Los modelos teóricos presentados en este artículo pretenden mostrar porqué el exponente de ¾ de la ley de Kleiber puede surgir de las restricciones que impone distribuir los recursos a través de redes de ramificación jerárquica
3DSIG 2014 Presentation: Systematic detection of internal symmetry in proteinsSpencer Bliven
These slides are from 3DSIG 2014, presented on July 11.
I describe our investigation of internal symmetry in protein structures. This is quite common (24% of domains), and has many implications for function, folding, and evolution.
I introduce the CE-Symm method, described in
Myers-Turnbull, D., Bliven, S. E., Rose, P. W., Aziz, Z. K., Youkharibache, P., Bourne, P. E., & Prlić, A. (2014). Systematic Detection of Internal Symmetry in Proteins Using CE-Symm. Journal of Molecular Biology, 426(11), 2255–2268. doi:10.1016/j.jmb.2014.03.010
I discuss the results from running CE-Symm across the PDB, as well as some particularly compelling examples.
See also my poster by the same title for more details.
Journal club presentation on:
Pandya, C., Brown, S., Pieper, U., Šali, A., Dunaway-Mariano, D., Babbitt, P. C., et al. (2013). Consequences of domain insertion on sequence-structure divergence in a superfold. Proceedings of the National Academy of Sciences of the United States of America, 110(36), E3381–7. doi:10.1073/pnas.1305519110
Austin Journal of Reproductive Medicine & Infertility is an international scholarly, peer review, Open Access journal, aims to promote the research in Reproductive Medicine that compact with prevention, analysis & management of reproductive problems.
Austin Journal of Reproductive Medicine & Infertility is a comprehensive Open Access peer reviewed scientific journal that covers multidisciplinary fields. We provide limitless access towards accessing our literature hub with colossal range of articles. The journal aims to publish high quality varied article types such as Research, Review, Short Communications, Case Reports, Perspectives (Editorials), Clinical Images.
Austin Journal of Reproductive Medicine & Infertility supports the scientific modernization and enrichment in Reproductive Medicine research community by magnifying access to peer reviewed scientific literary works. Austin Publishing Group also brings universally peer reviewed member journals under one roof thereby promoting knowledge sharing, collaborative and promotion of multidisciplinary science.
El equipo de investigadores formado por dos físicos (Jayanth Banavarr y Amos Maritan), un botánico (Todd Cooke) y un hidrólogo (Andrea Rinaldo) sugiere que las plantas y los animales llegaron a soluciones similares (evolutivamente hablando) para resolver el problema del uso eficiente de la energía, y que evolucionaron en respuesta a los mismos principios físicos.
Artículo escrito por Max Kleiber y publicado en 1932 en la revista Hilgardia (la primera publicación técnica de la Universidad de California relacionada con la agricultura), donde expone por primera vez sus conclusiones acerca del metabolismo animal y su relación con la masa corporal
3DSIG 2014 Presentation: Systematic detection of internal symmetry in proteinsSpencer Bliven
These slides are from 3DSIG 2014, presented on July 11.
I describe our investigation of internal symmetry in protein structures. This is quite common (24% of domains), and has many implications for function, folding, and evolution.
I introduce the CE-Symm method, described in
Myers-Turnbull, D., Bliven, S. E., Rose, P. W., Aziz, Z. K., Youkharibache, P., Bourne, P. E., & Prlić, A. (2014). Systematic Detection of Internal Symmetry in Proteins Using CE-Symm. Journal of Molecular Biology, 426(11), 2255–2268. doi:10.1016/j.jmb.2014.03.010
I discuss the results from running CE-Symm across the PDB, as well as some particularly compelling examples.
See also my poster by the same title for more details.
Journal club presentation on:
Pandya, C., Brown, S., Pieper, U., Šali, A., Dunaway-Mariano, D., Babbitt, P. C., et al. (2013). Consequences of domain insertion on sequence-structure divergence in a superfold. Proceedings of the National Academy of Sciences of the United States of America, 110(36), E3381–7. doi:10.1073/pnas.1305519110
Austin Journal of Reproductive Medicine & Infertility is an international scholarly, peer review, Open Access journal, aims to promote the research in Reproductive Medicine that compact with prevention, analysis & management of reproductive problems.
Austin Journal of Reproductive Medicine & Infertility is a comprehensive Open Access peer reviewed scientific journal that covers multidisciplinary fields. We provide limitless access towards accessing our literature hub with colossal range of articles. The journal aims to publish high quality varied article types such as Research, Review, Short Communications, Case Reports, Perspectives (Editorials), Clinical Images.
Austin Journal of Reproductive Medicine & Infertility supports the scientific modernization and enrichment in Reproductive Medicine research community by magnifying access to peer reviewed scientific literary works. Austin Publishing Group also brings universally peer reviewed member journals under one roof thereby promoting knowledge sharing, collaborative and promotion of multidisciplinary science.
El equipo de investigadores formado por dos físicos (Jayanth Banavarr y Amos Maritan), un botánico (Todd Cooke) y un hidrólogo (Andrea Rinaldo) sugiere que las plantas y los animales llegaron a soluciones similares (evolutivamente hablando) para resolver el problema del uso eficiente de la energía, y que evolucionaron en respuesta a los mismos principios físicos.
Artículo escrito por Max Kleiber y publicado en 1932 en la revista Hilgardia (la primera publicación técnica de la Universidad de California relacionada con la agricultura), donde expone por primera vez sus conclusiones acerca del metabolismo animal y su relación con la masa corporal
Se describe uno de los primeros casos documentados de percepción multisensorial: lo que desde entonces se denomina “efecto McGurk”. Si vemos un video sin sonido donde una persona vocaliza y repite la sílaba “ga” y simultáneamente escuchamos una grabación de esa misma persona que pronuncia la sílaba “ba”, lo que oímos es que pronuncia la sílaba “da”. Las “ga” mudas alteran nuestra percepción de las “ba” sonoras porque el cerebro integra lo que vemos y oímos al mismo tiempo
Entrevista completa que le hizo la periodista Marie A. Belloc a Julio Verne en otoño de 1894, y que fue publicada en la revista Strand Magazine en febrero de 1895.
Interleukin-1 targeting drugs in familial mediterranean fever: a case series ...José Luis Moreno Garvayo
Revisión de los artículos publicados que describen el uso de medicamentos cuyo objetivo es la interleucina-1 en el tratamiento de la fiebre mediterránea familiar. Se describen siete casos en todos los cuales el uso de estos medicamentos fue beneficioso.
El principal objetivo de este trabajo ha consistido en establecer una cronología y datación precisas de los yacimientos Musterienses de Eurasia, ya que éstos contienen las mejores pruebas de la sustitución de un grupo humano (los Neandertales) por otro (AMHs)
The article deals with the molecular and insilico analysis of compound heterozygosity to understand the complex interactions and effects of the genetic compounds in HCM.
Theriot E.C., Cannone J.J., Gutell R.R., and Alverson A.J. (2009).
The limits of nuclear encoded SSU rDNA for resolving the diatom phylogeny.
European Journal of Phycology, 44(3):277-290.
"Keeping up with the plant destroyers." My talk at The Royal Society, 7 March...Sophien Kamoun
Tackling emerging threats to animal health, food security and ecosystem resilience, The Royal Society, Monday 7 – Tuesday 8 March 2016. https://royalsociety.org/events/2016/03/emerging-fungal-threats/
Diapositivas de la charla que ofrecí sobre ciencia, arqueología y pensamiento crítico, en el marco de la segunda edición de las charlas Hablando de Ciencia en Málaga 2015
Recopilación de todos los resúmenes y comentarios que se han realizado en el blog Tertulias Literarias de Ciencia acerca del libro Mala Ciencia de Ben Goldacre
Se han hecho públicos los resultados de un prometedor trabajo encabezado por investigadores del Hospital Infantil de Boston y la Facultad de Medicina de Harvard, que ha conseguido recuperar, utilizando terapia génica, parte de la audición de ratones sordos. El artículo, que ha merecido la portada de la prestigiosa revista Science Translational Medicine, promete abrir un abanico terapéutico para el tratamiento de la sordera genética en los seres humanos.
The evolutionary history of the hominin hand since the last common ancestor o...José Luis Moreno Garvayo
Tocheri y colaboradores sostienen que las pruebas moleculares y fósiles tienen importantes consecuencias para la interpretación de la historia evolutiva de la mano dentro de la tribu Hominini. En primer lugar, la parsimonia apoya la hipótesis de que la mano del último ancestro común de los humanos y chimpancés es más probable que es pareciera a la de un gran simio actual en general (Pan, Gorilla, y Pongo), que a la de un simio africano en particular. En segundo lugar, proporciona un contexto para la interpretación de los cambios derivados de la mano que se han desarrollado en diferentes homínidos. Sin embargo, la mayoría de las características primitivas que es probable que estuvieran presentes en el último ancestro común de Pan y Homo se mantienen en las manos de Australopithecus, Paranthropus/primeros humanos, y Homo floresiensis.
Análisis de las proporciones internas de la mano (la longitud de los huesos largos del pulgar y el cuarto dedo) en relación con el tamaño corporal de una muestra de primates actuales y extintos. La muestra la conforma un total de 274 primates entre los que se incluyen macacos, mandriles, gibones, orangutanes, gorilas, chimpancés y Homo sapiens; además de algunas especies extintas de homininos (Ardipithecus ramidus, Australopithecus sediba y Homo neanderthalensis).
The authors report the discovery of Lomekwi 3, a 3.3-million-year-old archaeological site where in situ stone artefacts occur in spatiotemporal association with Pliocene hominin fossils in a wooded palaeoenvironment.
Descripción del mecanismo de acción de la colchina en el tratamiento de la fiebre mediterránea familiar, y de los nuevos medicamentos que se están empleando para tratar esta dolencia.
Evidence based recommendations for the practical management of familial medit...José Luis Moreno Garvayo
Revisión de la literatura acerca de cuestiones prácticas en relación con la fiebre mediterránea familiar. Sobre la base del análisis de los artículos publicados se exponen las recomendaciones de los expertos tras la celebración de una reunión en Israel donde se expusieron todos los puntos de vista.
Este artículo muestra los resultados de un experimento con un test (llamado cognitive reflection test ―CRT por sus siglas en inglés y cuya traducción puede ser “prueba de reflexión cognitiva”) diseñado por Shane Frederick, profesor de mercadotecnia en la Universidad de Yale. Se realizaron una serie de encuestas a estudiantes de varias universidades norteamericanas (entre ellas el MIT, la Universidad de Princeton, Carnegie Mellon y Harvard) con el objetivo de averiguar qué tipo de razonamiento sigue una persona al enfrentarse a un problema en su vida cotidiana.
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...
A general model for the origin of allometric scaling laws in biology
1. p888, which contains a Bam HI to Not I fragment
encoding a full-length profilin cDNA (16); p989,
which encodes a mutant form of profilin, Pfy1p-3,
lacking the last three amino acids (18); p890, which
contains the Bgl II to Stu I fragment from p182 (26),
encoding Bni1p(1227–1397); p813, which con-
tains the Bgl II to Not I fragment from p182, encod-
ing Bni1p(1414–1953); and p951, which contains
the Hpa I to Not I fragment from p182, encoding
Bni1p(1647–1953). The pJG4-5–derived plasmids
were p561, which contains the Bam HI to Not I
fragment from p532 (26), encoding Bni1p(1–1953);
p717, which contains the Bam HI to Eco47 III frag-
ment from p532, encoding Bni1p(1–1214); p558,
which contains the Eco 47III to Not I fragment from
p182, encoding Bni1p(1215–1953); p913, which
contains the Bgl II to Stu I fragment from p182,
encoding Bni1p(1227–1397); p929, which con-
tains the Bgl II to Not I fragment from p182, encod-
ing Bni1p(1414–1953); p952, which contains the
Hpa I to Not I fragment from p182, encoding
Bni1p(1647–1953); and p887, which contains the
Bam HI to Not I fragment encoding a full-length
profilin cDNA (16). The pACT-derived plasmid was
p1124, encoding full-length Act1p as isolated in a
catch and release screen (22). The pGAD-C–de-
rived plasmid was p688, encoding the COOH-ter-
minal 311 amino acids (478–788) of Bud6p, as
isolated in a catch and release screen (22).
29. For localization of Bni1p, SY2625 (11) cells carrying a
multicopy plasmid encoding either HA-tagged Bni1p
[pY39tet1 (9)] or nontagged Bni1p were induced to
form mating projections (12). HA-Bni1p was localized
by immunofluorescence with monoclonal antibody
HA.11(Berkeley Antibody Company) as described [J.
R. Pringle, A. E. M. Adams, D. G. Drubin, B. K. Haarer,
Methods Enzymol. 194, 565 (1991)]. For localization
of Bud6p, SY2625 cells expressing GFP-Bud6p (23)
or containing the control plasmid pRS316 (26) were
induced to form mating projections (12), then ob-
served by fluorescence microscopy with the use of a
fluorescein isothiocyanate filter set.
30. Yeast cells of strain B5459 (MATa pep4::HIS3
prb1⌬1-6R ura3 trp1 lys2 leu2 his3⌬200 can1) car-
rying p1025 (26) were grown to mid-log phase in
raffinose medium, and galactose was added to
induce the production of HA-tagged Bni1p(1215–
1953). After 1 hour, extracts were prepared by
grinding cells with glass beads in lysis buffer [0.6 M
sorbitol, bovine serum albumin (1%), 140 mM
NaCl, 5 mM EDTA, 50 mM tris-HCl (pH 7.6), 0.06%
Triton X-100, 2 mM phenylmethylsulfonyl fluoride,
aprotinin (10 g/ml)] as described (2). Escherichia
coli strain BL 21 (Novagen) was transformed with
pGEX-3X (Pharmacia) or p907 (26) and induced for
expression of GST or GST-profilin, respectively.
GST proteins were purified on glutathione-Sepha-
rose (Pharmacia) and washed twice with phos-
phate-buffered saline (PBS) [140 mM NaCl, 2.7
mM KCl, 10 mM Na2HPO4, 1.8 mM KH2PO4 (pH
7.3)]. Glutathione-Sepharose beads with GST or
GST-profilin bound were then added to the yeast
extract containing HA-Bni1p(1215–1953) and in-
cubated on ice. After 45 min, the beads were col-
lected and washed twice with PBS. The GST pro-
teins and associated proteins were eluted with glu-
tathione [10 mM glutathione, 50 mM tris-HCl (pH
8.0)] and subjected to immunoblot analysis with
antibodies to GST (Pharmacia) or the HA epitope
(29) as described (27).
31. We thank D. Amberg, B. Andrews, R. Brent, R.
Dorer, S. J. Elledge, S. Givan, B. K. Haarer, J.
Horecka, P. James, I. Sadowski, M. Tyers, and J.
Zahner for plasmids and yeast strains; B. Brand-
horst, J. Brown, N. Davis, S. Kim, B. Nelson, and I.
Pot for comments on the manuscript; and G. Poje
and I. Pot for assistance with experiments. Support-
ed by grants to C.B. from the Natural Sciences and
Engineering Research Council of Canada and the
National Cancer Institute of Canada; by a grant from
the Swiss National Science Foundation to M.P.; and
by NIH grant GM31006 to J.R.P.
2 December 1996; accepted 10 February 1997
A General Model for the Origin of Allometric
Scaling Laws in Biology
Geoffrey B. West, James H. Brown,* Brian J. Enquist
Allometric scaling relations, including the 3/4 power law for metabolic rates, are char-
acteristic of all organisms and are here derived from a general model that describes how
essential materials are transported through space-filling fractal networks of branching
tubes. The model assumes that the energy dissipated is minimized and that the terminal
tubes do not vary with body size. It provides a complete analysis of scaling relations for
mammalian circulatory systems that are in agreement with data. More generally, the
model predicts structural and functional properties of vertebrate cardiovascular and
respiratory systems, plant vascular systems, insect tracheal tubes, and other distribution
networks.
Biological diversity is largely a matter of
body size, which varies over 21 orders of
magnitude (1). Size affects rates of all bio-
logical structures and processes from cellu-
lar metabolism to population dynamics (2,
3). The dependence of a biological variable
Y on body mass M is typically characterized
by an allometric scaling law of the form
Y ϭ Y0Mb
(1)
where b is the scaling exponent and Y0 a
constant that is characteristic of the kind
of organism. If, as originally thought, these
relations reflect geometric constraints,
then b should be a simple multiple of
one-third. However, most biological phe-
nomena scale as quarter rather than third
powers of body mass (2–4): For example,
metabolic rates B of entire organisms scale
as M3/4
; rates of cellular metabolism,
heartbeat, and maximal population
growth scale as MϪ1/4
; and times of blood
circulation, embryonic growth and devel-
opment, and life-span scale as M1/4
. Sizes
of biological structures scale similarly: For
example, the cross-sectional areas of mam-
malian aortas and of tree trunks scale as
M3/4
. No general theory explains the ori-
gin of these laws. Current hypotheses,
such as resistance to elastic buckling in
terrestrial organisms (5) or diffusion of
materials across hydrodynamic boundary
layers in aquatic organisms (6), cannot
explain why so many biological processes
in nearly all kinds of animals (2, 3), plants
(7), and microbes (8) exhibit quarter-pow-
er scaling.
We propose that a common mechanism
underlies these laws: Living things are sus-
tained by the transport of materials
through linear networks that branch to
supply all parts of the organism. We de-
velop a quantitative model that explains
the origin and ubiquity of quarter-power
scaling; it predicts the essential features of
transport systems, such as mammalian
blood vessels and bronchial trees, plant
vascular systems, and insect tracheal
tubes. It is based on three unifying princi-
ples or assumptions: First, in order for the
network to supply the entire volume of
the organism, a space-filling fractal-like
branching pattern (9) is required. Second,
the final branch of the network (such as
the capillary in the circulatory system) is a
size-invariant unit (2). And third, the en-
ergy required to distribute resources is
minimized (10); this final restriction is
basically equivalent to minimizing the to-
tal hydrodynamic resistance of the system.
Scaling laws arise from the interplay be-
tween physical and geometric constraints
implicit in these three principles. The
model presented here should be viewed as
an idealized representation in that we ig-
nore complications such as tapering of
vessels, turbulence, and nonlinear effects.
These play only a minor role in determin-
ing the dynamics of the entire network
and could be incorporated in more de-
tailed analyses of specific systems.
Most distribution systems can be de-
scribed by a branching network in which
the sizes of tubes regularly decrease (Fig.
1). One version is exhibited by vertebrate
circulatory and respiratory systems, anoth-
er by the “vessel-bundle” structure of mul-
tiple parallel tubes, characteristic of plant
vascular systems (11). Biological networks
vary in the properties of the tube (elastic
to rigid), the fluid transported (liquid to
gas), and the nature of the pump (a pul-
satile compression pump in the cardiovas-
cular system, a pulsatile bellows pump in
the respiratory system, diffusion in insect
G. B. West, Theoretical Division, T-8, Mail Stop B285,
Los Alamos National Laboratory, Los Alamos, NM
87545, and The Santa Fe Institute, 1399 Hyde Park
Road, Santa Fe, NM 87501, USA.
J. H. Brown and B. J. Enquist, Department of Biology,
University of New Mexico, Albuquerque, NM 87131, and
The Santa Fe Institute, 1399 Hyde Park Road, Santa Fe,
NM 87501, USA.
*To whom correspondence should be addressed. E-mail:
jhbrown@unm.edu
SCIENCE ⅐ VOL. 276 ⅐ 4 APRIL 1997 ⅐ http://www.sciencemag.org122
2. tracheae, and osmotic and vapor pressure
in the plant vascular system). In spite of
these differences, these networks exhibit
essentially the same scaling laws.
For convenience we shall use the lan-
guage of the cardiovascular system, name-
ly, aorta, arteries, arterioles, and capillar-
ies; the correspondence to other systems is
straightforward. In the general case, the
network is composed of N branchings from
the aorta (level 0) to the capillaries (level
N, denoted here by a subscript c) (Fig.
1C). A typical branch at some intermedi-
ate level k has length lk, radius rk, and
pressure drop ⌬pk (Fig. 1D). The volume
rate of flow is ˙Qk ϭ rk
2
uk where uk is the
flow velocity averaged over the cross sec-
tion and, if necessary, over time. Each
tube branches into nk smaller ones (12), so
the total number of branches at level k is
Nk ϭ n0n1 . . . nk. Because fluid is con-
served as it flows through the system
˙Q0 ϭ Nk
˙Qk ϭ Nkrk
2
uk ϭ Ncrc
2
uc (2)
which holds for any level k. We next intro-
duce the important assumption, the second
above, that the terminal units (capillaries)
are invariant, so rc, lc, uc, and, consequently,
⌬pc are independent of body size. Because
the fluid transports oxygen and nutrients for
metabolism, ˙Q0 ϰ B; thus, if B ϰ Ma
(where
a will later be determined to be 3/4), then
˙Q0 ϰ Ma
. Equation 2 therefore predicts that
the total number of capillaries must scale as
B, that is, Nc ϰ Ma
.
To characterize the branching, we in-
troduce scale factors k ϵ rkϩ1/rk and ␥k ϵ
lkϩ1/lk. We shall prove that in order to
minimize the energy dissipated in the sys-
tem in the sense of the third principle
above, the network must be a convention-
al self-similar fractal in that k ϭ , ␥k ϭ
␥, and nk ϭ n, all independent of k (an
important exception is k in pulsatile sys-
tems). For a self-similar fractal, the num-
ber of branches increases in geometric pro-
portion (Nk ϭ nk
) as their size geometri-
cally decreases from level 0 to level N.
Before proving self-similarity, we first ex-
amine some of its consequences.
Because Nc ϭ nN
, the number of gener-
ations of branches scales only logarithmi-
cally with size
N ϭ
a ln͑M/Mo)
ln n
(3)
where M0 is a normalization scale for M
(13). Thus, a whale is 107
times heavier
than a mouse but has only about 70% more
branchings from aorta to capillary. The to-
tal volume of fluid in the network (“blood”
volume Vb) is
Vb ϭ k ϭ 0
N
NkVk ϭ k ϭ 0
N
rk
2
lknk
ϭ
͑n␥2
͒Ϫ͑N ϩ 1͒
Ϫ 1
͑n␥2
͒Ϫ1
Ϫ 1
nN
Vc (4)
where the last expression reflects the fractal
nature of the system. As shown below, one
can also prove from the energy minimiza-
tion principle that Vb ϰ M. Because n␥2
Ͻ
1 and N ϾϾ 1, a good approximation to Eq.
4 is Vb ϭ V0/(1 Ϫ n␥2
) ϭ Vc(␥2
)ϪN
/
(1 Ϫ n␥2
). From our assumption that cap-
illaries are invariant units, it therefore fol-
lows that (␥2
)ϪN
ϰ M. Using this relation
in Eq. 3 then gives
a ϭ Ϫ
ln n
ln͑␥2
͒
(5)
To make further progress requires knowl-
edge of ␥ and . We shall show how the
former follows from the space-filling fractal
requirement, and the latter, from the energy
minimization principle.
A space-filling fractal is a natural struc-
ture for ensuring that all cells are serviced
by capillaries. The network must branch so
that a group of cells, referred to here as a
“service volume,” is supplied by each capil-
lary. Because rk ϽϽ lk and the total number
of branchings N is large, the volume sup-
plied by the total network can be approxi-
mated by the sum of spheres whose diame-
ters are that of a typical kth-level vessel,
namely 4/3(lk/2)3
Nk. For large N, this es-
timate does not depend significantly on the
specific level, although it is most accurate
for large k. This condition, that the fractal
be volume-preserving from one generation
to the next, can therefore be expressed as
4/3(lk/2)3
Nk Ϸ 4/3(lkϩ1/2)3
Nkϩ1. This
relation gives ␥3
k ϵ (lkϩ1/lk)3
Ϸ Nk/Nkϩ1 ϭ
1/n, showing that ␥k Ϸ nϪ1/3
Ϸ ␥ must be
independent of k. This result for ␥k is a
general property of all space-filling fractal
systems that we consider.
The 3/4 power law arises in the simple
case of the classic rigid-pipe model, where
the branching is assumed to be area-pre-
serving, that is, the sum of the cross-sec-
tional areas of the daughter branches equals
that of the parent, so rk
2
ϭ nrk
2
ϩ1. Thus,
k ϵ rkϩ1/rk ϭ nϪ1/2
ϭ , independent of k.
When the area-preserving branching rela-
tion,  ϭ nϪ1/2
, is combined with the
space-filling result for ␥, Eq. 5 yields a ϭ
3/4, so B ϰ M3/4
. Many other scaling laws
follow. For example, for the aorta, r0 ϭ
ϪN
rc ϭ Nc
1/2
rc and l0 ϭ ␥ϪN
rc ϭ Nc
1/3
lc,
yielding r0 ϰ M3/8
and l0 ϰ M1/4
. This
derivation of the a ϭ 3/4 law is essentially a
geometric one, strictly applying only to sys-
tems that exhibit area-preserving branch-
ing. This property has the further conse-
quence, which follows from Eq. 2, that the
fluid velocity must remain constant
throughout the network and be indepen-
dent of size. These features are a natural
consequence of the idealized vessel-bundle
structure of plant vascular systems (Fig. 1B),
in which area-preserving branching arises
automatically because each branch is as-
sumed to be a bundle of nNϪk
elementary
vessels of the same radius (11). Pulsatile
mammalian vascular systems, on the other
hand, do not conform to this structure, so
for them, we must look elsewhere for the
origin of quarter-power scaling laws.
Some features of the simple pipe model
remain valid for all networks: (i) The quan-
tities ␥ and  play a dual scaling role: they
determine not only how quantities scale
from level 0 (aorta) to N (capillary) within
a single organism of fixed size, but also how
a given quantity scales when organisms of
different masses are compared. (ii) The frac-
tal nature of the entire system as expressed,
for example, in the summation in Eq. 4
leads to a scaling different from that for a
single tube, given by an individual term in
the series. These network systems must
therefore be treated as a complete integrat-
ed unit; they cannot realistically be mod-
eled by a single or a few representative
vessels. (iii) The scaling with M does not
Fig. 1. Diagrammatic examples of
segments of biological distribu-
tion networks: (A) mammalian cir-
culatory and respiratory systems
composed of branching tubes;
(B) plant vessel-bundle vascular
system composed of diverging
vessel elements; (C) topological
representation of such networks,
where k specifies the order of the
level, beginning with the aorta
(k ϭ 0) and ending with the capil-
lary (k ϭ N); and (D) parameters of
a typical tube at the kth level.
REPORTS
http://www.sciencemag.org ⅐ SCIENCE ⅐ VOL. 276 ⅐ 4 APRIL 1997 123
3. depend on the branching ratio n.
We next consider the dynamics of the
network and examine the consequences of
the energy minimization principle, which is
particularly relevant to mammalian vascu-
lar systems. Pulsatile flow, which dominates
the larger vessels (aorta and major arteries),
must have area-preserving branching, so
that  ϭ nϪ1/2
, leading to quarter-power
scaling. The smaller vessels, on the other
hand, have the classic “cubic-law” branch-
ing (10), where  ϭ nϪ1/3
, and play a
relatively minor role in allometric scaling.
First consider the simpler problem of
nonpulsatile flow. For steady laminar flow
of a Newtonian fluid, the viscous resistance
of a single tube is given by the well-known
Poiseuille formula Rk ϭ 8lk/rk
4
, where is
the viscosity of the fluid. Ignoring small
effects such as turbulence and nonlineari-
ties at junctions, the resistance of the entire
network is given by (14)
Z ϭ k ϭ 0
N Rk
Nk
ϭ k ϭ 0
N 8lk
rk
4
nk
ϭ
͓1 Ϫ ͑n4
/␥͒N ϩ 1
͔Rc
͑1 Ϫ n4
/␥͒nN
(6)
Now, n4
/␥ Ͻ 1 and N ϾϾ 1, so a good
approximation is Z ϭ Rc/(1 Ϫ n4
/␥)Nc.
Because Rc is invariant, Z ϰ Nc
Ϫ1
ϰ MϪa
,
which leads to two important scaling laws:
blood pressure ⌬p ϭ ˙Q0Z must be indepen-
dent of body size and the power dissipated
in the system (cardiac output) W ϭ ˙Q0⌬p ϰ
Ma
, so that the power expended by the
heart in overcoming viscous forces is a size-
independent fraction of the metabolic rate.
Neither of these results depends on detailed
knowledge of n, , or ␥, in contrast to
results based on Vb ϰ M, such as Eq. 5, a ϭ
3/4, and r0 ϰ M3/8
. From Eq. 2, ˙Q0 ϭ r0
2
u0,
which correctly predicts that the velocity of
blood in the aorta u0 ϰ M0
(2). However, an
area-preserving scaling relation  ϭ nϪ1/2
also implies by means of Eq. 2 that uk ϭ u0
for all k. This relation is valid for fluid flow
in plant vessels (because of the vascular bun-
dle structure) (11, 15) and insect tracheae
(because gas is driven by diffusion) (16);
both therefore exhibit area-preserving
branching, which leads to 3/4 power scaling
of metabolic rate. Branching cannot be en-
tirely area-preserving in mammalian circula-
tory systems because blood must slow down
to allow materials to diffuse across capillary
walls. However, the pulsatile nature of the
mammalian cardiovascular system solves the
problem.
Energy minimization constrains the net-
work for the simpler nonpulsatile systems.
Consider cardiac output as a function of all
relevant variables: W(rk, lk, nk, M). To sus-
tain a given metabolic rate in an organism
of fixed mass M with a given volume of
blood Vb(rk, lk, nk, M), the minimization
principle requires that the cardiac output be
minimized subject to a space-filling geome-
try. To enforce such a constraint, we use the
standard method of Lagrange multipliers (,
k, and M) and so need to minimize the
auxiliary function
F(rk, lk, n) ϭ W(rk, lk, nk, M)
ϩ Vb(rk, lk, nk, M) ϩ k ϭ 0
N
kNklk
3
ϩ MM
(7)
Because B ϰ Q0 and W ϭ ˙Q0
2
Z, this prob-
lem is tantamount to minimizing the im-
pedance Z, which can therefore be used in
Eq. 7 in place of W. First, consider the case
where nk ϭ n, so that we can use Eqs. 4 and
6 for Vb and Z, respectively. For a fixed mass
M, the auxiliary Lagrange function F,
which incorporates the constraints, must be
minimized with respect to all variables for
the entire system (rk, lk, and n). This re-
quires ץF/ץlk ϭ ץF/ץrk ϭ ץF/ץn ϭ 0, which
straightforwardly leads to k ϭ nϪ1/3
. More
generally, by considering variations with
respect to nk, one can show that nk ϭ n,
independent of k. The result, k ϭ nϪ1/3
, is
a generalization of Murray’s finding (17),
derived for a single branching, to the com-
plete network. Now varying M and mini-
mizing F in Eq. 7 (ץF/ץM ϭ 0) leads to Vb
ϰ M, which is just the relation needed to
derive Eq. 5. Although the result k ϭ nϪ1/3
is independent of k, it is not area-preserving
and therefore does not give a ϭ 3/4 when
used in Eq. 5; instead, it gives a ϭ 1. It does,
however, solve the problem of slowing
blood in the capillaries: Eq. 2 gives uc/ u0 ϭ
(n2
)ϪN
ϭ Nc
Ϫ1/3
. For humans, Nc Ϸ 1010
,
so uc/ u0 Ϸ 10Ϫ3
, in reasonable agreement
with data (18). On the other hand, it leads
to an incorrect scaling law for this ratio:
uc/ u0 ϰ MϪ1/4
. Incorporating pulsatile flow
not only solves these problems, giving the
correct scaling relations (a ϭ 3/4 and uc/ u0
ϰ M0
), but also gives the correct value for
uc/ u0.
A complete treatment of pulsatile flow
is complicated; here, we present a simpli-
fied version that contains the essential
features needed for the scaling problem.
When an oscillatory pressure p of angular
frequency is applied to an elastic (char-
acterized by modulus E) vessel with wall
thickness h, a damped traveling wave is
created: p ϭ p0
ei(t Ϫ 2z/)
. Here, t is time,
z is the distance along the tube, is the
wavelength, and p0 is the amplitude aver-
aged over the radius; the wave velocity
c ϭ 2. Both the impedance Z and the
dispersion relation that determines c are
derived by solving the Navier-Stokes
equation for the fluid coupled to the
Navier equations for the vessel wall (19).
In the linearized incompressible-fluid,
thin-wall approximation, this problem can
be solved analytically to give
ͩc
c0
ͪ2
Ϸ Ϫ
J2͑i3/2
␣͒
J0͑i3/2
␣͒
and Z Ϸ
c0
2
r2
c
(8)
Here ␣ ϵ (/)1/2
r is the dimensionless
Womersley number (13), and c0 ϵ (Eh/
2r)1/2
is the Korteweg-Moens velocity. In
general, both c and Z are complex functions
of , so the wave is attenuated and disperses
as it propagates. Consider the consequences
of these formulas as the blood flows through
progressively smaller tubes: For large tubes,
␣ is large (in a typical human artery, ␣ Ϸ
5), and viscosity plays almost no role. Equa-
tion 8 then gives c ϭ c0 and Z ϭ c0/r2
;
because both of these are real quantities,
the wave is neither attenuated nor dis-
persed. The r dependence of Z has changed
from the nonpulsatile rϪ4
behavior to rϪ2
.
Minimizing energy loss now gives hk/rk (and,
therefore, ck) independent of k and, most
importantly, an area-preserving law at the
junctions, so k ϭ nϪ1/2
. This relation en-
sures that energy-carrying waves are not
reflected back up the tubes at branch points
and is the exact analog of impedance
matching at the junctions of electrical
transmission lines (18). As k increases, the
sizes of tubes decrease, so ␣ 3 0 (in human
arterioles, for example, ␣ Ϸ 0.05), and the
role of viscosity increases, eventually dom-
inating the flow. Equation 8 then gives c Ϸ
i1/2
␣c0/4 3 0, in agreement with observa-
tion (18). Because c and, consequently,
now have imaginary parts, the traveling
wave is heavily damped, leaving an almost
steady oscillatory flow whose impedance is,
from Eq. 8, given by the Poiseuille formula;
that is, the rϪ4
behavior is restored. Thus,
for large k, corresponding to small vessels,
k ϭ nϪ1/3
. We conclude that for pulsatile
flow, k is not independent of k but rather
has a steplike behavior (Fig. 2). This picture
Fig. 2. Schematic variation of the Womersley num-
ber ␣k and the scaling parameters k and ␥k with
level number (k) for pulsatile systems. Note the
steplike change in k at k ϭ k from area-preserving
pulse-wave flow in major vessels to area-increasing
Poiseuille-type flow in small vessels.
SCIENCE ⅐ VOL. 276 ⅐ 4 APRIL 1997 ⅐ http://www.sciencemag.org124
4. is well supported by empirical data (18, 20,
21). The crossover from one behavior to the
other occurs over the region where the wave
and Poiseuille impedances are comparable in
size. The approximate value of k where this
occurs (say, k) is given by rk
2
/lk Ϸ 8/c0,
leading to N Ϫ k ϵ N Ϸ ln(8lc/c0rc
2
)/ln n,
independent of M. Thus, the number of
generations where Poiseuille flow dominates
should be independent of body size. On the
other hand, the crossover point itself
grows logarithmically: k ϰ N ϰ ln M. For
humans, with n ϭ 3 (21), N Ϸ 15 and
N Ϸ 22 (assuming Nc Ϸ 2 ϫ 1010
), where-
as with n ϭ 2, N Ϸ 24 and N Ϸ 34. These
values mean that in humans Poiseuille
flow begins to compete with the pulse
wave after just a few branchings, dominat-
ing after about seven. In a 3-g shrew,
Poiseuille flow begins to dominate shortly
beyond the aorta.
The derivation of scaling laws based on k
derived from Eqs. 7 and 8 (Fig. 2) leads to the
same results as before. For simplicity, assume
that the crossover is sharp; using a gradual
transition does not change the resulting scal-
ing laws. So, for k Ͼ k, define k ϵ Ͼ ϭ
nϪ1/3
and, for k Ͻ k, k ϵ Ͻ ϭ nϪ1/2
. This
predicts that area preservation only persists
in the pulsatile region from the aorta
through the large arteries, at most until k Ϸ
k. First consider the radius of the aorta r0: its
scaling behavior is now given by r0 ϭ
rcϾ
k ϪN
Ͻ
k
ϭ rcn1/3Nϩ1/6k
ϭ rc
n1/2NϪ1/6N
,
which gives r0 ϰ M3/8
and, for humans, r0/rc
Ϸ 104
, in agreement with data (2) . Using
Eq. 3 we obtain, for the ratio of fluid
velocity in the aorta to that in the capil-
lary, u0 / uc ϭ Nc(rc/r0)2
ϭ nN/3
u0 / uc Ϸ
250, independent of M, again in agree-
ment with data. Because ␥ reflects the
space-filling geometry, it remains un-
changed, so we still have l0 ϰ M1/4
. Blood
volume Vb, however, is more complicated
Vb ϭ
Vc
͑Ͼ
2
␥͒N ͭͩϾ
Ͻ
ͪ
2
¯
k
1 Ϫ ͑nϽ
2
␥͒
¯
k
1 Ϫ ͑nϽ
2
␥͒
ϩ ͫ1 Ϫ ͑nϾ
2
␥͒N
1 Ϫ ͑nϾ
2
␥͒
Ϫ
1 Ϫ ͑nϾ
2
␥͒
¯
k
1 Ϫ ͑nϾ
2
␥͒ ͬͮ (9)
This formula is a generalization of Eq. 4
and is dominated by the first term, which
represents the contribution of the large
tubes (aorta and arteries). Thus, Vb ϰ
nNϩ1/3
k ϰ n4/3
N, which, because it must
scale as M, leads, as before, to a ϭ 3/4. As
size decreases, the second term, represent-
ing the cubic branching of small vessels,
becomes increasingly important. This be-
havior predicts small deviations from
quarter-power scaling (a տ 3/4), observed
in the smallest mammals (2). An expres-
sion analogous to Eq. 9 can be derived for
the total impedance of the system Z. It is
dominated by the small vessels (arterioles
and capillaries) and, as before, gives ⌬p
and u0 ϰ M0
.
In order to understand allometric scal-
ing, it is necessary to formulate an integrat-
ed model for the entire system. The present
model should be viewed as an idealized
zeroth-order approximation: it accounts for
many of the features of distribution net-
works and can be used as a point of depar-
ture for more detailed analyses and models.
In addition, because it is quantitative, the
coefficients, Y0 of Eq. 1, can also, in prin-
ciple, be derived. It accurately predicts the
known scaling relations of the mammalian
cardiovascular system (Table 1); data are
needed to test other predictions. For exam-
ple, the invariance of capillary parameters
implies Nc ϰ M3/4
rather than the naı¨ve
expectation Nc ϰ M, so the volume serviced
by each capillary must scale as M1/4
, and
capillary density per cross-sectional area of
tissue, as MϪ1/12
.
A minor variant of the model describes
the mammalian respiratory system. Al-
though pulse waves are irrelevant because
the tubes are not elastic, the formula for Z is
quite similar to Eq. 8. The fractal bronchial
tree terminates in NA ϰ M3/4
alveoli. The
network is space-filling, and the alveoli play
the role of the service volume accounting
for most of the total volume of the lung,
which scales as M. Thus, the volume of an
alveolus VA ϰ M1/4
, its radius rA ϰ M1/12
,
and its surface area AA ϰ rA
2
ϰ M1/6
, so the
total surface area of the lung AL ϭ NAAA ϰ
M11/12
. This explains the paradox (22) that
AA scales with an exponent closer to 1 than
the 3/4 seemingly needed to supply oxygen.
The rate of oxygen diffusion across an alve-
olus, which must be independent of M, is
proportional to ⌬pO2
AA/rA. Thus, ⌬pO2
ϰ
MϪ1/12
, which must be compensated for by a
similar scaling of the oxygen affinity of he-
moglobin. Available data support these pre-
dictions (Table 1).
Our model provides a theoretical, mech-
anistic basis for understanding the central
role of body size in all aspects of biology.
Considering the many functionally inter-
connected parts of the organism that must
obey the constraints, it is not surprising that
the diversity of living and fossil organisms is
based on the elaboration of a few successful
designs. Given the need to redesign the
entire system whenever body size changes,
Table 1. Values of allometric exponents for variables of the mammalian
cardiovascular and respiratory systems predicted by the model compared
with empirical observations. Observed values of exponents are taken from (2,
3); ND denotes that no data are available.
Cardiovascular Respiratory
Variable
Exponent
Variable
Exponent
Predicted Observed Predicted Observed
Aorta radius r0 3/8 ϭ 0.375 0.36 Tracheal radius 3/8 ϭ 0.375 0.39
Aorta pressure ⌬p0 0 ϭ 0.00 0.032 Interpleural pressure 0 ϭ 0.00 0.004
Aorta blood velocity u0 0 ϭ 0.00 0.07 Air velocity in trachea 0 ϭ 0.00 0.02
Blood volume Vb 1 ϭ 1.00 1.00 Lung volume 1 ϭ 1.00 1.05
Circulation time 1/4 ϭ 0.25 0.25 Volume flow to lung 3/4 ϭ 0.75 0.80
Circulation distance l 1/4 ϭ 0.25 ND Volume of alveolus VA 1/4 ϭ 0.25 ND
Cardiac stroke volume 1 ϭ 1.00 1.03 Tidal volume 1 ϭ 1.00 1.041
Cardiac frequency Ϫ1/4 ϭ Ϫ0.25 Ϫ0.25 Respiratory frequency Ϫ1/4 ϭ Ϫ0.25 Ϫ0.26
Cardiac output E˙ 3/4 ϭ 0.75 0.74 Power dissipated 3/4 ϭ 0.75 0.78
Number of capillaries Nc 3/4 ϭ 0.75 ND Number of alveoli NA 3/4 ϭ 0.75 ND
Service volume radius 1/12 ϭ 0.083 ND Radius of alveolus rA 1/12 ϭ 0.083 0.13
Womersley number ␣ 1/4 ϭ 0.25 0.25 Area of alveolus AA 1/6 ϭ 0.083 ND
Density of capillaries Ϫ1/12 ϭ Ϫ0.083 Ϫ0.095 Area of lung AL 11/12 ϭ 0.92 0.95
O2 affinity of blood P50 Ϫ1/12 ϭ Ϫ0.083 Ϫ0.089 O2 diffusing capacity 1 ϭ 1.00 0.99
Total resistance Z Ϫ3/4 ϭ Ϫ0.75 Ϫ0.76 Total resistance Ϫ3/4 ϭ Ϫ0.75 Ϫ0.70
Metabolic rate B 3/4 ϭ 0.75 0.75 O2 consumption rate 3/4 ϭ 0.75 0.76
REPORTS
http://www.sciencemag.org ⅐ SCIENCE ⅐ VOL. 276 ⅐ 4 APRIL 1997 125
5. either during ontogeny or phylogenetic di-
versification, small deviations from quarter-
power scaling sometimes occur (3, 23).
However, when body sizes vary over many
orders of magnitude, these scaling laws are
obeyed with remarkable precision. More-
over, the predicted scaling properties do not
depend on most details of system design,
including the exact branching pattern, pro-
vided it has a fractal structure (24). Signif-
icantly, nonfractal systems, such as combus-
tion engines and electric motors, exhibit
geometric (third-power) rather than quar-
ter-power scaling (1). Because the fractal
network must still fill the entire D-dimen-
sional volume, our result generalizes to a ϭ
D/(D ϩ 1). Organisms are three-dimension-
al, which explains the 3 in the numerator of
the 3/4 power law, but it would be instruc-
tive to examine nearly two-dimensional or-
ganisms such as bryozoans and flatworms.
The model can potentially explain how
fundamental constraints at the level of in-
dividual organisms lead to corresponding
quarter-power allometries at other levels.
The constraints of body size on the rates at
which resources can be taken up from the
environment and transported and trans-
formed within the body ramify to cause
quarter-power scaling in such diverse phe-
nomena as rate and duration of embryonic
and postembryonic growth and develop-
ment, interval between clutches, age of first
reproduction, life span, home range and
territory size, population density, and max-
imal population growth rate (1–3). Because
organisms of different body sizes have dif-
ferent requirements for resources and oper-
ate on different spatial and temporal scales,
quarter-power allometric scaling is perhaps
the single most pervasive theme underlying
all biological diversity.
REFERENCES AND NOTES
___________________________
1. T. A. McMahon and J. T. Bonner, On Size and Life
(Scientific American Library, New York, 1983); J. T.
Bonner, The Evolution of Complexity by Means of
Natural Selection (Princeton Univ. Press, Princeton,
NJ, 1983); J. H. Brown, Macroecology (Univ. of Chi-
cago Press, Chicago, 1995).
2. K. Schmidt-Nielsen, Scaling: Why Is Animal Size so
Important? (Cambridge Univ. Press, Cambridge,
1984); W. A. Calder III, Size, Function and Life History
(Harvard Univ. Press, Cambridge, MA, 1984).
3. R. H. Peters, The Ecological Implications of Body
Size (Cambridge Univ. Press, Cambridge, 1983).
4. H. A. Feldman and T. A. McMahon, Respir. Physiol.
52, 149 (1983).
5. T. A. McMahon, Science 179, 1201 (1973).
6. M. R. Patterson, ibid. 255, 1421 (1992).
7. K. J. Niklas, Plant Allometry: The Scaling of Form and
Process (Univ. of Chicago Press, Chicago, 1994);
Am. J. Bot. 81, 134 (1994).
8. A. M. Hemmingsen, Rep. Steno Mem. Hosp.
(Copenhagen) 4, 1 (1950); ibid. 9, 1 (1960).
9. B. B. Mandelbrot, The Fractal Geometry of Nature
(Freeman, New York, 1977).
10. D’A. W. Thompson, On Growth and Form (Cam-
bridge Univ. Press, Cambridge, 1942).
11. K. Shinozaki et al., Jpn. J. Ecol. 14, 97 (1964); ibid.,
p. 133; see also M. H. Zimmerman, Xylem Structure
and the Ascent of Sap (Springer-Verlag, Berlin,
1983); M. T. Tyree and F. W. Ewers, New Phytol.
119, 345 (1991).
12. The branching of a vessel at level k into nk smaller
vessels (Fig. 1) is assumed to occur over some small,
but finite, distance that is much smaller than either lk
or lkϩ1. This relation is similar to that assumed in the
Strahler method [A. N. Strahler, Trans. Am. Geo-
phys. Union 34, 345 (1953); (11, 21)]. A generaliza-
tion to nonuniform branching, where the radii and
lengths at a given level may vary, is straightforward.
13. Normalization factors, such as M0, will generally be
suppressed, as in Eq. 1. In general, all quantities
should be expressed in dimensionless form; note,
however, that this does not guarantee that they are
size independent and scale as M0. For example, the
Womersley number, ␣ of Eq. 8, although dimension-
less, scales as M 1/4.
14. This formula is not valid for plant vessel bundles
because plants are composed of multiple parallel
vessel elements. Their resistance is given by Z ϭ
8l /Ncrc
4, where l is the length of a single vessel
element, rc is its radius, and Nc is their total number.
15. This relation holds for plant vessels from the roots to
the leaves, but not within leaves [M. J. Canney, Phi-
los. Trans. R. Soc. London Ser. B 341, 87 (1993)].
16. A. Krogh, Pfluegers Arch. Gesamte Physiol. Men-
schen Tiere 179, 95 (1920).
17. C. D. Murray, Proc. Natl. Acad. Sci. U.S.A. 12, 207
(1926).
18. C. G. Caro et al., The Mechanics of Circulation (Ox-
ford Univ. Press, Oxford, 1978).
19. J. R. Womersley, Philos. Mag. 46, 199 (1955);
J. Physiol. (London) 127, 553 (1955).
20. See, for example, A. S. Iberall, Math. Biosci. 1, 375
(1967) and T. F. Sherman, J. Gen. Physiol. 78, 431
(1981), which contain summaries of earlier data; also
M. Zamir et al., J. Biomech. 25, 1303 (1992) and J.
K.-J. Li, Comparative Cardiovascular Dynamics of
Mammals (CRC Press, Boca Raton, FL, 1996). Care
must be taken in comparing measurements with
prediction, particularly if averages over many suc-
cessive levels are used. For example, if Ak ϵ ͚krk
2 is
the total cross-sectional area at level k, then for the
aorta and major arteries, where k Ͻ k and the
branching is area-preserving, we predict A0 ϭ Ak.
Suppose, however, that the first K levels are grouped
together. Then, if the resulting measurement gives
AK, area-preserving predicts AK ϭ KA0 (but not AK ϭ
A0). It also predicts r0
3 Ϸ n 1/2͚Nkrk
3. Using results
from M. LaBarbera [Science 249, 992 (1990)], who
used data averaged over the first 160 vessels (ap-
proximately the first 4 levels), gives, for human be-
ings, A0 Ϸ 4.90 cm2, AK Ϸ 19.98 cm2, r0
3 Ϸ 1.95
cm3, and ͚Nkrk
3 Ϸ 1.27 cm3, in agreement with area
preservation. LaBarbera, unfortunately, took the fact
that AK A0 and r0
3 Ϸ ͚Nkrk
3 as evidence for cubic
rather than area-preserving branching. For small
vessels, where k Ͼ k, convincing evidence for the
cubic law can be found in the analysis of the arteriolar
system by M. L. Ellsworth et al., Microvasc. Res. 34,
168 (1987).
21. Y. C. Fung, Biodynamics (Springer-Verlag, New
York, 1984).
22. P. Gehr et al., Respir. Physiol. 44, 61 (1981).
23. P. M. Bennett and P. H. Harvey, J. Zool. 213, 327
(1987); A. F. Bennett, Am. Zool. 28, 699 (1988); P. H.
Harvey and M. D. Pagel, The Comparative Method in
Evolutionary Biology (Oxford Univ. Press, Oxford,
1991).
24. This is reminiscent of the invariance of scaling expo-
nents to details of the model that follow from renor-
malization group analyses, which can be viewed as a
generalization of classical dimensional analysis.
25. J.H.B. is supported by NSF grant DEB-9318096,
B.J.E. by NSF grant GER-9553623 and a Fulbright
Fellowship, and G.B.W. by the Department of Energy.
13 September 1996; accepted 12 February 1997
Flexibility in DNA Recombination: Structure of
the Lambda Integrase Catalytic Core
Hyock Joo Kwon, Radhakrishna Tirumalai, Arthur Landy,*
Tom Ellenberger*
Lambda integrase is archetypic of site-specific recombinases that catalyze intermolec-
ular DNA rearrangements without energetic input. DNA cleavage, strand exchange, and
religation steps are linked by a covalent phosphotyrosine intermediate in which Tyr342
is attached to the 3Ј-phosphate of the DNA cut site. The 1.9 angstrom crystal structure
of the integrase catalytic domain reveals a protein fold that is conserved in organisms
ranging from archaebacteria to yeast and that suggests a model for interaction with target
DNA. The attacking Tyr342
nucleophile is located on a flexible loop about 20 angstroms
from a basic groove that contains all the other catalytically essential residues. This
bipartite active site can account for several apparently paradoxical features of integrase
family recombinases, including the capacity for both cis and trans cleavage of DNA.
The integrase protein (Int) of Escherichia
coli phage lambda () belongs to a large
family of site-specific DNA recombinases
from archaebacteria, eubacteria, and yeast
(1–3) that catalyze rearrangements be-
tween DNA sequences with little or no
sequence homology to each other (4–8).
Like Int, many of these recombinases
function in the integration and excision of
viral genomes into and out of the chromo-
somes of their respective hosts. Others
function in the decatenation or segrega-
tion of newly replicated chromosomes,
conjugative transposition, regulation of
plasmid copy number, or expression of cell
surface proteins. Integrase family members
have the distinctive ability to carry out a
complete site-specific recombination reac-
H. J. Kwon and T. Ellenberger, Department of Biological
Chemistry and Molecular Pharmacology, Harvard Medi-
cal School, Boston MA 02115, and the Graduate Pro-
gram in Biophysics, Harvard University, Cambridge, MA
02138, USA.
R. Tirumalai and A. Landy, Division of Biology and Med-
icine, Brown University, Providence, RI 02912, USA.
*Corresponding authors.
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