Biophysics Maya - Summary Biopysics PDF

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Summary

Based on Yair Meiri's videos and notes, on lectures and seminars....

Description

Light- an electromagnetic (EM) transverse wave/ EM radiation. EM- magnetic and electric components. The EM radiation spectrum contains light in different frequencies, visible light is only a small segment (400-750nm)

Photons have no mass!! Wave – a disturbance that propagates in a medium. *light waves do not require a medium. Duality of light -Double slit experiment-the photoelectric effect- potassium plate lit with light in different frequencies. Some did not read a current at ammeter. The blue and green passed the "threshold frequency" and we got a current. Higher current (more electrons ejected from potassium atoms)  HIGHER INTENSITY (photon density of light) and not frequency (the energy). *** The intensity and the frequency of light are independent and unrelated! In order to react with the potassium plate (eager to give electrons), an energy of 2eV is required. Particle qualities: because it ionized the potassium plate and thus changed the material. (eV) E-energy of photon h- Planck's constant -frequency.

Minimals*Interference- Superposition of wave, which results in the generation of a new wave pattern. *Constructive- When the net intensity of the resultant wave is greater than the individual intensities. *Maximally constructive- The path difference between the two waves is an integer multiple of the wave length. , the peak of one of the waves is superimposed on the peak of the other wave. "adds up" *Maximally destructive- the path difference between the two waves is NOT an integer multiple of the wave length. , the peak of on

of the waves is superimposed on the Trough of the other wave."cancles out" *Destructive- When the net intensity of the resultant wave is less than the individual intensities. *Ascending order of energy- electronic, vibration, vibration. *Energy and momentum of a photon (c=speed of light).

(p=impulse)

X rays-

Maya Cohen & Magal Deutsch

X ray radiation is EM radiation resulting from collision of electrons in an anodic atom. X rays and gamma rays frequencies overlap (about 1018 Hz), the difference is that gamma rays result from the nucleus, while x rays form at the orbitals.

Generation of X rays

An x ray tube is made of a heated cathode (-), an anode (+) and a vacuum between them. Electrons are accelerated from the cathode to the anode to the anode (gaining 𝐸 kin) due to a voltage difference. They collide into the anodic atoms, and thus an x ray is released.

There are 2 ways of generating an x ray: 1. Characteristic Radiation Usually occurs when an electron has a high kinetic energy, due to a high voltage difference. In this case an electron collides an electron in the innermost shell of the anodic atom causing ionization, and thus a vacancy occurs. According to the lowest energy principle, an other electron drops from a higher orbital and fills the inner shell vacancy. Thereby energy is released in the form of an x ray / photon is discrete.

𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = ℎ𝑓=𝐸ℎ𝑖𝑔ℎ𝑒𝑟 𝑠ℎ𝑒𝑙𝑙 − 𝐸𝑙𝑜𝑤𝑒𝑟 𝑠ℎ𝑒𝑙𝑙 𝐸𝑘𝑖𝑛

𝑚𝑣 2 = 2

*Auger electrons- When an electron ionizes the inner electron in an anodic atom causing vacancy. Thereafter another electron from a higher shell comes to fill the vacancy, but instead of emitting energy as a photon, it transfers its energy to an electron in one of the higher shells, causing it to shoot out. This Process not effective because most of the energy in released in the form of heat.

2. Breaking Radiation This method is used in medical diagnostic procedures (50-150 𝐾𝑒 𝑉). Usually occurs when an electron has a lower kinetic energy. It collides with several anodic atoms and loses its kinetic energy in several steps. In this case the electron is attracted to the nucleus of the atom, and thus losing some of its kinetic energy in the form of an x ray photon. The higher the kinetic energy lost to the atom, the higher the frequency of the x ray will be. This is why the spectrum of breaking radiation is continuous, and not a sharp line.

𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = ℎ𝑓 = 𝐸𝑘𝑖𝑛 =

𝑚𝑣 2 2

𝑚𝑣 1 2

2

-

𝑚𝑣 2 2

2

(gets smaller after each collision)

(the accelerating electrons kinetic energy)

= 𝜆𝑚𝑖𝑛 𝑓𝑚𝑎𝑥 =𝑒𝑉 ℎ

is observed when the electron deaccelerates in a single step. The voltage

eU is high →electrons have more kinetic energy.

Absorption of x rays

Attenuation Coefficient (𝜇)- is calculated by the distance (x) at which only 36% of the radiation density in the tissue remains. 𝜇=

1 𝑥

The larger the value of 𝜇, the better the material absorbs, and thus the image will appear brighter. The attenuation Coefficient is proportional to: 1. The density of the absorbing substance. 2. The average atomic nr. of the absorbing substance (𝑧 3 )

𝐼 𝐼0

=𝑒

−𝜇𝑥

exponential

lan

𝐼 𝐼0

= -𝜇𝑥 linear

(

𝐼 𝐼0

is the transmittance, which is

antagonistic to the absorbance).

There are 3 important mechanisms leading to the absorption of x rays and 𝛾rays:

1. Photoeffect Like the characteristic radiation concept except that a photon ionized the atom instead of an electron, and an electron is ejected instead of an x ray photon. All of the energy of the x ray photon is absorbed in the atom of the absorbing tissue in a single time!

𝑚𝑒 𝑣𝑒 2

𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = hf =A+

2

𝑚𝑒 𝑣𝑒 2 2

A- ionization energy 𝐸𝑘𝑖𝑛 (

)- the ejected electron’s kinetic

energy

2. Compton Effect A photon ionizes several atoms in several steps. The ionized electron is located at the most outer shell instead of the inner shell, which is loosely bound to the nucleus. The electron is ejected and the photon is deflected, which decreases its frequency.

𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = hf =ℎ𝑓 ′ +A+

𝑚𝑒 𝑣𝑒 2 2

ℎ𝑓 ′ = The photons energy after the deflection.

3. Pair Production Occurs only when a high frequency photon and a heavy nucleus atom collide. The proton absorbs part of the momentum (mass and velocity) of the photon, and thus is pushed away releasing an electron and a positron (according to Einstein's equation E=𝑚𝑐 2 ). the positron will eventually collide with an electron, causing “annihilation”- A lot of energy is released in the form of two 𝛾rays in opposite directions.

𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = ℎ𝑓𝑚𝑖𝑛 = (𝑚𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 + 𝑚

𝑝𝑜𝑠𝑖𝑡𝑟𝑜𝑛

)𝑐

2

X Ray Crystallography

A technique used to identifying molecular structures using x rays.

In this process an x ray tube is aiming the crystallized molecule and a diffraction pattern appears on the screen as bright spots (diffraction fringes / constructive interference). * in order for the x ray beams to remain constructive, they have to remain synchronized and meet. Therefore rays hitting the lower part of the crystallized molecule have to go through a larger distance (1st, 2ond…..order).

X ray types: 1. 2. 3. 4.

Conventional- Planar (dentist) Fluoroscopy- live image CT- 3 dimensional Radiotherapy- destruction of tumors

Thermal Radiation, Light Absorption And Emission, Atomic And Molecular Spectra Maya Cohen

Thermal Radiation EM radiation which is generated due to thermal motion (kinetic energy). Depends only on the temperature, and NOT on the type of matter. Basically, any object with a temperature larger than 0 K (-273.15 C) emits thermal radiation. *Black body- The ideal black body absorbs all the spectrum of EM radiation, and thus has an absorption coefficient of 1µ.

The Heisenberg Uncertainty Principle: addresses the f act that it is impossible to get accurate results while measuring physical quantities . The principle states that the two properties of a particle, its position and momentum, are inversely proportional to each other. In other words, the more certain we will be about the position, the less certain we will be about its momentum.

Three Possible Error Sources: 1. The Heisenberg Uncertainty Principle. 2. The measurement itself altering the accuracy of the results of the experiment (like in an electrical circuit). 3. The inaccuracy of the measurement (faulty of the measuring device or its inaccuracy).

Atomic level Energy, Quantized Theory Each electron orbiting a nucleus has quantas- specific "energy packets" or" discrete energy levels" (can only have specific values) according to its position (energy shell). Free unbound electrons that have kinetic energy are NOT quantized, and can have a wide range of energies. The following experiment proves the quantizes nature of nucleus-bounded electrons:

The Frank-Hertz Experiment

Electrons were accelerated from the cathode (-) through a vacuum with mercury atoms, towards a grid (+)—The bigger the voltage difference between them was, the higher the energy of the electron was. In order to pass the grid and get to the anode (-) , an electron needed to at least have an energy amount equal to the voltage difference between the grid and the anode (0.5V), in order for a current to appear. Only electrons with 4.9eV were able to interact with the mercury atoms.

Electrons with a lower energy just passed through the mercury vapor, colliding with the atoms but not interacting with them, and passed the grid only if they had a sufficient amount of energy (more than 0.5V). Electrons with an energy between 4.9eV and 5.3eV (4.9eV+0.4eV) reacted with the mercury but didn't result in a current.

Absorption and Emission Spectra

*The Bohr model Light emitted from an atom corresponds to a specific quanta\energy packet of a nucleusbound electron (H for example, can only emit one specific wavelength\color). The amount of energy between n=2 and n=1 is larger than the amount of energy between n=3 and n=2, and gets smaller the further we get from the nucleus. Emission and absorption spectras are complimentary (each is composed of the colors which do not appear in the other). Beer- Lambert Law: R elates the attenuation (weakening) of light to the properties of the material through which the light is traveling .

𝐴 = 𝜀 ∙ ℓ ∙ 𝑐 = −𝑙𝑜𝑔𝑇 𝑇 =

𝐼° 𝐼

C- concentration in Molars -distance in cm

𝜀 - constantℓ

Every molecule has the ability to loose energy in three different ways: 1. Electronic (emitting radiation). 2. Rotation 3. Vibration

Rotation and vibration are non-radiative forms of losing energy, but they make the emission spectrum of a molecule wider (some energy is rotated or vibrated off before the radiation is emitted).

Fluorescence

Maya Cohen

Fluorescence is the ability to emit light or EM radiation after absorbing it. Fluoresce- to emit light or EM radiation. Fluorophore- a molecule which is a able to fluoresce. Fluorescence is a radiative way of losing energy, after being excited by light (photons). *Only three (phenylalanine, tyrosine, tryptophan) out of 20 amino acids that have the ability to fluoresce. And are endogenous- naturally take place in biological processes. Their absorption range is 260-280 nm.

The Jablonski Diagram

When a fluorophore is excited by a photon, an electron "jumps" from the ground state to a higher energy state. Kasha's Rule / Internal Conversion (IC) : A molecule will always be more stable when the electrons are within quantisized energy levels. An electron which is located between such levels, will rotate or spiral down to the closest semi-stable excited state level. This process is non-radiative! After the electron reaches a lower excited energy level, it can return to the ground state in either via radiative relaxation (Fluoresce, Phosphorescence, Delayed-fluorescence), or via non-radiative relaxation (Rotation, Vibration).

Fluorescence When the excited electron drops down to the ground state from the 𝑆1 level, emitting a photon. (Also possible after the electron has rotated or vibrated a bit from the 𝑆1 level.

Phosphorescence When the excited electron "jumps" to level 𝑇1 \Triplet State via inter-system crossing (ISC), and then relax down to the ground state, emitting a photon. *The triplet state is a forbidden state, because Pauli's exclusion principle is not valid (There are two electrons with the same spin in the same orbital).

Delayed-Fluorescence When the excited electron goes to the triplet states, returns to the former excited state via ISC and then relaxes down to the ground level, emitting a photon.

*Photobleaching- High intensity\long lasting excitation by photons, causing the destruction of a fluorophore's chemical structure, which therefore loses its the ability the fluoresce.

Emission and Absorption Spectra

Every fluorophore can only be excited by a light in a specific range of frequencies "excitation\absorption spectrum", and also emit light in a specific range of frequencies "emission spectrum". (The Bohr model and atomic level energy) . The absorption spectrum will always be "red shifted"\"strokes shift" (the peak of the emission spectrum will have a corresponding longer wavelength, than the peak of the absorption spectrum ), because of the energy reduced (via vibration and rotation and is released as heat) during IC and ISC for example. The fluorophore emits photons with lower energies than the energies it absorbs.

Absorption Spectroscopy A technique which measures how much a certain material absorbs light. The relation between the initial intensity and the resultant intensity, after traveling through a distance ℓ that has an absorption coefficient 𝜀 and a concentration C, is expresses in the Beer-Lambert Law 𝐴 = ℇℓ𝐶 𝐴 = −𝑙𝑜𝑔𝑇 𝑇 =

𝐼 𝐼°

𝐴 = −𝑙𝑜𝑔

𝐼 𝐼°

→ −𝑙𝑜𝑔

𝐼 𝐼°

= ℇ𝓵𝑪 = 𝒍𝒐𝒈

𝑰° 𝑰

A- absorption T- transmittance *We use this in order to build the previous graph.

Critical Fluorescence Parameters Quantum Yield

𝑄=

𝐾𝑓 𝐾𝑓 +𝐾𝐼𝐶 +𝐾𝐼𝑆𝐶

=

𝑛𝑟.𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛𝑠 𝑒𝑚𝑖𝑡𝑡𝑒𝑑 𝑛𝑟.𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛𝑠 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑

Fluorescence Lifetime The time during in which the nr. Of excited molecules decreases to

1

times (37%) it's initial 𝑒 value OR the characteristic time that a fluorophore spends in the excited state. 𝑡

𝐼(𝑡) = 𝐼° ∙ 𝑒 − 𝜏

.

‫ מה זה הפאי הלא גמור הזה והאם אני צריכה לדעת את‬,N ‫מה זה‬ ????‫זה‬

Applications –ImmunofluorescenceA technique used when we want to find out if a certain molecule exists on a membrane in a cell for example. In this technique a fluorescent-dyed antigen is added to a solution. If an antibody specific to the antigen comes in contact with it, they will stick together and the fluorescent color will fluoresce. *There are many other applications, but this example should suffice.

Fluorescence Microscopy Is used for attaining visual light emitted from fluorophores. Polychromatic light (containing all wavelengths) reaches the excitation filter, which only lets the specific wavelengths which can excite the fluorophore in. The dichroic mirror is translucent to emission spectrum, and reflects the absorption\excitation spectrum. Thus, all of the wavelengths which passed through the excitation filter are reflected and reach the sample. The sample contains fluorophores which are excited by the light, and emit light within a certain specific range. The emitted light reaches the dichroic mirror and passes right through it, since its translucent to it. It thereafter reaches the emission filter \ Barrier filter , which is a backup to the mirror, making sure that only emission spectrum wavelengths can reach the eye.

FRET

Fluorescence Resonance Energy Transfer \ Forster-type Energy Transfer\ SingletSinglet Resonance Energy Transfer.

The ability of two fluorophores to interact, transferring and receiving light energies. The fluorophore which is excited by the initial energy (donor molecule), transfers the energy to another fluorophore (acceptor molecule), which will fluoresce. This method is used to measuring distances, and measuring protein-protein interactions. There are three conditions for FRET to occur: 1. The fluorophores have to be strongly distance dependent (2-10nm). 2. The emission spectra of the donor molecule has to overlap with the absorption spectra of the acceptor molecule. 3. The fluorophores have to be in proper orientation.

Efficiency of fluorescence Fluorescence lifetime Photobleaching rate

Donor Molecule ↓ ↓ ↑

Acceptor Molecule ↑ ↑ ↓

Raman Scattering When photons are scattered from an atom or molecule , most photons are elastically scattered (Rayleigh scattering), so the scattered photons have the same energy before and after the interaction . There are two other possibilities though, which are inelastic: 1. Strokes: The photons lose some of their energy to the particle, and leaves with a lower frequency. 𝑓𝑠𝑐𝑡𝑟. = 𝑓° − ∆𝑓 2. Anti-Strokes: The photons gain energy from an electron in the particle which is in the process of relaxation (vibration and rotation), and leave with a higher frequency. 𝑓𝑠𝑐𝑡𝑟. = 𝑓° + ∆𝑓

Lasers

Maya Cohen

Lasers are used in medicine (diagnostics and therapeutic procedures- surgery), in research (spectroscopy, fluorescence microscopy ), in the industry (cutting and welding, printers )…

Spontaneous light Polychromatic Incoherence in time and space (scatters over distances) Low energy density Non-polarized (not all of the protons generated point in the same direction)

Laser light (stimulated and not spontaneous) Monochromatic Coherence in time and space (small and focused bandwidth). High energy density Polarized

Energy (Photon, kinetic energy, electric energy..) is introduced to a system and causes excitation of an electron. The excited electron has two ways of relaxing: 1. It spontaneously relaxes, emitting a photon. *this is a slower process (nm). 2. It is stimulated to relax by a photon, emitting a photon along with the stimulating photon (2 photons released). The stimulated photon has to have a specific amount of energy, matching the energy-difference between the shells the electron needs to travel. *This process is faster than fluorescence (10−12 piko seconds).

Light Amplification Normally most of the atoms are in ground state (only a few are excited because of random kinetic or thermal energy), but that is not powerful enough for laser light. ∆𝐽 < 0 𝑁 1 >> 𝑁2 "Population Inversion"- A process in which we introduce energy in the form of photons, electric current… to the system (Pumping), causing excitation. ∆𝐽 > 0 𝑁2 > 𝑁1

∆𝑱~𝑵𝟐 − 𝑵𝟏

𝑵𝟐 𝑵𝟏

∆𝑬

= 𝒆−𝒌𝑻

𝑁1 - nr. Of molecules in ground state. 𝑁1 - nr. Of molecules in excited state. After Population Inversion is completed, the atoms are stimulated by photons, and emit photons all at once. In order for Population Inversion to happen, the excited atoms have to have at least three energy levels (four ideally)- So that they stay excited and will not spontaneously relax down via vibration and rotation (IC\Kasha's rule).

Generation of Laser A tube filled with gas molecules is pumped, causing "Population Inversion". Then, the gas molecules are stimulated to relax by photons with a specific energy, emitting photons in the process. The photons (double the amount) continue moving in the tube, cause a chain reaction . When reaching the rear mirror (RM) they are reflected. The outcoupling mirror is slightly permeable to light, causing photons to exit the tube in a polarized state.

𝑳=

𝒏∙𝝀 𝟐

*Changing the distance L between...