Chemistry, what’s Next?: Probability, Quantum Mechanics with Bioscience

Chemistry, what’s Next?:Chemistry, what’s Next?:Probability, Quantum Mechanics Probability, Quantum Mechanics

with Biosciencewith Bioscience(Transcription Factors in a Cell)(Transcription Factors in a Cell)

2014.10.10

전승준고려대학교 화학과

Journey of My Quest in Science

81-84 Ion beam 실험 연구 (Laser spectroscopy)

84-86 Radical 의 고압 안정화 연구 (Pressure-induced Solid state Phase transition)

86-88 고체수소 및 산소 고압연구 (Metallic Hydrogen, Bose-Einstein Condensation, Quantum Solid)

89-95 분광학과 고압 , 계산화학

95-06 유기 비선형 광학물질연구 ( 조봉래 ) (2 차 유기 비선형광학 물질 , 이광자 형광 현미경 ) 98.3-99.2 UC Berkeley – Sabbatical (not Nano, rather Bio)

06-09 다차원 비선형 분광학 ( 조민행 )

11- 미래 Physical Chemistry for Bio Science (Docking, Folding, Network, Information, Probability etc..)

Chemistry, What’s Next? (in 1990)

“What will Chemistry do in the Next Twenty years?” George Whitesides , Angew. Chem. Int. Ed. Engl. 29, 1209(1990)

Fundamental Thought in Physics & chemistry

“Chemistry advances on two feet : one is utility(Technology), one curiosity(Science).” Curiosity drives breakthrough on Utility

Theory Things

Next Fundamental theory? from Life?

Chromosome & Chromatin

Chemistry Bio & Med Science

Ultimate Goal of Bio & Med Science : What is life?

Life - Macroscopic phenomena, not molecular level (dead of molecules ?)

We need its appropriate level description

Microscopic View

-Molecular science -Theory: Quantum Chemistry

-Experiment: Spectroscopy

-Statistical Treatments

Macroscopic View

-Thermodynamics -Statistical Thermodynamics

-Thermodynamics Function (T, P, V, etc)

High LevelLow Level

Mesoscopic scale description

There is no rigid definition for mesoscopic physics, but the systems studied are normally in the range of 100 nm (the size of a typical virus) to 1000 nm (the size of a typical bacterium). (By Wikiphedia)

But Condensed Matter Physics ,especially related with Nanofablication & Nanotechnology (Quantum Confinement effect, Interference effect, Charging effect, etc.)

not Bio & Med Science

Mesoscopic scale description

Atoms, Molecules : Quantum Mechanics ( 일반적으로 인간의 인지가 불가능 영역 ) among 4 kinds of forces : Electomagnetic

Bulk : Random, Probability, Statistics - Thermodynamics, Statistical thermodynamics

Can we accept everything of life only with QM, EM force, Random motion ?

Central Dogma (Francis Creek, 1958)

Jacob and Monod model of transcriptional regulation of the lac operon by lac repressor(1961)When lac repressor binds to a DNA sequence called the operator (O), which lies just upstream of the lacZ gene, transcription of the operon by RNA polymerase is blocked. Binding of lactose to the repressor causes a conformational change in the repressor, so that it no longer binds to the operator. RNA polymerase then is free to bind to the promoter (P) and initiate transcription of the lac genes; the resulting polycistronic mRNA is translated into the encoded proteins. [Adapted from A. J. F. Griffiths et al., 1993, An Introduction to Genetic Analysis,5th ed., W. H. Freeman and Co.]

1: RNA Polymerase, 2: Repressor, 3: Promoter,4: Operator, 5: Lactose, 6: lacZ, 7: lacY, 8: lacA.

Top: The gene is essentially turned off. There is no lactose to inhibit the repressor, so the repressor binds to the operator, which obstructs the RNA polymerase from binding to the promoter and making lactase.Bottom: The gene is turned on. Lactose is inhibiting the repressor, allowing the RNA polymerase to bind with the promoter, and express the genes, which synthesize lactase. Eventually, the lactase will digest all of the lactose, until there is none to bind to the repressor. The repressor will then bind to the operator, stopping the manufacture of lactase.

1965 Nobel prize

Operator site : 10-20 base pairs long

Lactase 합성

Facilitated diffusion (Theory & Exp.)

An experimental measurement of the associationrate between LacI and its operator sites provided a value ofaround 1010 M-1 s-1, 2 orders of magnitude higher than the diffusion limit(108 M-1 s-1 ). (from Smoluchowski equation & 최신 data) Riggs, A.; Bourgeois, S.; Cohn, M. J. Mol. Biol. 1970, 53, 401.Halford, S. E.; Marko, J. F. Nucleic Acids Res. 2004, 32, 3040.

The hypothesis of facilitated diffusion of LacI along DNA issupported by both theoretical and experimental analyses.-Winter, R. B.; Berg, O. G.; von Hippel, P. H. Biochem 1981,20, 6961. -von Hippel, P.H. and Berg, O.G. J. Biol. Chem. 1989 264, 675–678

Facilitated Target Locationboth 1D sliding and 3D Space hopping and jumping (intramolecular dissociation/reassociation events)

Adam, G. & Delbrück, M. Reduction of dimensionality in biological diffusion processes. in Structural Chemistry and Molecular Biology (eds. Rich, A. & Davidson, N.) 198–215 (W.H. Freeman and Company, San Francisco; London, 1968)

Searching a rare event : Global minimum of binding energy?

Targeting sites on DNA : a targeting site among 106 – 109 decoy sites on a long DNA molecule

Facilitated diffusion (Theory & Exp.)

Real –time Single Molecule observation(resolution diffraction limit) Xie group (Science 316, 1191(2007) )

1D diffusion constant :D1D ∼ 0.046 μm2 s−1

3D diffusion constant : D3D ∼ 3 μm2 s−1

Apparent diffusion constant : Deff ∼0.40 μm2 s−1

Deff = D3D(1 − F ) + FD1D/3 (F: fraction of time for nonspecific binding) F ∼ 90%

즉 non-specsific binding 후 1D sliding search 자리를 못 찾으면 다시 dissociation 하면서 3D search 를 통하여 다른 곳에 non-specific binding 과정을 반복하여 결국 자리를 찾아 specific binding.

반론 논문 : “RNA polymerase approaches its promoter without long-range sliding along DNA” L. J. FriedmannPNAS 110, 9740 (2013) 등등

Crowding in a cell

Eukaryotic Prokaryotic

Concentration of Macromolecules : 50-400g/L

베이즈 확률론 (Bayes’ probability)확률을 ' 지식의 상태를 측정 ' 하는 것이라고 해석하는 확률론

확률객관적 확률 (Objective Probability) : 발생 빈도 (frequency) 나 어떤 시스템의 물리적

주관적 확률 (Subjective Probability): 개인적인 믿음의 정도 (degree of belief) 로 측정

베이즈 식 (Bayes’ Formula) 두 확률변수의 사전확률과 사후확률의 관계를 나타내는 정리로서 , 새로운 데이터가 제시됨에 따라 갱신되는 사후확률을 구하는 방법을 제시함 . 즉 어떤 가설의 확률을 평가하기 위해서 사전 확률을 먼저 밝히고 새로운 관련 데이터에 의한 새로운 확률값을 변경함 .

P(B|A)P(A) = P(A|B) P(B)

P(B|A) = P(A|B)P(B)

P(A)

P(A), P(B) 는 사건 A, B 가 일어날 확률 , P(B|A) 는 A 가 일어난 상황에서 B 가 일어날 조건부 확률 . P(A|B) 도 역의 조건부 확률 .

A B

not A not B

(P(A) = P(A|B)P(B) + P(A|not B)p(not B))

베이즈 확률 (Bayes’ probability)

P(B|A) = P(A|B)P(B)

P(A)

P(B)

P(B|A)

P(A|B) P(A)

Bayes’ Probability

1000 명당 1 명 정도 걸리는 감염성 희귀병 (rare event)검사법 – 병 걸린 사람 99% 양성반응 , 건강한 사람 2% 양성반응

자기가 양성반응 – 병에 걸렸을 확률은 ? 99%?

감염자 비감염자

양성반응 99 1998 2097

음성반응 1 97902 97903

100 99900 100000

=0.047

B not B

ANot A

P(B|A) = P(A|B)P(B)

P(A)= 0.99x100/100000

2097/100000

사전확률 P(B) 를 data P(A|B) 를 사용하여 사후확률 P(B|A) 를 구함 5%!!!

not B B

not A AB1 B2 B3 Bi

전체 사상

일반적인 베이즈 식

Bayes’ Formula : Transcription Factors(TFs) Binding Dynamics

Event : bindingA - keep binding or fall apartB - binding a right site or wrong sites

A : the events that a searcher bound with any targeting site keeps binding with the site.not A : the events that a searcher falls apart immediately after binding with any targeting site.

B : the events of a searcher binding with right targeting sitesnot B : the events of a searcher binding with wrong targeting sites

The conditional probability P(B|A) : the probability of a really right targeting given an event that a searcher keeps binding

(P(B)+P(not B) =1)


a ≈ 10-6 , 1-a ≈ 1, P(A|B) ≈ 1 라고 하면

틀리 곳에 계속 머무를 확률이 매우 작아야 함 . 즉 , 틀린 곳이면 떨어져야 할 확률이 매우 커야 함 .

Probability Distribution of Bindings on docking

Assumption : Probability of binding depending on binding Energy

Distribution of Binding Energy on docking

↕

Probability Distribution of Binding

Normal distribution with probability means μ and standard deviations σ

P(A|B) , P(A|not B)

- diverse binding energies - thermal energy of the surroundings around binding sites


Condition for right targeting

P(B)p(A|B) >P(not B)p(A|notB)

>

where, a=σB2-σnB

2 , b=2(σnB2μB-

σB2μnB)

X : 어떤 site 에 결합하여 계속 결합을 유지할 확율


Probability distributions due to :- diverse binding energies - thermal energy of the surroundings around binding sites

P(B)≈10-6, P(not B)≈1, and μB>μnB. μB=0.9, μnB=0.3, σB

=0.03, σnB=0.05. 0.853 < x < 0.957

The distribution functions of P(not B)p(A|not B)(black) and P(B)p(A|B)(Red).

p and q are the x values of the crossing points of the two functions, which are shown in the two insets

What does the region x mean?

Discussion

- P(B|A) 가 1 에 접근하려면 P(A|B) 가 커야 하는 것이 아니라 P(A|not B) 가 매우 작아야 한다는 것 .

- 즉 , right site 에 결합했을 때 계속 결합하는 것 ( 계산상 어떤 값이든 상관없음 ) 보다 wrong site 에 즉시 떨어지는 것이 중요하다는 것 .

-그러면 어떻게 wrong sites 에 결합되는 순간 빨리 떨어지는가 ?

There exist flags on sites?

생명현상에서 고려해야 할 것 들

Probability : Negative Entropy(Schrodinger) Shannon Entropy (Information entropy) ?

Potential : pair potential & attraction-repulsion New force? :Casimir force, Krugman potential(?)

Random motion : Stochastic Brownian Rachet? A First-Passage Problem? New Fundamental theory : Quantum Mechanics for life Non-locality/Entanglements ?

Paul Klugman : The self-organizing Economy(1996) J Bates Clark medal 1991, Nobel Prize Economics 2008Peddling Prosperity (95) Pop Internationalism(96) etc.

Inverse Potential : 일반적 pair potential, long attraction-short repulsion Krugman: Urban morphogenesis – Edge city model - potential: multi interaction, short attraction-long repulsion - one dimensional cyclic boundary condition

Krugman potential

x: location of firmsRxz : distance between x and zA: centripetal (attr) B: centrifugal(repel)a > b 때문에 agglomeration 생김λ(z) : density of firms

Locations of market potential:

Quantum Mecheanics : very weird !!!

- Superposition: Schrodinger’s cat- Uncertainty principle : Entanglment- Probability

5th Solvay conf(1927) 6th Solvay conf(1930)

VS

Hidden Variable Copenhagen

Photon : Young (1803)

Single Electron : Tonomura(1989)

Electron : Jonsson(1961)

Neutron : Zeilinger(1988)

He : Carnal(1991)

Clusters : Toennies(1994)

C60 :Zeilinger(1999)

SM : 원자갯수 114 분자량 1298(2012)>10,000amu, 원자갯수 810(2013)

Quantum Mecheanics:Double slit interference

Quantum Mechanics:Einstein-Podolsky-Rosen(EPR) paradox

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys. Rev. 47, 777–780 (1935)

Bohm version(1950 년대 )

Einstein called this the ‘spooky-action-at-a-distance’, which he could not accept due to the violation of ‘principle of locality’.

QM : Hidden Variable

)()()( caNcbNbaN

Bell uses logic in his explanation of inequality equation.

Suppose a photon pair is emitted by a source in opposite directions.the following three categories in which all detections are with spin

up. a . detectable at 0° and its pair at 45º . b. detectable at 45º and its pair at 90º . c. detectable at 0º and its pair at 90º.

a b c a b c

>

a ab bC cc

=

1964 : Bell’s Inequality : QM( 국소성 부정 ) vs HV( 숨은변수 ) test 고안

Quantum Entanglement: M easurements on spatially separated quantum systems can instantaneously influence one another.

Q.M. predicts that the probability that two particles will be detected at spin up withan angle Φ between the detectors is as follows.

Inserting values in to equation 1, we get equation 2

which is evaluated as,

0.1464 ≥ 0.25

0.0732 + 0.0732 ≥ 0.25

which is not true.

Since, it does not satisfy the inequality, it must be non-local.

))2

90(sin(

2

1))

2

45(sin(

2

1))

2

45(sin(

2

1 22

2))2

(sin(2

1 Eq. 1

Eq. 2

Bell : Evaluated Equality

1970 년대 실험 Clauser Excited Ca 원자에서 나오는 빛의 편광방향 실험

1980 년대 초반 Photon 실험 증명 Aspect 1990 년대 후반 Multi-photon Entanglement Zeilinger

Q Computing, Q Cryptography, Q Teleportation etc.


Chemistry : 만들어내는 것 ( 합성 ) 유기화학 , 생물화학 , 무기화학 , 재료화학 등등

Physics : 생각하게 하는 것 이론 들 ( 양자물리학 등등 )

Basis for Breakthrough during 20th Cenrtury

Quantum Mechanics, RelativityFrom Matters(Atoms, Light, Stars, etc.)


만드는 것 :

-무엇을 (What) : 기능 ( 의약품 , 전자재료 등등 ) Function-Structure relation ; 생각하게 만듬

-어떻게 (How): 저분자 , 단위분자의 연결 고분자 , 의도한 순서대로 고분자 – 생각하게 만듬 (Merrifield method, Click chemistry)

Chemistry 일부 : 잘 만들기 위한 수단 생각하게 만드는 화학 - 물리화학 , 이론화학 , 분석화학 등

배경 – 물리학 기반

New fundamental theory on BioScience ?

생명현상의 화학반응을 기존의 모델 (QM, EM force, Random)로 설명 못한다면 어떻게 (How) 기술할 수 있을까 ?

Probability : Shannon Entropy (Information entropy) ?

Potential : non pair potential - Krugman potential ?

Random motion : Stochastic - A First-Passage Problem? New Fundamental theory : Quantum Mechanics for life Non-locality/Entanglements ?

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Chemistry, what’s Next?: Probability, Quantum Mechanics with Bioscience

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Transcript of Chemistry, what’s Next?: Probability, Quantum Mechanics with Bioscience