mcb-5008 exam 2

Buoyancy

Gravity-opposing force caused by the weight of displaced solvent. Depends on the molar mass, partial specific volume, and solvent density

Partial specific volume

Space occupied per mole of a protein

Friction

Force opposing motion in a fluid medium. Described empirically, with f/f0 ratio describing the deviation from sphericity

f0

Frictional coefficient of a sphere. When compared to measured f, refers to the frictional coefficient of an anhydrous sphere of the same volume

Stokes’ law

Describes the frictional coefficient of a sphere

Diffusion

Flux associated with concentration gradients driven by Brownian motion

Einstein-Sutherland equation

The diffusion coefficient is related to the frictional coefficient

Fluorescence correlation spectroscopy

At a particular concentration, a small volume will have a variable amount of fluorophores present that changes over time. The rate at which the fluorescence changes is related to the rate of diffusion as individual molecules enter and leave the viewing area. Performing an autocorrelation function on the fluorescent signal in a confocal microscope can be used to measure diffusion

FCS instrumentation

Confocal microscope (pinhole to exclude out-of-focus light). Beam splitter splits signal into two detectors, one of which is time-delayed to produce the lag time

Autocorrelation

Measures the correlation of a function with itself at different offsets (lag time)

FCS measurement and output

Measurement: fluorescence intensity within the Gaussian volume of the confocal image

Output: Autocorrelation versus lag time

Dual-color fluorescence cross-correlation spectroscopy

FCS technique that can be used to monitor association reactions. Excites and detects at two wavelengths to simultaneously monitor two fluorophore-labeled molecules. Following self-correlation, the two channels are cross-correlated to detect whether the red and green channels are moving together as part of the same complex – the cross-correlation curve indicates the fraction of co-diffusing species

Dynamic light scattering

Fluctuations in the intensity of scattered light is related to Brownian motion of particles within solution. Computing the temporal autocorrelation of the scattering intensity can solve for the diffusion coefficient

Siegert relation

Relates the intensity autocorrelation function measured during experiment to the diffusion coefficient. This is equal to a baseline factor (~1) plus the coherence factor times the square of the electric field autocorrelation function, which works out to be the exponent of D q² tau. Decay rate equals D q²

What if your sample is heterogenous in DLS?

For a mixture of non-interacting species, the intensity-weighted integral over a distribution of decay rates must be used. For a monomodal distribution, this can be solved with the cumulants method, where the second cumulant is a measure of polydispersity

Limitations of DLS

Very sensitive to aggregates - the intensity is related to r^6, meaning large particles give huge relative signals.

DLS reports on hydrodynamic diameters and not molecular weights.

AUC experimental setup

Centrifuge where samples are placed within cells not tubes.

Dual sector cell: Used in Sed. Vel. Contains two cavities for sample and reference

Multi sector cell: Used in sed. eq. Contains six smaller cavities for sample/reference for replicates / different concentrations

Sedimentation velocity setup and applications

Hydrodynamic measurement to study rate of sedimentation and diffusion.

Fill dual sector cell and spin at high speed, collecting many c vs r scans as a function of time.

Obtains the size, shape, and molecular weight. Useful for mixtures and complex systems, and new analyses work for interacting systems

Sedimentation equilibrium setup and applications

Thermodynamic measurement to analyze stable concentration gradients.

Fill six channel cells and spin at moderate speed, monitoring approach to equilibrium. Record final concentration gradient.

Gold standard for determining molecular weight and determines subunit stoichiometries. Useful for analyzing interacting systems, but not suitable for complex mixtures.

Tracer analytical ultracentrifugation

Old-school method where cell is fractionated and inserted tracers (radioactivity, fluorescence) are used to determine concentrations. Time-consuming

Absorbance detection in AUC

Uses a single-beam spectrophotometer.

Good sensitivity for proteins at specific wavelengths (280, 230 nm), but high noise and signal must be within linear concentration range for Beer-Lambert to apply.

Interference detection in AUC

Uses a Rayleigh interferometer - beams are split, passed through sample and reference, and recombined to give interference pattern.

Highly sensitive, gives great signal to noise, but not selective. Depends on changes in refractive index, so anything that changes RI will give signal. Dynamic range is basically unlimited

Forces in sed vel AUC

Sedimentation pushes to the edges, while friction and buoyant forces oppose

Sedimentation coefficient s

Describes how quickly a molecule moves through a fluid in a centrifugal field. Affected by mass, shape, solvent viscosity, and temperature.

As molecular weight increases, s increases.

s is independent of rotor speed.

Svedberg equation

Describes the relationship between s, D, and properties of the protein for homogenous non-interacting systems

Lamm equation

Differential equation which describes the relationship between concentration, radius, and time as sedimentation occurs, given s and D. Can be globally fit to determine these parameters

Time-derivative dcdt methods and g(s*)

Approximates the time derivative by subtracting closely-placed scans, removing time-invariant noise. Transforms axis from r to s*, which tells you how much material is sedimenting at each s* value. - g(s*) is the concentration of species with apparent sedimentation coefficient s*.

Better resolution, but only one peak

SEDFIT and c(s) distribution

Finite element analysis modeling the sedimentation and diffusion of particles.

Assumptions: continuous distribution of non-interacting particles of increasing size that are the same shape.

Yields sharp peaks and can resolve oligomers

Concentration dependence of s

s generally decreases with concentration as greater [P] makes backflow a larger contributor.

If s increases with concentration, this indicates mass action self-association.

Remember to take measurements at multiple concentrations

Forces at play in Sed Eq AUC

Flux of diffusion is balanced against flux of sedimentation

Integrated SE expression for homointeracting systems

The c(r) distribution is the sum of the cm( r) and cd( r) - relate each with equilibrium constant

Integrated SE expression of heteroassociation

Depends on the relative extinction coefficient of A and B. Fit for A and B independently at low concentration and K, then do a global analysis at multiple rotor speeds, concentrations, and wavelengths

What do fractional saturation plots look like with [P] « Kd, [L]?

Hyperbolic binding isotherm. Fit to find KdWha

What do fractional saturation plos look like with [P] » Kd?

Linear binding isotherm, used to find stoichiometry

What if Kd ~ [P]

Must split each concentration into bound / unbound, ultimately solve for [PL] with a quadratic and f = [PL]/[P]tot

Heat capacity

Relationship between the heat energy applied to a system and its temperature. Formally defined as dH/dT under conditions of constant pressure

DSC instrumentation

Differential refers to the sample versus reference cell

How is a DSC experiment run?

Power is applied to the sample and reference cell to increase the temperature at a steady rate

What does DSC measure?

The difference in power applied is measured as the excess heat q, which is required to undergo the phase transition when melting a protein. Directly measures the heat capacity

What do you get from a DSC curve?

The peak corresponds to the melting point, the difference in heat capacity is related to the number of hydrophobic residues, and the integral under the curve is the enthalpy change of unfolding

Why should a protein be refolded after DSC?

Thermodynamic equations apply only if the change is reversible. We need to make sure this is the case.

Isothermal titration calorimetry

Performs stepwise injection of ligand into a reaction cell containing a macromolecule. The excess heat evolved against the reference cell is measured and the data is fit to obtain the enthalpy change, stoichiometry, and equilibrium constant of the binding reaction, which can be used to solve for the free energy change, entropy change, and change in heat capacity

Requirements of ITC

Need a significant enthalpy change and large amount of material. 10 or more injections to define binding isotherm.

c parameter

Equal to the product of the stoichiometry n, protein concentration, and equilibrium constant K. Should be between 5 and 500.

ITC with low c

Signal is too weak to resolve.

ITC with high C

Binding curve is highly rectangular

SPR instrumentation

Sensor chip with thin gold film with a glass prism. Light source illuminates the chip, causing total internal reflection / SPR.

Detector measures change in intensity as a function of reflected angle

Detection of binding in SPR

Sensor chip has surface modifications allowing for attachment of immobilized receptors. Flow ligand and compare to flow cell without ligand

Advantages of SPR

Detects picomolar binding, high throughput, low sample requirements, real-time and label free, and works at low receptor density

Disadvantages of SPR

Expensive, immobilized ligand can create heterogeneity and can affect activity, and may be diffusion limited

Surface prep for carboxymethyl dextran chip

1. Unmodified surface

2. NHS/EDC activation of surface

3. Baseline after activation

4. Flow in ligand for binding

5. Immobilized ligand before deactivation

6. Deactivation

   1. Baseline - Rmax, where 7 - 3 is the amount of immobilized ligand

Alternate immobilization strategies

1. His-tagged protein and NTA (nickel chelation) - reusable

2. Biotin conjugation with streptavidin

3. Protein A/G and antibody

   1. Azide for copper click chemistry

SPR curve regimes

1. Baseline

2. Association - analyte plus buffer is injected

3. Dissociation - buffer only is injected until 50% saturation

4. Regeneration - regeneration buffer is injected to displace ligand

5. Return to baseline, repeat

Things to look out for in SPR

Mass-transport limited kinetics, ligand not saturating, large RI jumps and spikes, no replicates, narrow concentration range, large response (high ligand density)

kobs

Observed rate constant in pseudo first order conditions. kobs = kon[L] + koff

Mass transport limited kinetics in SPR

Visible as a linear regime in the binding isotherm and if changes to flow rate affects kinetics. Fix by increasing the flow rate or decreasing the number density of ligand

Biolayer interferometry

Uses an optical tip that is dipped into solution. White light passes through and reflects, creating an interference pattern between light that reflects from the optical layer and from the immobilized layer. Causes a wavelength shift that is dependent on thickness and caused by binding

Advantages of BLI

High throughput, avoids microfluidics, no bulk changes in system properties, can measure picomolar affinity

Disadvantages of BLI

Systematic error in kd values when compared to SPR, likely related to evaporation. Similar issues with diffusion-limited kinetics

Thermophoresis

Movement of molecules in response to a temperature gradient

What factors affect thermophoretic flow?

Area, hydration entropy, size, charge, conformation

MST instrument setup

Excitation light for fluorescence, infrared laser for heating

Phases of MST experiments

1. Bulk solution (F0)

2. Heat-induced thermophoretic flow

3. Stable state (F1)

4. Recovery

How is MST data analyzed?

Fnorm (or delta Fnorm) - the ratio of F1 to F0 - is computed from MST curves as a function of concentration of ligand

Atomic force microscopy

Measures z displacement of a surface using a nanoscopic silicon / silicon nitride tip with laser deflection cantilever.

Force is measured by deflection of the cantilever, which is related to Hooke’s law.

Contact mode

Tip is in physical contact with the sample.

Feedback system keeps the force constant atop the surface.

Useful only on hard surfaces - damaging

Tapping mode

AFM tip oscillates above the surface, contacting with each cycle

Measures attractive and repulsive forces as distance oscillates.

Feedback system maintains interaction amplitude

Minimizes damage, but slower scan speed

Non-contact mode

AFM tip oscillates above the sample.

Amplitude or frequency modulated, latter is better

Used to image live cells

Force extension mode

Macromolecule is attached to the surface and the tip. Piezoelectric positioners move until only a single macromolecule is attached, then pulls to obtain force-distance curve

Optical trapping

Light has momentum that can be used to generate force. Gaussian beam balances momentum changes to generate a restoring force on a 1 um bead, keeping it within a potential well. Inside this well, the bead experiences an approximately linear restoring force dependent on laser powerA

Applications of optical tweezers

1. DNA force extension curves - apply force to the bead immobilized on a surface and monitor extension

2. Monitoring movement of motor proteins

Mass photometry

Molecules that come into contact with a cover slip will give light scattering proportional to its mass. Perform interferometric spectroscopy, measuring the interference pattern caused by light interacting with adsorbed particle versus cover slip

MP instrumentation

Essentially a microscope. Polarized light reflects and is collected to form the image

MP data processing

Ratiometric images are calculated by taking the ratio of the moving average of the ahead frames over the moving average of the prior frames. Contrast peaks at the midpoint in space and time

Drawbacks of MP

1. Limited range of masses

2. Surface adsorption bias - better adsorbers give more signal

3. No structural information

4. Sensitive to buffer conditions / optical properties (simpler=better)

5. Requires extensive calibration curves

6. Artifacts from transient irrelevant oligomers

7. Requires statistical averaging and large number of counts - high concentration, hard to see rarer complexes

   1. Can’t see PTMs like mass spec canA

Applications of MP

Quantifying sample heterogeneity - can be used to measure the mass of many proteins at once within a complex mixture

Assessing packaging state of AAV gene therapy vectors

HDX

The amide backbone of proteins exchanges hydrogen for deuteron at a consistent rate in solution, subject to temperature and pH conditions.

Used to measure solvent accessibility due to dependence on secondary structure and protein folding state

Kinetics

Three rates - kop, kcl for protein conformation, and kch for exchange.EX

EX1 regime

Occurs when kinetics is limited by solvent accessibility - i.e kch » kcl, which is rate-limiting. Observed rate of HDX is equal to kcl, and the regime exhibits correlated exchange, moving over all at onceE

EX2 regime

Occurs when kinetics is limited by the deuterium exchange reaction - i.e kch « kcl. In this case, kHDX = Kop * kch. No correlated exchange - peaks move over gradually

Continuous labeling

Protein is incubated in D2O for continuous periods of time. Useful for steady-state conformational dynamics

Pulse labeling

Protein is incubated in D2O serially for shorter periods of time. Useful for dynamic processes, interactions that occur on a fast timescale, and binding or allosteric effects