2008/Picasso/index.php. The project has developed from an initial script entitled

‘Picasso Meets Crystallography’ emphasizing the concepts and history of crystallography to the more dramatically-rich version

entitled ‘Bernal’s Picasso’, which explores the relationships between Science and Art and is intended for wider theater audiences. The

presentation will discus the history of the project with vignettes of previous performances, its multiple facets and its future

development as a novel way to convey crystallography to wider audiences, and to explore in a dramatic context the role of

crystallography in today’s society

[1] Sphepherd-Barr, K. Science on Stage by (Princeton University Press, 2006),

 Abstract published in  Acta Cryst. (2014), A70, C1036, as part of the abstracts for the IUCr2014 23rd Congress.

D-Day and Crystallography

The events of June 6, 1944 and the ending  of WWII in the European front are all very well known. The press and  the electronic media will cover them in detail. However, in the context of the International Year of Crystallography (IYCr2014) what is less known is the personal connection between the planning of the landing of the allied forces in the beaches of Normandy and crystallography. Any connection? Are you kidding? Yes, there is!

Previously, the most  infamous amphibious landing in military history at Gallipoli  in WWI ended up in disaster. It was the only precedent for attempting to put large number of troops ashore without first capturing the port. The shadows of this debacle had provided in England the impetus  for the formation of various special units  under the umbrella of ‘Combined Operations’ (CO). To make ‘Overlord’ (the code name for the operation) a success there needed to be detailed knowledge about the nature of the Normandy shore, which included among many other pieces of information: i) safe approach for the ships and landing craft, free from mines and rocks; ii) the range of tides; mean high and low water marks; underwater obstacles;  iii) fortifications on the beaches; iv) beach gradients and dimensions, as well as exit routes from the beaches that would support tanks and heavy equipment; and v) local topography of the hinterland. As late as September 1943, no specific or current information about this issues was available.  All the data had to be gathered  without alerting the enemy to preserve the vital element of surprise.

Cover of the biography of J.D. Bernal by A. Brown. 'Sage' was a truly polymath of knowledge and was involved in the politics and social actions of his times (1901-1971).

Cover of the biography of J.D. Bernal by A. Brown. ‘Sage’ was a true polymath of knowledge and was involved in  the birth of protein and virus crystallography ( nurturing several Nobel prizes in the field)  and the politics and social actions of his time (1901-1971).

Lord Mountbatten and the high command of Operation Overlord had full confidence in John D. Bernal, ‘Sage’, who had proven himself invaluable in other strategic decisions and operations in earlier stages of WWII. It is not that he knew the answers  but rather that his muti-faceted, brilliant, scientific mind would ensure that no potential pitfall would go undiscovered. By early October 1943, Bernal was fully engaged in attacking the myriad of imponderable problems that the landing forces would have to face.

What I found most amazing about the involvement of ‘Sage’ on providing solid data on the beaches of D-day was his approach. The first time he looked at the maps and charts of the proposed operation Overlord beaches in Washington at the end of August, he recalled  a holiday visit ten years earlier to the beaches of Arromanches in the Normandy coast of France. He remembered the turbid water caused by a suspension of peat. This personal impression led him to read ‘Le Guide Bleu‘  of French beaches, a source of information disregarded by the British Naval Intelligence. This lead to consultations with London geologists and other more obscure sources.

Obviously, a critical unknown factor about the beaches chosen for landing was whether they could support the weight of armed vehicles, and particularly whether trucks and tanks would be able to drive across them without getting trapped in the wet sand of unknown texture or firmness. So Bernal, in his unique brilliancy, decided to consult obscure volumes in the British Museum and the Oxford Library about the geology and beach structure of the shores searching into the most remote sources, going back in time to the  adventures of William the Conqueror (Norman King of England 1066-1087) near Cherbourg. He got an unlimited pass to both libraries and consulted every volume of the Proceedings of the Linnean Society of Caen, starting in 1840, with special attention to the description of summer excursions of geologists, botanist, zoologists about the marshes of the surrounding country side.

One of the most valuable readings of Bernal were the contributions to the proceedings of Abbe Hue, a local priest, who was fascinated by the geology of the Bay of Calvados, who reported finding a Roman coin dating back to 230 A.D. From these and many other ‘scholarly’ readings Sage developed a picture of the region as a wooded valley with rocky edges on both sides. He dug into many other obscure sources, among them a twelfth century Norman epic, and detailed analysis of the names given to topographical features such as a low-lying promontory named ‘Hable de Heurtot’, the latter suggesting an earlier harbor.

With all these clues, Bernal suggested to the high command the gathering of more detailed information from air sorties to develop nautical charts after multiple reconnaissance flights at low altitude during moonless nights. During the three months before D-Day , 200,000 sorties were flown over enemy territory; many to divert suspicion but the majority to gather data to prepare for the landing.  Samples were also brought back to England from many of these beaches by heroic expeditions  by Scott-Bowden (Royal Corps of Engineers) and his accompanying sargent  Ogden-Smith. Of note is an expedition, a Pilotage Party, by the British Engineers to ‘Pointe du Hoc’ that would be a deadly obstacle for the Americans fighting to get a stronghold on Omaha beach. The observations and data gathering under guidance and leadership of Sage charted the basic topology of the shore line and then went on to characterize the waters  at La Baie de Seine, and the Bernieres and Calvados reefs that had caused many crushed hulls over the years. There was also the development of reliable tide tables for the coast and many other details. By the end of January, he submitted the final approval reports for the proposed beaches selected for operation Overlord, providing entry and exit routes for the heavy equipment (trucks and tanks, mainly)  taking into account the the mined areas and the topology and character of the different access beaches.

A detailed account of all this effort is given in A. Brown’s biography of Bernal (Chapter 12, see figure) and I refer the interested reader to this source for further information on the extraordinary life and accomplishments of J. D. Bernal. I do not think that the electronic resources available cover this aspect of Bernal’s biography nor the thorough geological and engineering preparations that undoubtedly contributed to the success of the operation.  True to his experimental and scientific character, Bernal wanted to see personally the beaches, promontories and terrain that he had so carefully charted before the invasion. Thus, he arranged to visit France on D-day+1 and was approved to go even though he had to dress in an appropriate military combat outfit that made him to look rather ‘unmilitary’ (see the above reference for details).

By staying an extra day in France, he managed to visit the land marshes  near the port of Courseulles and did find tanks and heavy equipment  stuck in the ditches as he had imagined it would happen. Nonetheless, it was clear that by D-day+1 the operation had been a success. He returned to Portsmouth and was rather pleased to see that all the preparatory work done at the ‘Combined Operations’ unit had resulted in a successful military operation.  His notebooks and reports speak of  the obstacles encountered on the beaches corresponding ‘in almost every detail to expectations’ from the provided charts. Taking into consideration the difficulties inBernalsPicasso-Muraltroduced by the unpredictable weather, he concluded that the methods and intelligence developed were adequate for the task.  The official reports of the high command of operation Overlord  concluded: 1) The element of surprise offset the rough weather encountered by the troops; 2) the heavy preliminary bombardment did not cause heavy material damage but affected the human defenders, effectively neutralizing the defenses. 3) although they were not effectively cleared and caused considerable damage to the incoming troops, the underwater obstacles were not sufficiently dense or effective to jeopardize the operation. In short, Overlord was a ‘planning triumph’ (1).

In summary, a prominent crystallographer and scientist of his time, played a major role ‘behind the scenes’ to the success of the events that took place seventy years ago today and that changed the course of history. May these brief lines be an homage to him and to so many anonymous others that worked on the herculean undertaking of preparing for the events of D-day.

(1)  Brown, A.  J.D. Bernal. The Sage of Science. (2005). Oxford University Press. I treasure my personal copy of this biography that I purchased on my visit to Birbeck College, May 12, 2006 as I was preparing my play ‘Bernal’s Picasso’ relating the historical encounter between J. D. Bernal and Pablo Picasso, on Nov. 12 1950 as recorded by the drawing of Picasso at Bernal’s flat at Torrington Sq. in London (see image).

Further details can be found at my website: www.uic.edu/labs/caz/picasso/

















The Ballad of the 2.8 Ångstroms Structure of SBMV

Comparison of the symmetry elements of a virus particle (right) with the seam structure of a soccer ball.

Fig. 1. Comparison of the symmetry elements of a virus particle (right) with the seam structure of a soccer ball.

The celebration of the International Year of Crystallography (IYCr2014) has prompted me to remember the celebration of a remarkable achievement of the early years of macromolecular crystallography, just twenty years after the first protein structures  (the two globins: myogoblin and hemoglogin) were solved. I was the fortunate participant in that singular event and inspired by the scientific achievement, the spirit of the group and the delight of the discovery, I was stirred to write a ballad to commemorate the event.  Sadly, the passing of Pete Seeger (1919-2014), the inspirer of the music for the ballad, has put a sorrowful taint in these lines. May these brief words, written by a scientist who greatly admired him, serve as a small homage so that he can appreciate how immense the influence of his songs and actions has been in our times.

Most people would associate the term “ballad” with past achievements that could go back as far as the origins of story telling.  It is certainly unusual to read or even hear this word associated with contemporary scientific events.  However, in the early nineteen seventies this modern research project in structural biology reminded me of the mighty feats of medieval heroes. For nine long years, several generations of valiant postdoctoral investigators, led by Prof. M.G. Rossmann, struggled to adapt the methodology of protein crystallography to the solution of the atomic structure of the first spherical virus particles. Viruses (from Latin virus, poison) are cellular parasites unable to reproduce by themselves.  The class of spherical (or isometric ) viruses was established to differentiate them from other plant viruses such as tobacco mosaic virus (TMV) that were more elongated, or fiber-like and generally helical. There were two other groups working on a similar endeavor. One at Harvard led by Prof. Stephen Harrison, focused on tomato bushy stunt virus (TBSV), at the time the best structurally characterized spherical virus. A second in Uppsala, Sweden, trying to solve the structure of satellite tobacco necrosis virus (SNTV), a very small satellite virus, under the aegis of Prof. Bror Strandberg.

The achievement established new methodology that is now routinely used, and the results obtained opened intriguing lines of research on the structure, function and evolution of viruses. As I worked on the project, the stanzas of a ballad came to my mind as the most natural way to express my admiration for the feat of all the participants. It was a way of documenting the main milestones of a journey of scientific discovery of which I was a lucky participant.  If you do not hear from the other groups, it is not because their achievement was less significant. Absolutely not; they simply could not find  their balladeer.

Southern Bean Mosaic Virus (SBMV) .  The virus of our story is Southern Bean Mosaic Virus (SBMV), a humble RNA-containing plant virus that infects bean plants in the South of the United States. Neither SMBV nor its relative TBSV were ever as famous as the animal viruses that are fashionable today as human pathogens (for instance, AIDS virus or common cold -rhino virus-). Small as viruses go (approx. 300 Å in diameter), non-enveloped, single-stranded, RNA plant viruses like them were easy to obtain in gram quantities from a few infected plants.  In addition, they were easy to crystallize and consequently they were the objects of a concerted effort to obtain their atomic structure by X-ray diffraction methods with conventional in-house X-ray sources.

Viruses had to be constructed from a few identical subunit.  The icosahedral symmetry of small spherical viruses had been proposed by Watson and Crick in the early fifties[1]. They hypothesized that the limited size of the coding material in a virus (either DNA or RNA), could only code for a few proteins and therefore the virus particle had to be assembled by the repetition of a single –or a few- protein chains. Therefore, they predicted that the virus envelopes would be highly symmetrical, and most likely icosahedral, containing at least twenty copies of the coat protein in the shell, or capsid.  The detailed arrangement of the proteins in the capsid on the surface, and a preliminary classification of icosahedral viruses was presented by Caspar and Klug in their classic 1962 paper [2].

The symmetry of the particle.  It is instructive to look at the geometrical arrangement of protein chains on the surface of a virus particle from the viewpoint of more familiar objects. Think of a mosaic tile of hexagonal entities covering a planar surface. A moment’s thought would make you realize that in order to curve a planar surface covered by hexagons you have to introduce a certain number of pentagonal links or tiles; otherwise the surface will always be flat (Fig. 1, lower part and right). A close look at a soccer ball composed of pentagonal and almost perfectly hexagonal parts (quasi-hexagonal in the jargon of virus crystallography, Q6) sawn together illustrates the concept (Fig. 1, left). Similar geometrical principles were used to build the celebrated geodesic domes of Richard Buckminster Fuller (1895-1983), and have now been seen again in a special form of carbon containing clusters of sixty atoms (referred to as fullerenes or buckyballs).  In fact, it was recognized by Caspar and Klug that the inspiration for their insight into virus structure sprung from the arrangement of components in the geodesic domes. Based on this conceptual framework, the geometric lattices underlying the construction of certain spherical virus permits their classification as T=1 (icosahedron: 60 protein subunits, 20 x 3), T=3 (180, larger virus containing 180 subunits, 60 x 3), T=4 (still more complex lattices containing 240 (60 x 4) protein subunits) and others (Figs. 2). This is a key parameter in understanding the three-dimensional structure and external appearance of icosahedral viruses(2).

The atomic Structure of Virus Particles. Nevertheless, there was yet no atomic model for an icosahedral virus particle well into the1970’s.  As initially proposed by Michael Rossmann., the crucial factor in the determination of the structure was the presence of several identical copies of the polypeptide chain in the asymmetric unit: i.e. the presence of non-crystallographic symmetry. In those days, the major hurdle was to devise algorithms and programs, which would allow averaging of enormous electron density maps, containing many millions of grid points, over the redundant copies in the asymmetric unit. These methods were also employed to solve the structure of the common cold virus (rhinovirus) and are today standard in the structure determination of viruses and large protein complexes made up of several identical copies. The structure of the polypeptide chain of the different subunits of SBMV eventually emerged from the electronic density maps and I had the priviledge of building the atomic model (Fig.2).

Atomic structure of the entire  virus particle of SBMV shown with computer graphics. Each subunit is shown as the Carbon alpha tracing in different colors to depict the different geometric environment within the icosahedral shell.

Fig. 2. Atomic structure of the entire virus particle of SBMV shown with computer graphics. Each subunit is shown as the Carbon alpha tracing in different colors to depict the different geometric environment within the icosahedral shell. Red: 5-fold; Blue: 3-fold, quasi-6-fold; Green: 2-fold. Compare with the schematic depiction of Fig.1 (right); each triangle-shaped unit corresponds to one polypeptide chain.  Copyright CAZ. 

One of the most striking results of the structure determination of SBMV was the similarity of folds between the protein making the capsids of TBSV[3]and SBMV[4], and later STNV[5]. This unifying principle had an enormous impact in understanding the structure, function, evolution and diversity of a wide spectrum of viruses. The X-ray structure of SBMV was soon  followed  in 1982 by the complete amino acid sequence of the capsid protein and then the different amino acids could be related to their function in the assembly and disassembly of the virion particle.   The impact that this early work on virus has had in the virus of structural virology can be appreciated in Fig. 3,  reproduced from a recent publication by the Protein Data Bank, attempting to extract trends in data deposition[6]. There are now near 400 viral structures deposited in the PDB [6]. This remarkable figure shows how the different groups that have published crystallographic structures of viruses since the early structures appeared in the late 1970s and early 1980s, are all interconnected and related to the pioneer achievements of the structures of the three viruses related above: TBSV, SBMV, STNV (Fig. 3).

The detailed structural analysis of virus structures is being used to understand how virus particles infect their host cells and to design drugs against the common rhinovirus and other viral pathogens[7]. The epic feat of the determination of the first atomic structures of viruses should be part of the folklore of macromolecular crystallography.

Inter-connection among the different structural groups that have solved and deposited virus structures at the PDB. For more details consult Fig. 11 for reference [6].

Fig. 3.  Inter-connection among the different structural groups that have solved and deposited virus structures at the PDB. For more details consult Fig. 11 for reference [6]. This figure reproduced with permission from Herman et al. Copyright by Elsevier, FESB and Oxford University Press. All rights reserved.

The entire original  text of the ballad in English has been published in the official journal of Spanish Society of Virology (SEV, Revista de la Sociedad Española de Virología, 2013; Volume 13(3), 66-69) (www.cbm.uam.es/sev/revista.html) and is appended below. You can follow the entire text of the Ballad with some explanatory notes in Spanish. I am extracting here the most relevant ones as published on Chapter 22 of Crystals and Life (https://www.uic.edu/labs/caz/crystals/index.html)  with some clarifications. You can consult this chapter also to fully appreciate the structural relationships among the different viruses as they were unveiled in the early 1980s.


Notes to some stanzas of the Ballad of the 2.8 Å Structure of SBMV

M.G.R. began to work on small plant viruses soon after the structure of lactic dehydrogenase (LDH) had been published.  He went to Upssala, Sweden for a sabbatical leave in the laboratory of Bror Strandberg.

LDH has now been solved

 I must find something to do

Rossmann fold has been proposed

 I’ll take a sabbatical leave  (repeat)

And I’ll look at the STNV.

Soon after the return from the sabbatical leave he started to work on SMBV. Afternoon tea was a ritual at that time in the laboratory with a distinctly international flavor, and where the work progress was discussed.

Shall we start by growing some crystals?

 It’s only a matter of weeks

 After that we can write some proposals

 For the future of SBMV (repeat)

 You should drink your afternoon tea.

Although M.G.R.’s dream was to solve viruses ab initio, he soon realized that heavy atom derivatives were a safer route at the time. Of course, he continued to sail in Lake Freeman, Indiana.

Heavy-atoms must now be found

Playing chemists is all we must do

 One alone will be safer ground

For the structure of SBMV (repeat)

  I’m sailing the Indiana sea.

 After eight years of work, the atomic model of SBMV slowly grew as a metallic sculpture made up of Kendrew parts in a forest of  metal rods within a Richard’s Box. M.G.R. kept bumping his head against the top of the box, so he purchased a hard hat, which he rigorously wore for his building sessions with me.

Eight years have already passed

Many people have done their best

 I won’t say the struggle has finished

 For the structure of SBMV (repeat)

I’ll buy a helmet for me.

The fold of SBMV turned out to be a beta-barrel (or jelly-roll) almost identical to the one already described by Steve Harrison and colleagues for the structure of TBSV.

After so many years of labor

All we have is a barrel of sheet

Old Steve did us a favor

With the structure of TBSV (repeat)

We can trace our SBMV.


The entire original text of the ballad was sung at a party at the Rossmann’s residence on Sunday, November 4, 1979 to celebrate the solution of the three-dimensional structure of  SBMV.  The melody was adapted from a song by Pete Seeger (the grandfather of American folk music) that I heard on the radio one beautiful Autumn morning on my way to the lab. The entire ballad was meant to be an homage to all participants in the project of the three-dimensional structure of SBMV. Many of them I have met through the years at meetings and conferences. I shared with others hours of effort, frustration and excitement in the basement of the Lilly Hall of Life Sciences at Purdue University, West Lafayette, Indiana. The years spent in that laboratory still bring cherished memories.  A unique laboratory whose day-to-day routine was masterly orchestrated by Sharon Wilder. To all of them (the unsung heroes of this ballad), and to many others who participated in less visible ways, I want to express my deep appreciation: Sherin Abdel-Meguid, Toshio Akimoto, J.E. (Jack) Johnson, Andrew G.W. Leslie, Ivan Rayment, Michael G. Rossmann, Ira Smiley, Dietrich Suck, Tomitake Tsukihara and Mary Ann Wagner. I am just a modest minstrel, the troubadour of this epic feat.



(1). Crick, F. H. C. & Watson, J. D. Nature (1956), 177, 473-475.

(2). Caspar, D. L. D. & Klug, A. Cold Spring Harbor Symp. Quant. Biology (1962) 27, 1-24;

(3). Harrison, S. C., Olson, A. J., Schutt, C. E. Winkler, F. K. & Bricogne, G. Nature (1978) 276, 368-373.

(4). Abad-Zapatero, C., Abdel-Meguid, S.S., Johnson, J. E., Leslie, A. G. W., Rayment, I., Rossmann, M. G., Suck, D., & T. Tsukihara. Nature (1980) 286, 33-39.

(5). Liljas, A. et al. J. Mol. Biol. (1982), 195, 93-108.

(6) Berman, H. et al. FEBS Letters (2013), 587, 1036-1045.

(7) Perutz, M. From a Tomato Virus to Tumor and Influenza Viruses. Chapter 8.  In  Protein Structure. New Approaches to Disease and Therapy. W.H. Freeman and Company. 1992. New York.


The Ballad of the 2.8 Å Structure of SBMV (Complete text)


LDH has now been solved                                                     [1]

I must find something to do

Rossmann fold has been proposed

I’ll take a sabbatical leave.

I’ll take a sabbatical leave

And I’ll look at the STNV.


Would you like to get some experience?                                  [2]

It will help your future a lot

It’s your turn to do some big science

Come to work on the SBMV

If you work on the SBMV

You’ll have your afternoon tea.


Shall we start by growing some crystals?                                [3]

It’s only a matter of weeks

After that we can make some proposals

For the future of SBMV

If you work on the SBMV

You should have your afternoon tea.


Would you like to collect some data?                                     [4]

It will take only several months

I am sure we will have some errata

In the work on the SBMV

If you work on the SBMV

You must have your afternoon tea.


We should now process some native                                       [5]

My programs will make it go fast

After that we’ll have new perspective

On the structure of SBMV

For the structure of SBMV

We still drink our afternoon tea.


Heavy-atoms must now be found                                          [6]

Playing chemists is all we must do

One alone will be safer ground

For the structure of SBMV

For the structure of SBMV

I’ve sailed the Indiana Sea.


Other films must now be processed                                        [7]

Small changes is all that we need

More files will have to be accessed

For the structure of SBMV

For the structure of SBMV

I’ve sailed the Caribbean Sea.


Tsukihara computes day and night                                      [8]

MR-map must be calculated

Might longer that I’d have liked

For the structure of SBMV

For the structure of SBMV

I’ll have the cell constants at least.


Eight years have already passed                                          [9]

Many people have done their best

I won’t say the fight has finished

For the structure of SBMV

For the structure of SBMV

I’ll buy a helmet for me.


After so many years of labor                                                [10]

All we have is a barrel of sheet

Old Steve did us a favor

With the structure of TBSV

With the structure of TBSV

We can trace our SBMV.


Michael Rossmann explains evolution                                  [11]

For the virus it’s easy to do

Old Steve reacts with emotion

To the Structure of SBMV

Since the structure of SBMV

Is like the one of TBSV.


Pat will do some more prediction                                          [12]

Only thing he can do without labor

It will give bad reputation

To the structure of TYMV

For the structure of TYMV

Older brother of SBMV.


With the virus structure in my hand                                    [13]

New ideas and projects arise

This is only the start of the fun

With the structure of SBMV

With the structure of SBMV

I’ll take a sabbatical leave.


If I can reduce my sabbatical                                                              [14]

I could certainly go to Israel                                

On the way I’ll make some proposal

For the structure of STNV

For the structure of STNV

Little brother of SBMV.


What comes after sabbatical                                                 [15]

Ribosomes, proteosomes, you name it.

This man is a structural radical

Since the structure of SBMV

With the structure of SBMV

We have had our pizza free.