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Molecular Motors Dave Wee 24 Sept 2003 Mathematical & Theoretical Biology Seminar
Molecular Motors
Dave Wee24 Sept 2003
Mathematical & Theoretical Biology Seminar
Overview
¡ Types of motors and their working mechanisms.
¡ Illustrate the importance of motors using the example of :l ATP-Synthasel Chromatin remodeling motor (ACF)
¡ Discuss the importance of molecular motor modeling in system wide modeling of biological systems.
¡ Illustrate the modeling of protein motion using Brownian motion concept.
Types of Motors
1. Pump- Membrane protein that transports ions and small
molecules across the membrane.
2. Rotary Motor- Membrane-bound structure having a spinning
shaft, while the motor is fixed on the membrane.- E.g. ATP Synthase.
3. Linear Motor- Mostly found in cytoplasm.- Need a track to “walk on”. Filaments and
microtubules serve as tracks.- E.g. Myosin, Kinesin, Dynein.
Rotary Motor – ATP Synthase
¡ Found on bacterial and mitochondria membrane.
¡ ATP manufacturer which is the fuel that powers many other biochemical processes.
¡ Has 2 rotary motors acting in opposition – F0 and F1motors. Each operates on an entirely different mechanism.
¡ F0 motor :l Localization – Membrane.l Energy source – Transmembrane electromotive force.
¡ F1 motor :l Localization – Cytoplasm.l Energy source – ATP hydrolysis.
ATP Synthase 2nd Structure
Cytoplasm
Periplasm
F1 Motor Structure
¡ Shaft l ?-subunit.l Surrounded by 6
alternating a and ßsubunits.
¡ ATP binding sitesl 6 ATP binding sites, each
nestles in the cleft between the a and ßsubunits.
l Only 3 can catalyze the hydrolysis of ATP.
l These catalytic sites are mostly in the ß-subunits, with a few but crucial residues in the a-subunits.
F1
F0
F1 Motor Mechanism – Power Stroke
1. An ATP molecule diffuses by Brownian motion into an open catalytic site, and is only weakly bound.
2. The catalytic site wraps around it tightly by progressively forming up to 15-20 H-Bonds.
3. This binding transition from weak to tight pulls the top part of the ßsubunit towards the bottom part, like a hinge to about 30o.
4. Binding free energy -> Power stroke with nearly constant force.
5. At the end of binding transition, some elastic energy is stored in the ß-sheet.
F1 Motor Mechanism – Exhaust Stroke
1. ATP is hydrolyzed to ADP and P.
2. The free energy of hydrolysis and the formation of 2 product molecules weaken the binding from the catalytic site.
3. The binding force is so weak such that thermal fluctuations can knock the products out of the catalytic site.
4. The elastic energy stored in the ß-sheet is released during this stage and the top part of the ß subunit returns to its original open state.
F1 Motor Mechanism – Complete Stroke
¡ 1 bend of a ß-sheet rotates the shaft in a single step of 120o, with a brief pause at 90o.
¡ When the 3 catalytic sites hydrolyze sequentially, they drives the rotation of the shaft. (See animation)
¡ The unbending of a ß-sheet will help the bending of its neighbour ß-sheet.
F0 Motor Structure
¡ Has between 10 to 14 c-subunits assembled in a cylinder (cn cylinder) , attached to the shaft and ? -subunit.
¡ Has a transmembraneassembly consisting of the A and B subunits.
¡ The cn cylinder interfaces with the transmembrane assembly.
¡ Rotor :l Shaft, cn cylinder & ? -subunit.
¡ Stator(Stationary) :l a-ß and A-B subunits & d.
F1
F0
F0 Motor – Driving Force
¡ Driven by ion-motive force, ? µc across a membrane. ? µc contributed by :l Ion(H+/Na+) concentration gradient, ? pH. l Electrical potential difference, ? f .
¡ Thus, l ? µc = ? pH + ? f
F0 Motor Mechanism
¡ Ionic driving force :l Concentration at periplasm is higher than at cytoplasm.
¡ Electrical driving force :l A “blocking +ve charge” in the stator.l A -ve charge array wrapped around the cn cylinder.
¡ Mechanism :1. Rotor turns anti-clockwise due to electrical driving force.2. Once a –ve site reaches the input channel, a +ve ion from the
periplasm binds to it.3. Since potential on its left is lower than on the right (as a result of the
+ve blocking charge), the rotor continues to turn anti-clockwise.4. Once it moves out of the stator, the +ve ion quickly dissociates from
the site because of its low concentration in the cytoplasm.5. (See animation)
Linear Motors – Background
¡ Myosinl Moves on actin filaments.l 18 different families.
¡ Kinesinl Moves on microtubules.l 10 different families.
¡ Dyneinl Moves on microtubules.l 2 different families.
¡ Each family consists of up to several dozen members.
¡ Each member may vary very significantly in makeup and function even within the same family.
Linear Motors – Generic Structure
¡ Motor domainl ATP binding site – Virtually identical in structure
for all 3 types of motors, even though sequence homology is very low!
l Track binding site
¡ Accessory structural motifsl Mechanical amplifiers
¡ Coiled-coil domainsl Dimerizationl Regulationl Interactions with other molecular, eg, cargo
Linear Motors – Generic Behavior
¡ Exist as monomers, dimers, trimers or tetramers.
¡ Can take 1 or more steps before dissociating.
¡ Processive motors move along the track for long distances without detaching. They are individualist and long distance runners.
¡ Non-processive motors lose contact to the track usually after 1 cycle. They work as a team and are optimized for brief, fast interactions, such as in the muscles. They are 100m sprinters.
Linear Motors – Generic Mechanism
1. ATP binds to motor domain and is hydrolyzed.
2. Loss of ?-phosphate group from ATP creates a space that will cause a rearrangement (movement) of the ATP binding site. This is called the 1st level of amplification.
3. The amplification is propagated to the track binding site causing it to change its structure too.
4. The 2nd level of amplification (more powerful and useful) involves the mechanical amplifiers. This is where myosin, kinesin and dynein differs in operation.
Myosin – In Detail
Accessory structural motifs
Coiled-coil domains
Motor domain
High-resolution electron micrograph
Myosin – In Detail
¡ Green arrow – propagation of structural change upon ATP hydrolysis from ATP binding site to track binding site.
¡ Red arrow – the 1st level amplification is relayed to the mechanical amplifier. In myosin, the amplifier is a a-helical lever, that swings up and down up to an angle of 70o.
¡ Due to biological requirements in muscles, most myosins are non-processive motors.
¡ Both Myosin V (g) and Myosin I (h) uses their tail domains (part of the coiled-coil domain) to bind to their cargo.
Motor domain of myosin
Kinesin – In Detail
Accessory structural motifs
Coiled-coil domains
Motor domain
High-resolution electron micrograph
Kinesin – In Detail
¡ Green arrow – same as in myosin.
¡ Red arrow – same as in myosin. However, in kinesin, the amplifier is a flexible neck linker. It can be docked to the motor at times.
¡ 2 proposed models of movement :l Hand-over-hand modell “inchworm” type model
Kinesin – In Detail
¡ a – Direct interaction.¡ b – Interaction mediated by a linker
protein.¡ c – Interaction mediated by a linker
complex.
Dynein – In Detail
Accessory structural motifs
Motor domain
High-resolution electron micrograph
Dynein – In Detail
¡ Mechanistic analysis is severely hampered by the lack of a high-resolution structure. But it is believed that the propagation of ATP hydrolysis is transmitted from the right side to the left side.
Linear Motors – Other issues
1. Diffusion effects & forces generated2. Directionality of movement3. Regulation of motors’ behaviors4. Cellular functions & importance of motors
1. Diffusion Effects & Forces Generated
¡ Diffusion affects processive motors only.¡ Movement along the track may entail both
a mechanical component and a diffusive component, with different motors using different proportion of each.
¡ A single motor can move its cargo many times its own size through viscouscytoplasm at near maximum speed.
2. Directionality of movement
¡ Microtubules :l Polar. The +ve end is fast
growing while –ve end is slow growing.
l The –ve end is the anchor point. They can anchor to other microtubules to form a network.
¡ The myth of motors moving to +ve ends only is shattered when some myosin and kinesinmembers can move to –ve ends too!
¡ How and which part of the motor determines its direction is still unknown.
3. Regulation of motors’ behaviors
¡ 2 ways to regulate motors :l Turning the motor on/off.l Inhibit/promote its interaction with cargo.
¡ Possible mechanisms :l Phosphorylation – -ve regulator of cargo binding of
several motors. Causes detachment from cargo in some cases.
l Intramolecular interactions – Tail domain (important for binding to cargo) can inhibit the motor domain, thus prevent it from moving.
¡ Cooperative behaviors :l A motor can pass its cargo to a motor of a different
class when it is being inhibited or when the “terrain” is not its forte.
l Some organelles switch tracks from actin filaments to microtubules and vice versa, showing evidence of cooperating between myosin and kinesin.
4. Cellular functions & importance of motors
¡ Transportation (including mRNAs)¡ Ciliary movement or contraction¡ Energy generation¡ Cellular homeostasis¡ Cell architecture and cytoskeletal
remodelling¡ Chromatin assembly
4. Cellular functions & importance of motors
1. Retrograde transport of centrosomal components
2. Anterograde and retrograde transport of intermediate filaments
3. Anterograde and retrograde transport of ribonucleoprotein(RNP) complexes
4. Myosin, kinesin and dyneinmotors interact with components of the microtubule plus-end complex
5. Anchorage of dynein at the actin-rich cell cortex
6. Interaction of a kinesin-like protein with actin
7. Catenin-mediated anchorage of dynein at adherens junctions
4. Cellular functions & importance of motors
1. Myosin myopathies – muscle disorder2. Griscelli syndrome – pigmentation disorder3. Hearing loss4. Retinitis pigmentosa – photoreceptor
degeneration5. Primary ciliary dyskinesia6. Kartagener syndrome – situs inversus7. Polycystic kidney disease8. Virus transport9. Anthrax susceptibility10. Neurodegenerative diseases
4. Cellular functions & importance of motors
¡ Interesting but yet unanswered questions :l How does a motor finds its cargo?l What directs it to the correct target destination
(especially the microtubules network is so complicated)?
l How is its activity regulated? Can it have variable speed?
l When a motor has unloaded its cargo, what will happen to it? Would it be dissociated or U-turn back to carry more cargo???
This is just the beginning…
¡ As more knowledge on motors regulatory mechanisms and their new biological roles are discovered, it will be shown that motors are important in almost all areas of biological processes.
¡ Hence, to model and study a biological system’s behavior, the modeling of motor dynamics must be incorporated into gene network modeling. This could be a new direction in system modeling.
Chromatin Assembly – Background
¡ DNA is packaged into a periodic nucleoprotein complex, known as chromatin.
¡ The basic repeating unit of chromatin is the nucleosome.
¡ Each nucleosome consists of :l 8 histone proteins (H2A, H2B,
H3, H4) x 2l 146bp of DNA turns around
these proteins
Chromatin Assembly – Background
H4
11 nm
H2B
H3H4
H2B
H2A
H3
H2A
Nucleosome bead (8 histones + 146 nucleotide pairs of DNA)
Linker DNA (approx 50 bp)
DNA
Chromatin Assembly
¡ Chromatin assembly happens in :l DNA replication in S phase of cell cycle.l DNA repair, transcription and histone exchange.
¡ Factors needed for chromatin assembly :l Histone-chaperone complex
¡ Chaperone deliver histones to the appropriate chromatin assembly sites.
l ATP-utilizing chromatin assembly and remodelling factor (ACF)¡ A processive ATP-driven motor that tracks on DNA.
¡ (see fig 1)
Chromatin Assembly
¡ in vitro, ACF can assemble the nucleosomesperiodically, a remarkable biological feat!
¡ 2 models are proposed :l Iterative-annealing model (fig 2 & 3)l Directed-deposition model (fig 4)
¡ ACF is also responsible for chromatin remodeling – a very important factor controlling gene activity!
Stochastic Modeling of Protein Motion
¡ Protein motion is dominated by Brownian motion. Its velocity is dependent on the random thermal fluctuation of surrounding water molecules.
¡ This is important because it allows proteins to move against an opposing force by utilizing occasional large thermal fluctuation.
¡ Even if 2 proteins start at the same position at t=0, they will have different paths after some time.
¡ Hence, this is a stochastic process.
Stochastic Modeling of Protein Motion
¡ Formulationl 1-D flow, xn = x(t)l x(t) is approximated by a discrete random
variable, with constant time step, ? t.
¡ Assumptionsl Markov processl At each ? t,
¡ it can only take 1 step of length ? x¡ it must either move left or right¡ P(right) = P(left) = 0.5
¡ Objectivel To derive the probability density function for
finding the protein’s displacement at time t.
Stochastic Modeling of Protein Motion
¡ At any time n? t, the total # of steps taken is n = Rn + Lnl Rn : # of steps to the rightl Ln : # of steps to the leftl Thus, P(Rn = r) = nCr(0.5)r(0.5)n-r = nCr(0.5)n
¡ We have, xn = ? x(Rn - Ln) = ?x(2Rn - n)¡ Making Rn the subject, Rn = ½(xn/? x + n)¡ But xn/? x is the # of unit lengths the
protein is located. We let it be k.¡ So, Rn = ½(k + n)
¡ Finally, P(k|n, t) = nC½(k + n)(0.5)n
Stochastic Modeling of Protein Motion
¡ Results:l See fig 12.2
¡ It can also be shown that :l E(xn) = 0l Var(xn) = ((? x)2/? t)t
References
1. Manfred Schliwa & Gunther Woehlke, Molecular motors, Nature Vol 422, 2003, p759-765
2. Reinhard Lipowsky, Molecular motors and Stochastic Models, LNP 557, 2000, p21-31
3. Chapter 12, Molecular motors : Theory, p321-356
4. George Oster & Hongyun Wang, Chapter 8, How protein motors convert chemical energy into mechanical work, p207-227
5. Karl A. Haushalter & James T. Kadonaga, Chromatin assembly & DNA-translocating motors, Nature, 2003, p613-620
6. H. Wang & G. Oster, Ratchets, power strokes, and molecular motors, Applied Physics A, 2002, p315-323
7. Peter Bayley, Biophysical studies of the cytoskeleton, European Biophysics Journal, 1998, p429-430
