Monte-Carlo-simulations of voltage fluctuations in biological membranes in the case of small numbers of transport units

Kleutsch, B.; Frehland, E.

doi:10.1007/bf00196346

Cited by 6 publications

(4 citation statements)

References 18 publications

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“…where i is the index of the possible event, k is the first-order rate constant of the event (s Ϫ1 ), R is a uniformly distributed, uncorrelated random number chosen from the interval 0-1, and t is the resulting execution time that the ith event requires (s) (10,12,13). The final step in each iteration is to choose the member of the event list that has the shortest execution time, as calculated with Eq.…”

Section: Methodsmentioning

confidence: 99%

Estimates of lateral and longitudinal bond energies within the microtubule lattice

VanBuren

Odde²,

Cassimeris

2002

Proc. Natl. Acad. Sci. U.S.A.

234

371

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We developed a stochastic model of microtubule (MT) assembly dynamics that estimates tubulin-tubulin bond energies, mechanical energy stored in the lattice dimers, and the size of the tubulin-GTP cap at MT tips. First, a simple assembly͞disassembly state model was used to screen possible combinations of lateral bond energy (⌬G Lat) and longitudinal bond energy (⌬GLong) plus the free energy of immobilizing a dimer in the MT lattice (⌬G S) for rates of MT growth and shortening measured experimentally. This analysis predicts ⌬G Lat in the range of ؊3.2 to ؊5.7 kBT and ⌬GLong plus ⌬GS in the range of ؊6.8 to ؊9.4 kBT. Based on these estimates, the energy of conformational stress for a single tubulin-GDP dimer in the lattice is 2.1-2.5 k BT. Second, we studied how tubulin-GTP cap size fluctuates with different hydrolysis rules and show that a mechanism of directly coupling subunit addition to hydrolysis fails to support MT growth, whereas a finite hydrolysis rate allows growth. By adding rules to mimic the mechanical constraints present at the MT tip, the model generates tubulin-GTP caps similar in size to experimental estimates. Finally, by combining assembly͞ disassembly and cap dynamics, we generate MT dynamic instability with rates and transition frequencies similar to those measured experimentally. Our model serves as a platform to examine GTPcap dynamics and allows predictions of how MT-associated proteins and other effectors alter the energetics of MT assembly.M icrotubule (MT) dynamic instability plays a critical role in chromosome movement and separation during mitosis. MTs grow, shorten, and transition between these states at rates governed by the presence of various MT effectors, such as divalent cations, MT-associated proteins (MAPs), and drugs such as Taxol (1).MTs are composed of heterodimer subunits of ␣-and ␤-tubulin. A guanine nucleotide (GTP or GDP) is positioned on the ␤ monomer opposite the interface between the two monomers, where it is hydrolyzable (if it is GTP) and exchangeable. The ␤ monomer end of the dimer faces the (ϩ) end of the MT, which is the end of more active dynamics and kinetochore attachment during cell division. The ␣ monomer faces the (Ϫ) end of the MT, which originates at the centrosome. MTs are thought to transition from a state of growth to a state of rapid shortening, termed a ''catastrophe'', when the tubulin-GTP ''cap'' is stochastically lost from the tip of the MT. The tubulin-GTP cap must exist because it has been demonstrated that tubulin-GTP subunits are added to the ends during assembly. A tubulin-GTP cap, however, has not been detected in experiments with porcine brain tubulin, and therefore must be small. Experiments suggest that the cap must be less than Ϸ200 dimers (2-4). Presumably, the transition from rapid shortening to growth, termed ''rescue,'' occurs when the tubulin-GTP cap is reestablished.Interactions at the surfaces of adjacent dimers occur through discrete lateral and longitudinal noncovalent bonds. Thermodynamic studies of MT assembly are unable to qua...

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Section: Methodsmentioning

confidence: 99%

Estimates of lateral and longitudinal bond energies within the microtubule lattice

VanBuren

Odde²,

Cassimeris

2002

Proc. Natl. Acad. Sci. U.S.A.

234

371

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“…To model MT dynamics, we use a Monte Carlo event-based approach (17,18,29,30). In this approach, one event takes place per iteration of the simulation.…”

Section: Model and Methodsmentioning

confidence: 99%

“…For an event that should occur with frequency f (s ÿ1 ), the waiting time to the next occurrence of the event is sampled from an exponential distribution with mean 1/f. If more than one event is possible (e.g., association or dissociation of a tubulin dimer at a particular MT, or association of a tubulin dimer to either of several MTs), then the waiting time of each event has to be sampled and the event with the shortest waiting time be implemented (17,29,30).…”

Section: Model and Methodsmentioning

confidence: 99%

Compartment Volume Influences Microtubule Dynamic Instability: A Model Study

Janulevicius

Pelt

Ooyen

2006

Biophysical Journal

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Microtubules (MTs) are cytoskeletal polymers that exhibit dynamic instability, the random alternation between growth and shrinkage. MT dynamic instability plays an essential role in cell development, division, and motility. To investigate dynamic instability, simulation models have been widely used. However, conditions under which the concentration of free tubulin fluctuates as a result of growing or shrinking MTs have not been studied before. Such conditions can arise, for example, in small compartments, such as neuronal growth cones. Here we investigate by means of computational modeling how concentration fluctuations caused by growing and shrinking MTs affect dynamic instability. We show that these fluctuations shorten MT growth and shrinkage times and change their distributions from exponential to non-exponential, gamma-like. Gamma-like distributions of MT growth and shrinkage times, which allow optimal stochastic searching by MTs, have been observed in various cell types and are believed to require structural changes in the MT during growth or shrinkage. Our results, however, show that these distributions can already arise as a result of fluctuations in the concentration of free tubulin due to growing and shrinking MTs. Such fluctuations are possible not only in small compartments but also when tubulin diffusion is slow or when many MTs (de)polymerize synchronously. Volume and all other factors that influence these fluctuations can affect MT dynamic instability and, consequently, the processes that depend on it, such as neuronal growth cone behavior and cell motility in general.

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“…The differential equations were solved numerically using a fourthorder predictor-corrector algorithm (Gear, 1971). Monte Carlo simulations on a single Na+ channel were performed using the non-uniform time method outlined previously by Kleutsch & Frehland (1991). The equilibrium distribution of channels was initially calculated for the chosen holding potential.…”

Section: Computer Simulations Of Channel Activitymentioning

confidence: 99%

The equine periodic paralysis Na+ channel mutation alters molecular transitions between the open and inactivated states.

Tsushima

Sah

McCutcheon

et al. 1996

The Journal of Physiology

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1. The Nae channel mutation associated with equine hyperkalaemic periodic paralysis (HPP) affects a highly conserved phenylalanine residue in an unexplored region of the a-subunit. This mutation was introduced into the rat skeletal muscle Na+ channel gene at the corresponding location (i.e. F1412L) for functional expression and characterization in Xenopus oocytes. 2. In comparison with wild-type (WT) channels, equine HPP channels showed clear evidence for disruption of inactivation: increased time-to-peak current, slowed rates of whole-cell current decay, significant increases in sustained current, rightward shifts in the steady-state inactivation curve by 9 5 mV, a 6-fold acceleration in the rate of recovery from inactivation at -80 mV, decreased number of blank single-channel sweeps, repetitive opening of single channels throughout depolarizing steps, increased open probability per sweep, and an increased mean open time. 3. The observed disruption of inactivation in HPP occurred without measurable changes in steady-state activation and first latency kinetics of channel opening. 4. Kinetic modelling demonstrates that the equine HPP phenotype can be simulated by altering the rate constants for transitions entering and leaving the inactivated states resulting from an energetic destabilization of the inactivated state. 5. These results suggest that the highly conserved cytoplasmic end of the third transmembrane segment (S3) in the fourth internal repeat domain (domain IV) plays a critical role in Nae channel inactivation.Action potentials in nerve, heart and skeletal muscle arise from the co-ordinated activity of voltage-gated Nae channels.Resting Na+ channels respond to membrane depolarizations by opening and then entering a stable, inactivated state, producing a brief influx of Na+ ions at the onset of each depolarization (for review see Bezanilla & Stefani, 1994).

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Monte-Carlo-simulations of voltage fluctuations in biological membranes in the case of small numbers of transport units

Cited by 6 publications

References 18 publications

Estimates of lateral and longitudinal bond energies within the microtubule lattice

Estimates of lateral and longitudinal bond energies within the microtubule lattice

Compartment Volume Influences Microtubule Dynamic Instability: A Model Study

The equine periodic paralysis Na+ channel mutation alters molecular transitions between the open and inactivated states.

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