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Cellular mechanics I

2018. 2nd term

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Various Science

Biology Physics Chemistry

Biology is the science of life. ...

Biologists study the structure, function, growth, origin, evolution and distribution of living organisms.

Biology is the natural science that studies life and living organisms, including their physical structure, chemical processes, molecular interactions, physiological mechanisms, development and evolution

• The dictionary definition of physics is “the study of matter, energy, and the interaction between them”, but what that really means is that physics is about asking fundamental questions and trying to answer them by observing and experimenting.

• Physics is the natural science that studies matter and its motion and behavior through space and time and that studies the related entities of energy and force.

• Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.

• Chemistry is the study of matter, its properties, how and why substances combine or separate to form other substances, and how substances interact with energy.

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Newton’s 3 Laws (Mechanics)

Isaac Newton

1642-1727

James Clerk Maxwell

1831-1879

(Electricity & Magnetism) Maxwell’s 4 Equations

J. Willard Gibbs

1839-1903

Gibb’s Free Energy

(Thermodynamics)

Erwin Schrödinger

1887-1961

Schrodinger’s Equation

(Quantum Mechanics)

Ludwig Boltzmann

1844-1906

S= k·log W

(Stat. Mechanics of Entropy)

Physics is about great laws

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Evolution -- Life evolved from simpler forms

--One of the best tested scientific theories around

Evolution is a series of tricks/random events

Build complex beings from simpler parts

Often many ways of doing this

Our life form is just one.

Charles Darwin, Age 51, 1860,

On the Origin of Species

Does biology have any great theories or law?

Gregor Johann Mendel

(1822 –1884)

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Biophysics

• Biophysics is an interdisciplinary science that applies the approaches and methods of physics

to study biological systems.

• Biophysics applies the principle of physics and chemistry and the methods of methodical

analysis and computer modeling to biological system, with the ultimate goal of

understanding at a fundamental level the structure, dynamics, interactions, and ultimately

the function of biological system.

• Biophysics covers all scales of biological organization, from molecular to organismic and

population.

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Biophysics_New fields

• A new filed of sciences

• 1892 – Karl Pearson termed biophysics

• Modern, interdisciplinary field of science for understanding biological phenomenon.

• Explanations based on physical and mathematical concepts

• Investigations and experiments with physical instruments

• Bragg at the Cavendish Lab Cambridge

Bio

Thermodynamics

Electricity

Mathematics

Acoustics

Hydrodynamics

Mechanics

Magnetism

Optics

Kinetics

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Bio-physics-engineering

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What is the goal of biophysics?

• Create simplified models of biological systems

- If all life follows the same basic rule, what is it?

• Make quantitative predictions and experimental test

• Develop new technology

• Advance understanding about bio-system

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What are biophysicist working on?

• Research in biochemistry and biophysics is focused on numerous process central to understanding life.

• Biophysicists study life at every level, from atoms and molecules to cells, organisms, and environments

• Several groups use biochemical and structural approaches to address the basic principle governing

protein folding, function and biological recognition.

• Using in vitro approaches, the central steps in biological information transfer are being analyzed, from

maintenance of the genome to protein synthesis, sorting and processing.

- How do protein machines work?

- How do systems of never cells communicate?

- How do proteins pack DNA into viruses?

- How do viruses invade cells?

- How do cells move?

- What are the mechanical properties of cells? How does this relate to disease?

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1. Biophysics at the molecular level:

• Determination and prediction of protein structures

• Single-molecule spectroscopy

• Molecular motors

• The protein folding problem

• DNA-protein interactions

…..…

2. Biophysics at the cellular level:

• Transport within and across cell membranes

• Structure and properties of cell membranes

• Propagation of neural signals

• Cytoskeleton and cell movements

• Cytokinesis

….…

3. Biophysics at multicellular and higher levels:

• Tissue and biomedical engineering

• Physical and mathematical physiology

• Biomechanics and bio-rheology

• Population dynamics and theory of evolution

• Mathematical epidemiology

….…

Some aspects of biophysics

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Luigi Galvani

• Electro-Physiology

• Discovered Bio-electricity

• 1787, Frog muscle experiment

• Physicist, biologist, and philosopher

• Luigi Galvani touched the nerves of a frog's spinal cord with metal electro

des which caused contractions of the leg muscles.

• Electricity is the language of the nervous system.

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DNA structure

1895 X-rays discovered by Roentgen

1914 First diffraction pattern of a crystal made by

Knipping and von Laue

1915 Theory to determine crystal structure from

diffraction pattern developed by Bragg

1953 DNA structure solved by Watson and Crick

Max Theodor Felix von Laue

German physicist who won the

Nobel Prize in Physics in 1914 for

his discovery of the diffraction of

X-rays by crystals

Sir William Lawrence Bragg,

31 March 1890 – 1 July 1971

Australian-born British physicist and X-

ray crystallographer, discoverer (1912) of

Bragg's law of X-ray diffraction, which is

basic for the determination of crystal

structure

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Coherence of light waves mean they have the same phase and frequency Diffraction: Spreading of light passing through a small aperture or around a sharp edge

Double slit interference

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• Destructive interference

ΔL = (2n+1)λ/2

n = 0, 1, 2, ……

• Constructive interference

ΔL = nλ n = 0, 1, 2, ……

http://vsg.quasihome.com/interfer.htm

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X-ray interacts with matter

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• Incoming X-rays are electromagnetic waves that exert a force on atomic electrons.

• The electrons will begin to oscillate at the same frequency and emit radiation in all directions.

e-

Coherent scattering by an atom

• Coherent scattering by an atom is the sum of this scattering by all of the electrons.

• Electrons are at different positions in space, so coherent scattering from each generally has different phase relationships.

• At higher scattering angles, the sum of the coherent scattering is less.

2q

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Diffraction patterns

Two successive CCD detector images with a crystal rotation of one degree per image:

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Diffraction of X-rays by crystals

• The science of X-ray crystallography originated in 1912 with the discovery by Max von Laue that crystals diffract X-rays.

• Von Laue was a German physicist who won the Nobel Prize in Physics in 1914 for his discovery of the diffraction of X-rays by crystals.

Max Theodor Felix von Laue (1879 – 1960)

X-ray diffraction pattern from a single-crystal sample

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After Von Laue's pioneering research, the field developed rapidly, most notably by physicists William Lawrence Bragg and his father William Henry Bragg.

In 1912-1913, the younger Bragg developed Bragg's law, which connects the observed scattering with reflections from evenly-spaced planes within the crystal. William Lawrence Bragg

William Henry Bragg

Diffraction of X-rays by crystals

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Diffractogram 51

The best X-ray scattering on DNA (Franklin and Gosling, 1952). Only diffractograms with enough order can be analyzed quantitatively by applying the theory if X-ray scattering on helical molecules.

Rosalind Elsie Franklin (1920-1958)

Her X-ray diffraction produced the most beautiful pattern that could be analyzed quantitatively.

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DNA is a double helix!

A model is built in the Cavendish laboratory in Cambridge consistent with all the discernible features of the diffractogram 51...

Saturday February 28, 1953.

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The distinctive “X” in this X-ray photo is the telltale pattern of a helix

Because the X-ray pattern is so regular, the

dimension of the helix must be constant.

For example, the diameter of the helix stays

the same.

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The helix’s pitch, or its degree of rise, can be

calculated from the angle the “X” makes with

the horizontal axis.

If we distort the helix, you can get an idea

how the helical pitch is related to the X-ray

pattern.

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In an X-ray diffraction pattern, the closer the spots, the larger the actual distance. So the horizontal bars actually correspond to helical turns. The vertical distance between the bars is a measure of the height of the one helical turn.

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Since, we know the height of one helical repeat (34 Å ) and we know the distance between the stacked base

pairs (3.4 Å ), there must be 10 nucleotides per helical repeat.

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Central dogma of molecular biology

• DNA mRNA protein

• DNA TRANSCRIBES to mRNA

• Process is called transcription

• mRNA TRANSLATES to proteins

• Process is called translation

• Actually makes amino acids, which come

together to make proteins

DNA molecules serve as templates for either complementary DNA strands during the process

of replication or complementary RNA during the process of transcription.

RNA molecules serve as a template for ordering amino acids by ribosomes during protein

synthesis.

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Molecular biophysics

• For biological systems to function, interactions occur between many different types of molecules: DNA,

RNA, Protein, Lipids, etc.

• To ensure that biological systems function appropriately, such interactions must be carefully regulated

• Wide range of biophysical chemistry approaches are useful for studying these interactions

• Interactions between molecules are central to how cells detect and respond to signals and affect:

• Gene expression (transcription & translation)

• DNA replication, repair and recombination

• Signalling

• And many other processes....

• Interactions are mainly mediated by many weak chemical bonds (van der Waals forces, hydrogen

bonds, hydrophobic interactions)

• Accumulation of many bonds influences affinity and specificity of interactions

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Structure and Conformation of Biological Molecules

Structure Function Relationships

Conformational Transitions

Ligand Binding and Intermolecular Binding

Diffusion and Molecular Transport

Membrane Biophysics

DNA and Nucleic Acid Biophysics

Protein Biophysics

Energy Flow and Bioenergetics

Thermodynamics

Statistical Mechanics

Kinetics

Molecular Machines

Allosterics

Examples of molecular biophysics

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Protein structure

Primary structure

Assembly

Secondary structure

Folding

Tertiary structure

Packing

Quaternary structure

Interaction

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Protein folding

Transcription DNA RNA Polypeptide Functional protein

Translation Folding

Linear nucleic acid

Linear nucleic acid

Linear amino acid sequence

Three dimensional

structure

• Proteins fold spontaneously under physiological conditions

- In the equilibrium between the denatured state (unfolded or partially unfolded) and the native state

(folded, biologically functional), under physiological conditions the vast majority of molecules are in

the native state

Denaturation

Renaturation

Primary structure Unfolded structure Inactive collection of many random structures

Tertiary structure Folded structure Active 3-dimensional structure of protein

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Protein structure analysis

• Experimental determination and analysis

• Repositories

• Protein Data Bank

• Molecular Modeling DataBase

• Resolution

• X-Ray Crystallography

• NMR Spectroscopy

• Mass Spectroscopy (next week)

• Fluorescence Resonance Energy Transfer

• Computational determination and analysis

• Databases

• CATH (Class, Architecture, Topology,

Homologous superfamily)

• SCOP (Structural Classification Of Proteins)

• FSSP (Fold classification based on Structure-

Structure alignment of Proteins)

• Prediction

• Ab-initio, theoretical modeling, and

conformation space search

• Homology modeling and threading

• Energy minimization, simulation and Monte

Carlo

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Protein Data Bank

• The Protein Data Bank was established at

Brookhaven National Labs in 1971 as an archive

of biological macromolecular crystal structures.

• Since October 1998, the PDB database has been

managed by the Research Collaboratory for

Structural Bioinformatics (RCSB), which is a

consortium consisting of Rutgers, the State

University of New Jersey; The San Diego

Supercomputer Centre at the University of

California, San Diego; and the National Institute

of Standards and Technology.

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• The PDB archive contains macromolecular structure data on proteins, nucleic acids, protein-nucleic acid

complexes, and viruses. Files in its holdings are deposited by the international user community and

maintained by the RCSB PDB staff. Approximately 50-100 new structures are deposited each week. They

are annotated by RCSB and released upon the depositor's specifications. PDB data is freely available

worldwide.

• As of 14 March 2017, 127352 structures have been deposited in the PDB

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• Crystallize and immobilize single, perfect protein

• Bombard with X-rays, record scattering diffraction

patterns

• Determine electron density map from scattering

and phase via Fourier transform:

• Use electron density and biochemical knowledge

of the protein to refine and determine a model

X-Ray crystallography

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• Nuclear Magnetic Resonance

• Protein in aqueous solution, motile and tumbles/vibrates with thermal motion

• NMR detects chemical shifts of atomic nuclei with non-zero spin, shifts due to electronic environment

nearby

• Determine distances between specific pairs of atoms based on shifts, “constraints”

• Use constraints and biochemical knowledge of the protein to determine an ensemble of models

determining constraints

NMR Spectroscopy

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• FRET described as a “molecular ruler”

• segments of a protein are tagged with fluorophores

• energy transfer occurs when donor and acceptor interact, falls off as 1/d6 where d is separation between

donor and acceptor

• donor and acceptor must be within 50 Å,

acceptor emission sensitive to distance change

• can determine pairs of side chains that are separated when unfolded and close when folded

Fluorescence resonance energy transfer

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Optical trap

Conservation of linear momentum

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Single molecule studies of DNA binding proteins using optical tweezers, Analyst, 2006

Nucleic-acid polymerases

Optical tweezers configurations used to study RNA polymerase.

(a) A single trap configuration is shown. One end of the DNA

is attached to a glass coverslip via a digoxigenin–

antidigoxigenin linkage, while RNA polymerase is attached

to an optically trapped bead via an avidin–biotin bond.

The bead position is maintained by stage motion to

provide constant tension (typically from right to left).

(b) A schematic of a dual-trap configuration is shown. An RNA

polymerase–DNA complex is trapped by two optical traps

simultaneously. The left DNA end is manipulated via a

digoxigenin–antidigoxigenin linkage, while RNA

polymerase is attached via an avidin–biotin interaction. In

this figure, the upstream end of DNA is linked to the left

bead so that RNAP transcribes from right to left. The

tension of the DNA–RNAP complex was kept constant

during transcription by moving left stronger trap.

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Single monomers of HIV-1-PR were

manipulated as depicted in Fig.

Themolecules were stretched and relaxed

by moving the pipette relative to the

optical trap, while the applied force and

molecular extension were measured.

As the protein unfolds and refolds under

tension its extension suddenly changes,

generating discontinuities (rips) in the

stretching and relaxation traces that can

be analyzed to gain insight into the kinetic

and mechanical properties of the molecule.

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Magnetic tweezer

The energy of a superparamagnetic particle in a magnetic field B is given by:

𝑼 = −𝒎 ∙ 𝑩

𝑭 = −𝜵𝑼=𝜵 𝒎 ∙ 𝑩

The force experienced by the particle is given by the negative gradient of the energy.

For small external fields, the magnetic moment is

linear in the external field. In this case, the force

is proportional to the gradient of the square of

the magnetic field

𝑭 =𝝌𝑽

𝝁𝟎𝛁 𝑩 𝟐

For large fields, the magnetic moment of the

beads reaches the saturation value msat and the

force is proportional to the gradient of the

magnetic field

𝑭 = 𝜵 𝒎𝒔𝒂𝒕 ∙ 𝑩

F