Física do Corpo Humano - edisciplinas.usp.br · distribuída de acordo com uma curva normal (Gaussiana). Na forma comum do CLT: a variável aleatória deve ser identicamente distribuída

Mecnica Estatstica Soft Glassy Materials (estrutura)

Fsica do Corpo Humano(Fsica aplicado a Fisiologia)

Adriano M. Alencar

Laboratrio de Microrreologia e fisiologia Molecular (LabM2)Departamento de Fsica GeralInstituto de FsicaUniversidade de So Paulo

11 de maro de 2013


Princpios

Mecnica estatstica, ou termodinmica estatstica o ramo dafsica que aplica probabilidades para o estudo datermodinmica.Microscpico (tomo/Molcula) Macroscpico

A BA B


Princpios


A BA B

A AAA


Princpios


A BA BP=4*1/4

A A A A


Princpios


A BA BP=3/32A A A A

P=4*1/4 P=3*1/4 P=2*1/4 P=1*1/4


Princpios


A BA B

P=1/32

A A A AP=4*1/4 P=3*1/4 P=2*1/4 P=1*1/4

P=3/32

AAA

AP=4*1/4*1/4*1/4

P=1/64

AA AA

P=(4*1/4*1/4)

P=(2*1/4*1/4)


Princpios

Teorema do Limite Central (CLT)

Dado certas condies, a mdia de um nmero suficientegrande de variveis aleatrias, cada uma com uma mdiae varincia bem definida, ser aproximadamentedistribuda de acordo com uma curva normal (Gaussiana).

Na forma comum do CLT: a varivel aleatria deve seridenticamente distribuda.Outras formas: convergncia tambm ocorre paradistribuies no idnticas, desde que elas estejam deacordo com certas condies.


Princpios


Dado certas condies, a mdia de um nmero suficientegrande de variveis aleatrias, cada uma com uma mdiae varincia bem definida, ser aproximadamentedistribuda de acordo com uma curva normal (Gaussiana).Na forma comum do CLT: a varivel aleatria deve seridenticamente distribuda.

Outras formas: convergncia tambm ocorre paradistribuies no idnticas, desde que elas estejam deacordo com certas condies.


Princpios


Dado certas condies, a mdia de um nmero suficientegrande de variveis aleatrias, cada uma com uma mdiae varincia bem definida, ser aproximadamentedistribuda de acordo com uma curva normal (Gaussiana).Na forma comum do CLT: a varivel aleatria deve seridenticamente distribuda.Outras formas: convergncia tambm ocorre paradistribuies no idnticas, desde que elas estejam deacordo com certas condies.


Princpios

0.0

0.1

0.2

0.3

0.4

2 1 13 3 2

34.1% 34.1%

13.6%2.1%

13.6% 0.1%0.1%2.1%

http://www.youtube.com/watch?v=AUSKTk9ENzghttp://www.youtube.com/watch?v=XAuMfxWg6eI

http://www.youtube.com/watch?v=AUSKTk9ENzghttp://www.youtube.com/watch?v=XAuMfxWg6eI


Princpios


Polmeros

Polmeros: Somos feitos disso!

Polmeros OrgnicosTratamento:M. Continua e M.E.Possibilitou a vidaMotores Orgnicos(90% de Eficiencia)

Estrutura atmica do filamento de actina (proteina/polmero)


Polmeros


Polmeros Orgnicos

Tratamento:M. Continua e M.E.Possibilitou a vidaMotores Orgnicos(90% de Eficiencia)



Polmeros


Polmeros OrgnicosTratamento:M. Continua e M.E.

Possibilitou a vidaMotores Orgnicos(90% de Eficiencia)



Polmeros


Polmeros OrgnicosTratamento:M. Continua e M.E.Possibilitou a vida

Motores Orgnicos(90% de Eficiencia)



Polmeros


Polmeros OrgnicosTratamento:M. Continua e M.E.Possibilitou a vidaMotores Orgnicos(90% de Eficiencia)



Polmeros

Energia versus Comprimento (Lei de Escala)

Para um cabo de 20:1, mantendo a proporo 20:1

1 Energia de toro (Lei de Potncia)2 Energia de Fratura (Lei de Potncia)

Energia eletrosttica de uma casca esfrica


Polmeros


Para um cabo de 20:1, mantendo a proporo 20:11 Energia de toro (Lei de Potncia)

2 Energia de Fratura (Lei de Potncia)



Polmeros


Para um cabo de 20:1, mantendo a proporo 20:11 Energia de toro (Lei de Potncia)2 Energia de Fratura (Lei de Potncia)



Polmeros

grees of freedom is to consider collective excitations. Forexample, phonons characterize the vibrations of a crys-talline solid and magnons describe collective excitations ofmagnetic spins.

Indeed, physicists talk of -ons of all kinds. The bio-logical setting provides a loose analogy because somebiological structures are characterized with the label -somes, which derives from the Greek word for body.The term refers to macromolecular assemblies that aremade from multiple molecular components that act in acollective fashion to perform multiple functions. Some ofthe most notable examples include the ribosome, used inprotein synthesis; the nucleosome, which is the individualpacking unit for eukaryotic DNA; the proteasome, an as-sembly that mediates protein degradation; and the tran-scriptisome, which mediates gene transcription. By mech-anisms and principles that are still largely unknown,proteins assemble into -somes, perform a task, and thendisassemble again.

One of the most pleasing examples of biological col-lective action is revealed by the machines of the so-calledcentral dogma. The term refers to the set of processeswhereby DNA is copied (replication), genes are read andturned into messenger RNA (transcription), and finally,messenger RNA is turned into the corresponding proteinby ribosomes (translation). Such processes involve multi-ple layers of orchestration that range from the assemblyof macromolecular complexes to the simultaneous actionof multiple machines to the collective manner in whichcells may undertake the processes. Figure 3 shows the ma-chines of the central dogma in bacteria engaged in theprocesses of transcription and translation simultaneously.

The theme of collective action is also revealed in theflow of information in biological systems. For example, theprecise spatial and temporal orchestration of events that oc-curs as an egg differentiates into an embryo requires thatinformation be managed in processes called signal trans-duction. Biological signal transduction is often broadly pre-sented as a series of cartoons: Various proteins signal by in-teracting with each other via often poorly understoodmeans. That leads to a very simple representation: a net-work of blobs sticking or pointing to other blobs. Despite lim-ited knowledge, it should be possible to develop formal the-ories for understanding such processes. Indeed, the generalanalysis of biological networkssystems biologyis nowgenerating great excitement in the biology community.

Information flow in the central dogma is likewise oftenpresented as a cartoon: a series of directed arrows show-ing that information moves from DNA to RNA to proteins,and from DNA to DNA. But information also flows fromproteins to DNA because proteins regulate the expressionof genes by binding to DNA in various ways. Though all bi-ologists know that interesting feature of information flow,central-dogma cartoons continue to omit the arrow thatcloses the loop. That omission is central to the differencebetween a formal theory and a cartoon. A closed loop in aformal theory would admit the possibility of feedback andcomplicated dynamics, both of which are an essential partof the biological information management implemented bythe collective action of genes, RNA, and proteins.

Understanding collective effects in the cell will requiremerging two philosophical viewpoints. The first is that lifeis like a computer program: An infrastructure of machinescarries out arbitrary instructions that are encoded into DNA

www.physicstoday.org May 2006 Physics Today 41

Electrostatic energyof a spherical shell

Binding energy of anelectron in a box

Bending ofa 20:1 rod

Chemicalbonds

Fracture ofa 20:1 rod

Proton

Nucleus

Thermal energy

10010 310 610 910 1210 15

10 30

10 25

10 20

10 15

10 10

1010

105

10 5

100

LENGTH (meters)

EN

ER

GY

(jou

les)

Figure 2. The confluence of energy scales is illustrated in this graph, which shows how thermal, chemical, mechanical, andelectrostatic energies associated with an object scale with size. As the characteristic object size approaches that at which mo-lecular machines operate (shaded), all the energies converge. The horizontal line shows the thermal energy scale kT which, ofcourse, does not depend on an objects size. We estimate binding energy (purple) by considering an electron in a box; for com-parison, the graph shows measured binding energies for hydrogen bonds (square), phosphate groups in ATP (triangle), and co-valent bonds (circle), along with characteristic energies for nuclear and subatomic particles. In estimating the bending energy(blue), we took an elastic rod with an aspect ratio of 20:1 bent into a semicircular arc, and to compute the fracture energy(green) we estimated the energy in chemical bonds in a longitudinal cross section of the rod. The electrostatic energy (orange)was obtained for a spherical protein with singly charged amino acids of specified size distributed on the surface.

Maquinaria molecular: Ligao de Hidrognio (quadrado), grupos de fosfato em ATP (triangulo), ligaes

covalentes (crculo), energia de toro (azul), energia de fratura (verde), energia eletrosttica (laranja).

[Rob Phillips and Stephen R. Quake, Physics Today (2006)]


Motor muscular

entists have no general theory for their assembly or oper-ation. The basic physical principles are individually wellunderstood; what is lacking is a framework that combinesthe elegance of abstraction with the power of prediction.

Proteins are quite different from the simple diatomicmolecules that represent the traditional border betweenphysics and chemistry; they are enormously large, and formany purposes quantum mechanics plays a negligible rolein their function. Of course, if the question of interest hap-pens to be the chemistry that takes place in the active siteof an enzyme, one must ultimately look to quantum me-chanics as the basis for understanding. Quantum me-chanics can be neglected in the same sense that it is ig-nored in dynamical descriptions of everyday objects: Onthe smallest length scales, all atoms are fundamentallyquantum, but Plancks constant is not needed to formulateand apply the principle of least action. Indeed, one wouldbe hard put to describe many physical phenomena, rang-ing from protein behavior to critical phenomena to galax-ies, if a fully quantum mechanical description were re-quired. Proteins as molecules are polymers, and can often

be treated with a combination of continuum mechanicsand statistical mechanics. They act, in other words, as es-sentially classical objects.

How much can one molecule do? Consider, for exam-ple, ATP (adenosine triphosphate) synthase. This macro-molecular assembly, only about 10 nanometers on a side, isan essential part of the cellular factory that produces ATP,the universal energy currency of life. We will not get intothe details of the biological role of ATP synthase in the cell,but consider merely what it is capable of doing in isolation:It is a rotary motor. In the presence of a proton gradient,this remarkable machine turns a spindle as it adds phos-phate groups to molecules of adenosine diphosphate to pro-duce ATP.2 And every day, as discussed in box 1, the cellsin your body perform this phosphate-addition reaction toproduce roughly your body weight in ATP molecules.

But that is not all: ATP synthase can run in reverse.It can consume ATP, and with each ATP molecule that ishydrolyzed, the central shaft of ATP synthase turns by 120degrees, directly converting chemical to mechanical en-ergy. That reverse operation was explicitly demonstratedthrough a series of elegant experiments in which a molec-ular propeller was attached to the shaft and then imagedwith optical microscopy (see figure 1).3 The propeller ro-tated in the presence of ATP, with absolute thermodynamicefficiencies of up to 90%. Despite the tremendous stridesmade in nanotechnology, no device of similar functionalitycan yet be fabricated with inorganic materials. Further-more, many questions remain about the basic principlesby which molecular machines such as ATP synthase con-vert chemical energy to mechanical forces.

Working in a noisy environmentAs noted in our introductory remarks, molecular machinesoperate at energies and lengths common to a host of dif-ferent processes. In addition to being intriguing, thatregime adds to the challenge of analyzing the cells ma-chines. Figure 2 shows how thermal, chemical, mechani-cal, and electrostatic energies scale with the size of an as-sociated object, and illustrates the confluence of energies.As the characteristic size approaches that of biologicalmacromolecules, all the energies converge. The conver-gence is remarkable, since the energies range over 20 or-ders of magnitude as object size scales from subatomic tomacroscopic; its existence is an opportunity for complexphysical phenomena and processes that are evidently uti-lized by life. Broadly speaking, the interplay between ther-mal and deterministic forces is what gives rise to the richbehavior of molecular machines. For example, thermal ef-fects permit such processes as diffusion, conformational

www.physicstoday.org May 2006 Physics Today 39

TIME (seconds)0

0

1

2

3

4

5

6

7

8

50 100

RE

VO

LU

TIO

NS

a

b

Figure 1. The incredibly small motor ATP synthase adds aphosphate group to adenosine diphosphate to makeadenosine triphosphate. When run in reverse, it convertschemical energy stored in ATP to mechanical energy ofrotation. (a) An actin filament (pink) added to the shaft ofthe ATP synthase enables the shafts rotation to be imagedwith an optical microscope. Each ATP-to-ADP reactioncauses the actin propeller to rotate counterclockwise by120. In the experiment depicted here,3 a subcomplex ofthe ATP synthase was attached to a bead (orange) andcover slip. (b) The plot shows the discrete shifts in pro-peller position that accompany the chemical reactions.The inset tracks locations of the propeller. Note the singleclockwise rotation just before the 50-second mark; a ther-mal fluctuation has caused the propeller to rotate in thewrong direction. (Images courtesy of Kazuhiko KinositaJr, Waseda University, Japan.)

(Video)

[R. Yasuda et al., Cell 93, 1117 (1998)]http://www.k2.phys.waseda.ac.jp/F1movies/F1Step.htm

http://www.k2.phys.waseda.ac.jp/F1movies/F1Step.htm


Motor muscular

O Sistema Acto-Miosina presente empraticamente todas as celulas eucariontes(com ncleo)


Motor muscular

O Sistema Acto-Miosina presente empraticamente todas as celulas eucariontes(com ncleo)

Relaxed

Actin

Myosin

Contracted


Motor muscular

reading...

http://www.youtube.com/watch?v=oHDRIwRZRVI

actin.movMedia File (video/quicktime)

http://www.youtube.com/watch?v=oHDRIwRZRVI


Motor muscular

A maquinaria celular funcionaprxima a KBT ( 90% de eficincia) ;KBT Energia associada a temperatura T

Como , para as clulas, viver prximo de KBT ?


Motor muscular

A maquinaria celular funcionaprxima a KBT ( 90% de eficincia) ;KBT Energia associada a temperatura TComo , para as clulas, viver prximo de KBT ?


Vidros

Estado amorfo do ponto de vista molecularSolido sem cristalizao significante

KBT No conduz o sistema para o equilbrioATP hidrolise = 25KBT


Vidros

Estado amorfo do ponto de vista molecularSolido sem cristalizao significanteKBT No conduz o sistema para o equilbrio

ATP hidrolise = 25KBT


Vidros

Estado amorfo do ponto de vista molecularSolido sem cristalizao significanteKBT No conduz o sistema para o equilbrioATP hidrolise = 25KBT

Mecnica EstatsticaPrincpiosPolmerosMovido a Adenosina Trifosfato (ATP)Motor muscular

Soft Glassy Materials (estrutura)Vidros

Documents

Física do Corpo Humano - edisciplinas.usp.br · distribuída de acordo com uma curva normal (Gaussiana). Na forma comum do CLT: a variável aleatória deve ser identicamente distribuída