Protein-protein ratchets: stochastic simulation and application to processive enzymes.

Interaction between a protein and a series of binding sites on a cytoskeletal substrate can create a resistance, or "protein friction," as the protein is moved along the substrate. If attachment and detachment rates are specified asymmetrically, this resistance can depend on the direction of movement, and the binding interaction acts as a ratchet. Stochastic computer simulations have been used to examine this type of protein-protein interaction. The performance of a protein-protein ratchet in the piconewton and nanometer range is significantly limited by thermal fluctuations, which in experimental measurements with single molecules are evident as Brownian motion. Simulations with a two-component model combining a conventional motor enzyme model with a protein-protein ratchet confirm previous suggestions that the processive movement of a single motor enzyme molecule against a load, as seen in experiments with inner arm dynein molecules, might be made possible by an accessory protein interaction that prevents backward slippage. When this accessory protein interaction is defined so that it acts as a ratchet, backward slippage can be prevented with minimal interference with forward progression.

Stochastic simulation of processive and oscillatory sliding using a two-headed model for axonemal dynein.

Computer simulations have been used in an attempt to understand experimental observations of processive and oscillatory sliding by one or a few axonemal dyneins. A simple two-headed model has been examined using stochastic simulation methods. To explain the experimental observations, the model must be capable of taking backward steps, as well as forward steps, and there must be hysteresis in switching between forward or backward stepping. When the effects of Brownian movement on motor strain are included, it is not possible to obtain oscillations as regular as the experimental records by using motor strain to regulate switching between forward or backward stepping.

Bending patterns of ATP-reactivated sea urchin sperm flagella following high salt extraction for removal of outer dynein arms.

Two procedures were used for extraction of demembranated sea urchin sperm flagella with increased KCl concentrations, to remove outer dynein arms. Extraction with 0.55 M KCl in the Triton-demembranation solution produced a rapid fall in average sliding velocity to 50% of its unextracted value, with extensive changes in bending behavior of the distal half of the flagellum. Extraction with 0.42 M KCl following demembranation and activation by incubation with cAMP produced a more gradual fall in sliding velocity, reaching 50% of the unextracted value after 180 sec extraction. This procedure produced somewhat more normal bending patterns. In both cases, the bending pattern of the basal region of the flagellum is altered very little by extraction, in agreement with data from Chlamydomonas mutant flagella deficient in outer arm dyneins.

Computer simulation of flagellar movement: VII. Conventional but functionally different cross-bridge models for inner and outer arm dyneins can explain the effects of outer arm dynein removal.

Outer arm dynein removal from flagella by genetic or chemical methods causes decreased frequency and power, but little change in bending pattern. These results suggest that outer arm dynein operates within bends to increase the speed of bend propagation, but does not produce forces that alter the bending pattern established by inner arm dyneins. A flagellar model incorporating different cross-bridge models for inner and outer arm dyneins has been examined. The inner arm dynein model has a hyperbolic force-velocity curve, with a maximum average force at 0 sliding velocity of about 14 pN for each 96 nm group of inner arm dyneins. The outer arm dynein model has a very different force-velocity curve, with a maximum force at about 10-15% of V(max). The outer arm dynein model is adjusted so that the unloaded sliding velocity for a realistic mixture of inner and outer arm dyneins is twice the unloaded sliding velocity for the inner arm dynein model alone. With these cross-bridge models, a flagellar model can be obtained that reduces its sliding velocity and frequency by approximately 50% when outer arm dyneins are removed, with little change in bending pattern. The addition of outer arm dyneins, therefore, gives an approximately 4-fold increase in power output against viscous resistances, and outer arm dyneins may generate 90% or more of the power output. Cell Motil.

Mechanical components of motor enzyme function.

Motor enzymes use energy from ATP dephosphorylation to generate movement by a mechanical cycle, moving and pushing in one direction while attached to their cytoskeletal substrate, and recovering by moving relative to their substrate to a new attachment site. Mainstream models assert that movement while attached to the substrate results from preexisting strain in the attached motor. The additional underlying ideas can be described in terms of three components for strain amplification: a rotating lever arm, multiple attached states, and elastic compliance. These components determine how energy is recovered during the mechanical cycle and stored in a strained motor. They may coexist in a real motor; the challenge is to determine the contributions of each component. Because these components can generate similar relationships between strain energy and strain, standard measurements of motor function do not discriminate easily between these components. However, important information could be is provided by observations that suggest weak coupling between chemical and mechanical cycles, observations of negative force and movement events in single motor experiments, and the discovery that two motors that move in opposite directions have very similar structures. In models incorporating changes in conformation between attached states, these observations are only explained easily if the conformational changes are tightly coupled to changes in the strength of motor-substrate binding.

Reactivation at low ATP distinguishes among classes of paralyzed flagella mutants.

Paralyzed flagella (pf) mutants of Chlamydomonas have been distinguished by the inability of the intact cells to move. Demembranated flagella from these mutants are also immotile when reactivated under standard conditions, with millimolar ATP concentrations. Three of these pf mutants were previously found to be motile when reactivated under 3 alternate reactivation conditions: low ATP concentration (< or =50 microM); 0.1 mM ATP combined with >0.5 mM ADP; or 0.1 mM ATP combined with non-reactivating ATP analogs anthraniloyl ATP or methylanthraniloyl ATP. We have now surveyed all pf mutants in the Chlamydomonas Culture Collection and discovered that a great majority of these mutants can move under these alternate nucleotide conditions. Only pf22 and pf23, mutants missing multiple subsets of dynein arms, did not reactivate under those conditions. This suggests that the paralysis observed in most pf mutants is the result of inhibition by physiological ATP. Except for pf12, which has an abnormally symmetric bending pattern, all other pf mutants exhibit asymmetric bending patterns similar to wild-type. Previously, motility that was restored by the presence of suppressor mutations was found to lack the normal asymmetry of wild-type flagella or the suppressor by itself. The waveform of pf mutants at alternate reactivation conditions in the absence of suppressor shows that pf mutants with radial-spoke or central-pair defects are capable of asymmetric bending similar to wild-type. A complete radial-spoke/central-pair complex is not essential for the production of asymmetric bending patterns. Furthermore, this suggests that the symmetric waveform observed previously in suppressed pf mutants is due to the interaction between the pf and suppressor mutations.

Transient disruptions of axonemal structure and microtubule sliding during bend propagation by Ciona sperm flagella.

Demembranated sperm flagella of Ciona were reactivated at increased salt concentrations (0.45 to 0.5 M K acetate). In addition to a decrease in amplitude of propagated bends, some flagella switch between "stable" and "transient" bending cycles. In the transient bending cycles, there is increased intermicrotubule sliding, in the direction that forms a new principal bend at the base of the flagellum, during the first half of a bending cycle. The magnitude of this increased sliding may be as much as 1 radian, or 0.06 micron between adjacent doublet microtubules. Most transient bending patterns also show a characteristic disruption of axonemal structure, involving separation between strands of microtubule doublets over a distance of up to 5 microns, occurring within a principal bend, typically about 16 microns from the base of the flagellum. The disruptions usually disappear after the principal bend propagates beyond the region of the disruption. Formation of these disruptions requires additional sliding, in the direction that would form a principal bend at the base of the flagellum, of up to about 0.3 micron. Formation of these disruptions may be explained by weakening of structural interactions by increased salt concentration and transverse forces, proportional to curvature and transmitted force, that will tend to separate doublets in a bend. These observations indicate that an actively beating flagellum possesses active sliding capability that is activated but not expressed during normal bend initiation and propagation. The initiation and propagation of flagellar bends may not be explicable solely in terms of local activation and inactivation of dynein-driven sliding.

Microtubule sliding, bend initiation, and bend propagation parameters of Ciona sperm flagella altered by viscous load.

The effect of altered viscous resistance on flagellar bending has been reexamined, utilizing ATP-reactivated sperm flagella from Ciona and newer methods that resolve metachronous and synchronous components of microtubule sliding and allow the examination of bend initiation as well as bend propagation. Large changes in amplitude and wavelength of bend propagation occur with little change in bend initiation parameters, other than frequency, indicating that bend initiation and bend propagation are regulated by quite different mechanisms. At increased viscosity, reduced amplitude of propagating bends, measured as metachronous shear amplitude, is associated with both reduced amplitude during bend initiation and amplitude adjustment after bends begin to propagate. This combination of effects was seen previously when reduced amplitudes were induced by increased salt concentration, and it was suggested to be caused by an imbalance between active moments and viscous resistances. However, in contrast to the results at increased salt concentrations, which involved significant reduction in bend curvature and little reduction in wavelength, increased viscosity causes very little change in curvature and causes a major reduction in wavelength. This difference can be explained by a model of flagellar bending in which inner arm dyneins have primary responsibility for maintaining bend curvature and outer arm dyneins have primary responsibility for performing work against viscous resistances. Both sets of dyneins would be inhibited by increased salt concentration, but increased viscous resistance would be irrelevant to the operation of inner arm dyneins.

Weakly-coupled models for motor enzyme function.

In strongly-coupled models for motor enzyme function, such as the original Huxley (1957) model for muscle, ATP binding and subsequent hydrolysis are required for the detachment and reattachment of every force-producing cross-bridge. In weakly-coupled models, cross-bridges can be 'mechanically detached' without ATP binding when they have been pushed far beyond their free energy minimum and have accumulated so much strain that the attached state is less stable than the detached state. Weakly-coupled models assume that these mechanically detached cross-bridges can rejoin the pool of detached molecules that can reattach as force-producing cross-bridges, without going through an ATP hydrolysis cycle. This paper bases this assumption on a thermodynamically rigorous model for interaction between a motor enzyme molecule and binding sites on a cytoskeletal protein filament, equivalent to other examples of ligand binding interactions. It attempts to identify more clearly the features that must be added to the idea of ligand binding equilibrium to simulate a weakly-coupled motor enzyme model. Models that assume a vectorial conformational change and a longitudinal series elastic element appear to be incompatible with the assumptions of weakly-coupled cross-bridge models. A stochastic computational method has been used to examine the properties of these models. The computations have examined the behaviour of a model containing a four-state ATPase cycle, but the model is computationally a nine-state model because a force-generating attached state is allowed to equilibrate with different detached states at negative and at positive distortions, and because three adjacent sites are considered as possible attachment sites for each of the two attached states of the ATPase cycle.

Multiple protein kinase activities required for activation of sperm flagellar motility.

A specific peptide inhibitor of the cyclic AMP (cAMP)-dependent protein kinase (PKI-peptide) is a very effective inhibitor of the cAMP-dependent activation of motility of Ciona spermatozoa, when PKI-peptide is present at the beginning of incubation of demembranated spermatozoa with cAMP and ATP. Under conditions where approximately 120 sec is required for full activation of motility, the window of sensitivity to the PKI-peptide lasts for only 25-30 sec. Examination of sperm pellet proteins labeled with 32P ATP during activation reveals a major 25 kDa phosphoprotein and 2 minor phosphoproteins whose phosphorylation is highly sensitive to to inhibition by the PKI-peptide and essentially complete during this early phase. These sperm proteins appear to be immediate substrates for cAMP-dependent protein kinase, and phosphorylation of one or more of these appears to be requires, but not sufficient, for activation of motility. The phosphorylation of other proteins is reduced or eliminated when PKI-peptide is present at the beginning of incubation, but is unaffected by later addition of PKI-peptide. Some of these substrates appear to be likely candidates for axonemal proteins that must be phosphorylated during the later stages of incubation in order to complete the activation process. This selection is based upon a high degree of inhibition by inclusion of PKI-peptide or other inhibitors at the start of the incubation process, on near-completion of their phosphorylation by the end of the 2 min incubation period required for the activation of motility, and evidence that these proteins are phosphorylated during in vivo activation of motility. Although these observations suggest the presence of a second kinase activity that is upregulated by the initial activation of the cAMP-dependent protein kinase, assays using exogenous substrates have not yet been able to identify such a kinase activity.

Sperm chemotaxis: egg peptides control cytosolic calcium to regulate flagellar responses.

Fragmentary evidence indicates that intracellular [Ca2+] (Cai) mediates sperm chemotaxis. However, neither correlations of swimming responses to chemoattractant-induced alterations of Cai nor explanations of how chemoattractant gradients control Cai exist. Here Cai increases produced by the egg peptide speract-not previously known to cause flagellar responses--were prolonged by treatment with 3-isobutyl-1-methylxanthine (IBMX). Flagellar waveform asymmetry then increased 40% and swimming paths became tightly circular. Moreover, both responses required external Ca2+ (as does sperm chemotaxis to eggs and egg products). Cai increases by the established chemotactic peptide resact also required external Ca2+ and were enhanced by IBMX. Therefore, diverse egg peptides may use fundamentally similar mechanisms to control Cai and thereby swimming behavior in chemotaxis. Repetitive increasing additions of speract produced adaptive membrane potential and Cai responses indicating that sperm can detect increasing gradients of egg peptide over a broad concentration range. We offer a model in which shallow or decreasing gradients elevate Cai and redirect swimming paths but sufficiently steep gradients keep Cai low and swimming linear until the egg is reached. A negative-feedback loop, initiated by cGMP-mediated activation of sperm K+ channels and terminated by subsequent inactivation of guanylyl cyclase, may coordinate gradient detection with control of Cai. Continued stimulation of more receptors by steeply increasing gradients of egg peptide thus maintains membrane hyperpolarization and suppresses Ca2+ entry and Cai elevation. The molecular basis for chemotaxis therefore is explained as translation of the spatial gradient of peptide concentration into changes in K+ channel activity in the time domain.

Control of flagellar bending: a new agenda based on dynein diversity.

Observations that were interpreted to provide evidence for equivalent functions of all axonemal dyneins should be reinterpreted, and models based on this assumption should be abandoned. In the future, attempts to understand the mechanisms for flagellar bending, oscillation, and bend propagation should start from the assumption that each type of axonemal dynein may have a specific function. At least three distinct functions can now be identified: bend initiation, maintenance of the angle of propagating bends, and generation of power to overcome viscous resistances. Only the last of these three functions is an outer arm dynein function.

Microtubule sliding in reduced-amplitude bending waves of Ciona sperm flagella: bending waves attenuated by lithium.

The distinct damped, or attenuated, bending pattern observed when demembranated sperm flagella of the tunicate, Ciona, are reactivated in the presence of 2 mM Li+ has been analysed in detail. In these patterns, bends are initiated at the base of the flagellum, but die out after they start to propagate along the flagellum, so that little or no bending is seen in the distal half of the flagellum. A quantitative descriptive analysis shows that the distinctive feature of this attenuation of bending wave amplitude is an asymmetric interbend decay, or slippage, occurring, on average, only at the transitions between a reverse bend and the preceding principal bend. This attenuation is combined with a significant amount of synchronous sliding in the distal half of the flagellum and a decrease in propagation velocity of transitions between bends in the mid-region of the flagellum. Computer simulations demonstrate that the synchronous sliding in the distal half of these flagella can be an entirely passive consequence of the mechanical interaction between active sliding and bending in the basal third of the flagellum and viscous resistances to movement of the distal region of the flagellum through the fluid environment. The current computer models do not contain a mechanism for asymmetric interbend decay that can reproduce these attenuated bending patterns.

Dynein heavy chain isoforms and axonemal motility.

The translocation of dynein along microtubules is the basis for a wide variety of essential cellular movements. Dynein was first discovered in the ciliary axoneme, where it causes the directed sliding between outer doublet microtubules that underlies ciliary bending. The initiation and propagation of ciliary bends are produced by a precisely located array of different dyneins containing eight or more different dynein heavy chain isoforms. The detailed clarification of the structural and functional diversity of axonemal dynein heavy chains will not only provide the key to understanding how cilia function, but also give insights applicable to the study of non-axonemal microtubule motors.

Microtubule sliding in reduced-amplitude bending waves of Ciona sperm flagella: resolution of metachronous and synchronous sliding components of stable bending waves.

Microtubule sliding associated with the bending of reactivated flagella of demembranated spermatozoa of the tunicate, Ciona, has been analyzed using a descriptive model that permits quantitation of metachronous and synchronous components of sliding. Reduced-amplitude bending waves, obtained by addition of increased salt (K acetate), lithium, or vanadate to the reactivation solutions, have been examined. Increased K acetate can decrease bend angle by as much as 70% with little change in frequency. In all cases, a decrease in the amplitude, or bend angle, of propagated bends is measured as a decrease in the metachronous component of sliding and is associated with a reduction in the growth of new bends after they begin to propagate during the second half-cycle of bend development. At higher K acetate concentrations, bend growth during the second half-cycle of bend development is very strongly reduced and may even become negative. A disparity between the rates of bend growth in the first and second half-cycles of bend development corresponds to a large amount of synchronous sliding in the distal portion of the flagellum. When the synchronous sliding component is large, the sliding velocity in a propagating bend decreases to near-0 values and may even reverse its direction as the bend propagates through the mid-region of the flagellum. Since these large perturbations of sliding velocity do not interfere with regular propagation of bends with nearly constant bend angle, the bend propagation mechanism cannot operate by metachronous control of the velocity of sliding, and is unlikely to operate by local monitoring of either the amount or velocity of sliding. These observations therefore argue against models in which active sliding is regulated by shear or sliding velocity, and make curvature-controlled models relatively more attractive. In many cases, a reduction in sliding during bend initiation (the first half-cycle of development of new bends) also contributes to the decreased amplitude of propagated bends. These changes in bend initiation are similar in both full-length flagella and in flagella shortened by breakage. The amount of sliding that occurs during bend initiation is relatively independent of the distribution of sliding between metachronous and synchronous components in the distal part of the flagellum. These observations therefore provide additional evidence that bend initiation and bend propagation are independent and separable processes.

Activation of Ciona sperm motility: phosphorylation of dynein polypeptides and effects of a tyrosine kinase inhibitor.

A high molecular mass dynein ATPase polypeptide and a 18-20 kDa dynein light chain of Ciona sperm flagella are phosphorylated during in vivo activation of motility or in vitro activation of motility by incubation with cyclic AMP. A similar level of phosphorylation of these proteins is obtained by incubation of washed, demembranated spermatozoa with catalytic subunit of cyclic AMP-dependent protein kinase, under conditions where there is no activation of motility until a supernatant component is added. Therefore, phosphorylation of these dynein polypeptides is not sufficient for activation of motility. Activation of motility in vitro by incubation with cyclic AMP can be completely inhibited by a random copolymer of glutamate and tyrosine that inhibits tyrosine kinase activity. Under these conditions, much of the protein phosphorylation associated with activation of motility is also inhibited. These new results suggest that regulation of motility of these spermatozoa may involve a multicomponent kinase cascade rather than a simple phosphorylation of a protein 'switch' by the cyclic AMP-dependent kinase. A 53 kDa axonemal phosphoprotein band, identified as band M1, shows the strongest correlation with activation of motility in these experiments.