Differential contribution of Bud6p and Kar9p to microtubule capture and spindle orientation in S. cerevisiae

In Saccharomyces cerevisiae, spindle orientation is controlled by a temporal and spatial program of microtubule (MT)-cortex interactions. This program requires Bud6p/Aip3p to direct the old pole to the bud and confine the new pole to the mother cell. Bud6p function has been linked to Kar9p, a protein guiding MTs along actin cables. Here, we show that Kar9p does not mediate Bud6p functions in spindle orientation. Based on live microscopy analysis, kar9Delta cells maintained Bud6p-dependent MT capture. Conversely, bud6Delta cells supported Kar9p-associated MT delivery to the bud. Moreover, additive phenotypes in bud6Delta kar9Delta or bud6Delta dyn1Delta mutants underscored the separate contributions of Bud6p, Kar9p, and dynein to spindle positioning. Finally, tub2C354S, a mutation decreasing MT dynamics, suppressed a kar9Delta mutation in a BUD6-dependent manner. Thus, Kar9p-independent capture at Bud6p sites can effect spindle orientation provided MT turnover is reduced. Together, these results demonstrate Bud6p function in MT capture at the cell cortex, independent of Kar9p-mediated MT delivery along actin cables.     

Bud6 directs sequential microtubule interactions with the bud tip and bud neck during spindle morphogenesis in Saccharomyces cerevisiae

In budding yeast, spindle polarity relies on a precise temporal program of cytoplasmic microtubule-cortex interactions throughout spindle assembly. Loss of Clb5-dependent kinase activity under conditions of attenuated Cdc28 function disrupts this program, resulting in diploid-specific lethality. Here we show that polarity loss is tolerated by haploids due to a more prominent contribution of microtubule-neck interactions to spindle orientation inherent to haploids. These differences are mediated by the relative partition of Bud6 between the bud tip and bud neck, distinguishing haploids from diploids. Bud6 localizes initially to the bud tip and accumulates at the neck concomitant with spindle assembly. bud6Delta mutant phenotypes are consistent with Bud6's role as a cortical cue for cytoplasmic microtubule capture. Moreover, mutations that affect Bud6 localization and partitioning disrupt the sequential program of microtubule-cortex interactions accordingly. These data support a model whereby Bud6 sequentially cues microtubule capture events at the bud tip followed by capture events at the bud neck, necessary for correct spindle morphogenesis and polarity.     

Dynamic positioning of mitotic spindles in yeast: role of microtubule motors and cortical determinants

In the budding yeast Saccharomyces cerevisiae, movement of the mitotic spindle to a predetermined cleavage plane at the bud neck is essential for partitioning chromosomes into the mother and daughter cells. Astral microtubule dynamics are critical to the mechanism that ensures nuclear migration to the bud neck. The nucleus moves in the opposite direction of astral microtubule growth in the mother cell, apparently being "pushed" by microtubule contacts at the cortex. In contrast, microtubules growing toward the neck and within the bud promote nuclear movement in the same direction of microtubule growth, thus "pulling" the nucleus toward the bud neck. Failure of "pulling" is evident in cells lacking Bud6p, Bni1p, Kar9p, or the kinesin homolog, Kip3p. As a consequence, there is a loss of asymmetry in spindle pole body segregation into the bud. The cytoplasmic motor protein, dynein, is not required for nuclear movement to the neck; rather, it has been postulated to contribute to spindle elongation through the neck. In the absence of KAR9, dynein-dependent spindle oscillations are evident before anaphase onset, as are postanaphase dynein-dependent pulling forces that exceed the velocity of wild-type spindle elongation threefold. In addition, dynein-mediated forces on astral microtubules are sufficient to segregate a 2N chromosome set through the neck in the absence of spindle elongation, but cytoplasmic kinesins are not. These observations support a model in which spindle polarity determinants (BUD6, BNI1, KAR9) and cytoplasmic kinesin (KIP3) provide directional cues for spindle orientation to the bud while restraining the spindle to the neck. Cytoplasmic dynein is attenuated by these spindle polarity determinants and kinesin until anaphase onset, when dynein directs spindle elongation to distal points in the mother and bud.     

Stable preanaphase spindle positioning requires Bud6p and an apparent interaction between the spindle pole bodies and the neck

Faithful partitioning of genetic material during cell division requires accurate spatial and temporal positioning of nuclei within dividing cells. In Saccharomyces cerevisiae, nuclear positioning is regulated by an elegant interplay between components of the actin and microtubule cytoskeletons. Regulators of this process include Bud6p (also referred to as the actin-interacting protein Aip3p) and Kar9p, which function to promote contacts between cytoplasmic microtubule ends and actin-delimited cortical attachment points. Here, we present the previously undetected association of Bud6p with the cytoplasmic face of yeast spindle pole bodies, the functional equivalent of metazoan centrosomes. Cells lacking Bud6p show exaggerated movements of the nucleus between mother and daughter cells and display reduced amounts of time a given spindle pole body spends in close association with the neck region of budding cells. Furthermore, overexpression of BUD6 greatly enhances interactions between the spindle pole body and mother-bud neck in a spindle alignment-defective dynactin mutant. These results suggest that association of either spindle pole body with neck components, rather than simply entry of a spindle pole body into the daughter cell, provides a positive signal for the progression of mitosis. We propose that Bud6p, through its localization at both spindle pole bodies and at the mother-bud neck, supports this positive signal and provides a regulatory mechanism to prevent excessive oscillations of preanaphase nuclei, thus reducing the likelihood of mitotic delays and nuclear missegregation.     

Cortical Num1p interacts with the dynein intermediate chain Pac11p and cytoplasmic microtubules in budding yeast

Num1p, a cortical 313-kD protein, controls cytoplasmic microtubule (cMT) functions and nuclear migration through the bud neck in anaphase cells. A green fluorescent protein (GFP)-Num1p fusion protein localizes at the bud tip and the distal mother pole of living cells, apparently forming cMT capture sites at late anaphase. In addition, galactose-induced GFP-Num1p is seen at the bud neck and in lateral regions of the mother cortex. The bud tip location of Num1p depends on Bni1p but does not require Kar9p, Dyn1p, or cMTs, whereas cMT contacts with polar Num1p dots are reduced in cells lacking Dyn1p. Num1p associates with the dynein intermediate chain Pac11p in the presence of Dyn1p, and with the alpha-tubulin Tub3p, as shown by coimmune precipitation of tagged proteins. Num1p also forms a complex with Bni1p and Kar9p, although Num1p is not required for Bni1p- and Kar9p-dependent nuclear migration to the bud neck in preanaphase cells.Our data suggest that Num1p controls nuclear migration during late anaphase by forming dynein-interacting cortical cMT capture sites at both cellular poles. In addition, Num1p may transiently cooperate with an associated Bni1p-Kar9p complex at the bud tip of early anaphase cells.     

The Bud14p-Glc7p complex functions as a cortical regulator of dynein in budding yeast

Regulated interactions between microtubules (MTs) and the cell cortex control MT dynamics and position the mitotic spindle. In eukaryotic cells, the adenomatous polyposis coli/Kar9p and dynein/dynactin pathways are involved in guiding MT plus ends and MT sliding along the cortex, respectively. Here we identify Bud14p as a novel cortical activator of the dynein/dynactin complex in budding yeast. Bud14p accumulates at sites of polarized growth and the mother-bud neck during cytokinesis. The localization to bud and shmoo tips requires an intact actin cytoskeleton and the kelch-domain-containing proteins Kel1p and Kel2p. While cells lacking Bud14p function fail to stabilize the pre-anaphase spindle at the mother-bud neck, overexpression of Bud14p is toxic and leads to elongated astral MTs and increased dynein-dependent sliding along the cell cortex. Bud14p physically interacts with the type-I phosphatase Glc7p, and localizes Glc7p to the bud cortex. Importantly, the formation of Bud14p-Glc7p complexes is necessary to regulate MT dynamics at the cortex. Taken together, our results suggest that Bud14p functions as a regulatory subunit of the Glc7p type-I phosphatase to stabilize MT interactions specifically at sites of polarized growth.     

Microtubule interactions with the cell cortex causing nuclear movements in Saccharomyces cerevisiae

During mitosis in budding yeast the nucleus first moves to the mother-bud neck and then into the neck. Both movements depend on interactions of cytoplasmic microtubules with the cortex. We investigated the mechanism of these movements in living cells using video analysis of GFP-labeled microtubules in wild-type cells and in EB1 and Arp1 mutants, which are defective in the first and second steps, respectively. We found that nuclear movement to the neck is largely mediated by the capture of microtubule ends at one cortical region at the incipient bud site or bud tip, followed by microtubule depolymerization. Efficient microtubule interactions with the capture site require that microtubules be sufficiently long and dynamic to probe the cortex. In contrast, spindle movement into the neck is mediated by microtubule sliding along the bud cortex, which requires dynein and dynactin. Free microtubules can also slide along the cortex of both bud and mother. Capture/shrinkage of microtubule ends also contributes to nuclear movement into the neck and can serve as a backup mechanism to move the nucleus into the neck when microtubule sliding is impaired. Conversely, microtubule sliding can move the nucleus into the neck even when capture/shrinkage is impaired.     

The cortical protein Num1p is essential for dynein-dependent interactions of microtubules with the cortex

In budding yeast, the mitotic spindle moves into the neck between the mother and bud via dynein-dependent sliding of cytoplasmic microtubules along the cortex of the bud. How dynein and microtubules interact with the cortex is unknown. We found that cells lacking Num1p failed to exhibit dynein-dependent microtubule sliding in the bud, resulting in defective mitotic spindle movement and nuclear segregation. Num1p localized to the bud cortex, and that localization was independent of microtubules, dynein, or dynactin. These data are consistent with Num1p being an essential element of the cortical attachment mechanism for dynein-dependent sliding of microtubules in the bud.     

Control of mitotic spindle position by the Saccharomyces cerevisiae formin Bni1p

Alignment of the mitotic spindle with the axis of cell division is an essential process in Saccharomyces cerevisiae that is mediated by interactions between cytoplasmic microtubules and the cell cortex. We found that a cortical protein, the yeast formin Bni1p, was required for spindle orientation. Two striking abnormalities were observed in bni1Delta cells. First, the initial movement of the spindle pole body (SPB) toward the emerging bud was defective. This phenotype is similar to that previously observed in cells lacking the kinesin Kip3p and, in fact, BNI1 and KIP3 were found to be in the same genetic pathway. Second, abnormal pulling interactions between microtubules and the cortex appeared to cause preanaphase spindles in bni1Delta cells to transit back and forth between the mother and the bud. We therefore propose that Bni1p may localize or alter the function of cortical microtubule-binding sites in the bud. Additionally, we present evidence that other bipolar bud site determinants together with cortical actin are also required for spindle orientation.     

Spindle polarity in S. cerevisiae: MEN can tell

Spatial coordination between the axis of the spindle and the division plane is critical in asymmetric cell divisions. In the budding yeast S. cerevisiae, orientation of the mitotic spindle responds to two intertwined programs dictating the position of the spindle poles: one providing the blueprint for built-in pole asymmetry, the other sequentially confining microtubule-cortex interactions to the bud and the bud neck. The first program sets a temporal asymmetry to limit astral microtubules to a single pole prior to spindle pole separation. The second enforces this polarity by allowing these early formed microtubules to undergo capture at the bud cell cortex while stopping newly formed microtubules once cortical capture shifts to the bud neck. The remarkable precision of this integrated program results in an invariant pattern of spindle pole inheritance in which the "old" spindle pole is destined to the bud. An additional layer of asymmetry is superimposed to couple successful chromosomal segregation between the mother and the bud with mitotic exit. This is based on the asymmetric localization to the committed daughter-bound pole of signaling components of the mitotic exit network. This system operates irrespective of intrinsic spindle polarity to ensure that it is always the pole translocating into the bud that carries the signal to regulate mitotic exit.     

The cortical localization of the microtubule orientation protein, Kar9p, is dependent upon actin and proteins required for polarization

In the yeast Saccharomyces cerevisiae, positioning of the mitotic spindle requires both the cytoplasmic microtubules and actin. Kar9p is a novel cortical protein that is required for the correct position of the mitotic spindle and the orientation of the cytoplasmic microtubules. Green fluorescent protein (GFP)- Kar9p localizes to a single spot at the tip of the growing bud and the mating projection. However, the cortical localization of Kar9p does not require microtubules (Miller, R.K., and M.D. Rose. 1998. J. Cell Biol. 140: 377), suggesting that Kar9p interacts with other proteins at the cortex. To investigate Kar9p's cortical interactions, we treated cells with the actin-depolymerizing drug, latrunculin-A. In both shmoos and mitotic cells, Kar9p's cortical localization was completely dependent on polymerized actin. Kar9p localization was also altered by mutations in four genes, spa2Delta, pea2Delta, bud6Delta, and bni1Delta, required for normal polarization and actin cytoskeleton functions and, of these, bni1Delta affected Kar9p localization most severely. Like kar9Delta, bni1Delta mutants exhibited nuclear positioning defects during mitosis and in shmoos. Furthermore, like kar9Delta, the bni1Delta mutant exhibited misoriented cytoplasmic microtubules in shmoos. Genetic analysis placed BNI1 in the KAR9 pathway for nuclear migration. However, analysis of kar9Delta bni1Delta double mutants suggested that Kar9p retained some function in bni1Delta mitotic cells. Unlike the polarization mutants, kar9Delta shmoos had a normal morphology and diploids budded in the correct bipolar pattern. Furthermore, Bni1p localized normally in kar9Delta. We conclude that Kar9p's function is specific for cytoplasmic microtubule orientation and that Kar9p's role in nuclear positioning is to coordinate the interactions between the actin and microtubule networks.     

Spindle Polarity in S. cerevisiae: MEN Can Tell

Spatial coordination between the axis of the spindle and the division plane is critical in asymmetric cell divisions. In the budding yeast S. cerevisiae, orientation of the mitotic spindle responds to two intertwined programs dictating the position of the spindle poles: one providing the blueprint for built-in pole asymmetry, the other sequentially confining microtubule-cortex interactions to the bud and the bud neck. The first program sets a temporal asymmetry to limit astral microtubules to a single pole prior to spindle pole separation. The second enforces this polarity by allowing these early formed microtubules to undergo capture at the bud cell cortex while stopping newly formed microtubules once cortical capture shifts to the bud neck. The remarkable precision of this integrated program results in an invariant pattern of spindle pole inheritance in which the "old" spindle pole is destined to the bud. An additional layer of asymmetry is superimposed to couple successful chromosomal segregation between the mother and the bud with mitotic exit. This is based on the asymmetric localization to the committed daughter-bound pole of signaling components of the mitotic exit network. This system operates irrespective of intrinsic spindle polarity to ensure that it is always the pole translocating into the bud that carries the signal to regulate mitotic exit.

Key Words:

Cell cycle, Polarity, checkpoint, Microtubule, Cortical cues     

Microtubules Orient the Mitotic Spindle in Yeast through Dynein-dependent Interactions with the Cell Cortex

Proper orientation of the mitotic spindle is critical for successful cell division in budding yeast. To investigate the mechanism of spindle orientation, we used a green fluorescent protein (GFP)–tubulin fusion protein to observe microtubules in living yeast cells. GFP–tubulin is incorporated into microtubules, allowing visualization of both cytoplasmic and spindle microtubules, and does not interfere with normal microtubule function. Microtubules in yeast cells exhibit dynamic instability, although they grow and shrink more slowly than microtubules in animal cells. The dynamic properties of yeast microtubules are modulated during the cell cycle. The behavior of cytoplasmic microtubules revealed distinct interactions with the cell cortex that result in associated spindle movement and orientation. Dynein-mutant cells had defects in these cortical interactions, resulting in misoriented spindles. In addition, microtubule dynamics were altered in the absence of dynein. These results indicate that microtubules and dynein interact to produce dynamic cortical interactions, and that these interactions result in the force driving spindle orientation.     

The role of the proteins Kar9 and Myo2 in orienting the mitotic spindle of budding yeast

BACKGROUND: Two genetic 'pathways' contribute to the fidelity of nuclear segregation during the process of budding in the yeast Saccharomyces cerevisiae. An early pathway, involving Kar9p and other proteins, orients the mitotic spindle along the mother-bud axis. Upon the onset of anaphase, cytoplasmic dynein provides the motive force for nuclear movement into the bud. Loss of either pathway results in nuclear-migration defects; loss of both is lethal. Here, to visualize the functional steps leading to correct spindle orientation along the mother-bud axis, we imaged live yeast cells expressing Kar9p and dynein as green fluorescent protein fusions. RESULTS: Transport of Kar9p into the bud was found to require the myosin Myo2p. Kar9p interacted with microtubules through the microtubule-binding protein Bim1p and facilitated microtubule penetration into the bud. Once microtubules entered the bud, Kar9p provided a platform for microtubule capture at the bud cortex. Kar9p was also observed at sites of microtubule shortening in the bud, suggesting that Kar9p couples microtubule shortening to nuclear migration. CONCLUSIONS: Thus, Kar9p provides a key link between the actin cytoskeleton and microtubules early in the cell cycle. A cooperative mechanism between Kar9p and Myo2p facilitates the pre-anaphase orientation of the spindle. Later, Kar9p couples microtubule disassembly with nuclear migration.     

Interactions among Rax1p, Rax2p, Bud8p, and Bud9p in marking cortical sites for bipolar bud-site selection in yeast

In the budding yeast Saccharomyces cerevisiae, selection of the bud site determines the axis of polarized cell growth and eventual oriented cell division. Bud sites are selected in specific patterns depending on cell type. These patterns appear to depend on distinct types of marker proteins in the cell cortex; in particular, the bipolar budding of diploid cells depends on persistent landmarks at the birth-scar-distal and -proximal poles that involve the proteins Bud8p and Bud9p, respectively. Rax1p and Rax2p also appear to function specifically in bipolar budding, and we report here a further characterization of these proteins and of their interactions with Bud8p and Bud9p. Rax1p and Rax2p both appear to be integral membrane proteins. Although commonly used programs predict different topologies for Rax2p, glycosylation studies indicate that it has a type I orientation, with its long N-terminal domain in the extracytoplasmic space. Analysis of rax1 and rax2 mutant budding patterns indicates that both proteins are involved in selecting bud sites at both the distal and proximal poles of daughter cells as well as near previously used division sites on mother cells. Consistent with this, GFP-tagged Rax1p and Rax2p were both observed at the distal pole as well as at the division site on both mother and daughter cells; localization to the division sites was persistent through multiple cell cycles. Localization of Rax1p and Rax2p was interdependent, and biochemical studies showed that these proteins could be copurified from yeast. Bud8p and Bud9p could also be copurified with Rax1p, and localization studies provided further evidence of interactions. Localization of Rax1p and Rax2p to the bud tip and distal pole depended on Bud8p, and normal localization of Bud8p was partially dependent on Rax1p and Rax2p. Although localization of Rax1p and Rax2p to the division site did not appear to depend on Bud9p, normal localization of Bud9p appeared largely or entirely dependent on Rax1p and Rax2p. Taken together, the results indicate that Rax1p and Rax2p interact closely with each other and with Bud8p and Bud9p in the establishment and/or maintenance of the cortical landmarks for bipolar budding.     

Subcellular localization of the interaction of bipolar landmarks Bud8p and Bud9p with Rax2p in Saccharomyces cerevisiae diploid cells

In Saccharomyces cerevisiae, the bud site selection of diploid cells is regulated by at least four persistent landmarks, Bud8p, Bud9p, Rax1p, and Rax2p. Bud8p and Bud9p are essential for the establishment of bipolar budding and localize mainly to the distal and the proximal poles, respectively. Their subcellular localizations are regulated through interaction with Rax1p/Rax2p. We investigated when and where Bud8p and Bud9p physically interact with Rax2p in vivo using a split-GFP method. GFP fluorescence showed that Bud8p physically interacted with Rax2p at the proximal or distal pole in unbudded cells; a physical interaction was also observed at the opposite pole to the growing bud in mother cells with a large-size bud. Bud9p physically interacted with Rax2p at the birth scar in budded mother cells. These observations suggest that the interaction of Rax2p with Bud8p and Bud9p may contribute to the translocation of bipolar landmarks to the correct sites.     

The role of the lissencephaly protein Pac1 during nuclear migration in budding yeast

During mitosis in Saccharomyces cerevisiae, the mitotic spindle moves into the mother-bud neck via dynein-dependent sliding of cytoplasmic microtubules along the cortex of the bud. Here we show that Pac1, the yeast homologue of the human lissencephaly protein LIS1, plays a key role in this process. First, genetic interactions placed Pac1 in the dynein/dynactin pathway. Second, cells lacking Pac1 failed to display microtubule sliding in the bud, resulting in defective mitotic spindle movement and nuclear segregation. Third, Pac1 localized to the plus ends (distal tips) of cytoplasmic microtubules in the bud. This localization did not depend on the dynein heavy chain Dyn1. Moreover, the Pac1 fluorescence intensity at the microtubule end was enhanced in cells lacking dynactin or the cortical attachment molecule Num1. Fourth, dynein heavy chain Dyn1 also localized to the tips of cytoplasmic microtubules in wild-type cells. Dynein localization required Pac1 and, like Pac1, was enhanced in cells lacking the dynactin component Arp1 or the cortical attachment molecule Num1. Our results suggest that Pac1 targets dynein to microtubule tips, which is necessary for sliding of microtubules along the bud cortex. Dynein must remain inactive until microtubule ends interact with the bud cortex, at which time dynein and Pac1 appear to be offloaded from the microtubule to the cortex.     

Astral Microtubule Dynamics in Yeast: A Microtubule-based Searching Mechanism for Spindle Orientation and Nuclear Migration into the Bud

Localization of dynein–green fluorescent protein (GFP) to cytoplasmic microtubules allowed us to obtain one of the first views of the dynamic properties of astral microtubules in live budding yeast. Several novel aspects of microtubule function were revealed by time-lapse, three-dimensional fluorescence microscopy. Astral microtubules, about four to six in number for each pole, exhibited asynchronous dynamic instability throughout the cell cycle, growing at 0.3–1.5 μm/min toward the cell surface then switching to shortening at similar velocities back to the spindle pole body (SPB). During interphase, a conical array of microtubules trailed the SPB as the nucleus traversed the cytoplasm. Microtubule disassembly by nocodozole inhibited these movements, indicating that the nucleus was pushed around the interior of the cell via dynamic astral microtubules. These forays were evident in unbudded G1 cells, as well as in late telophase cells after spindle disassembly. Nuclear movement and orientation to the bud neck in S/G2 or G2/M was dependent on dynamic astral microtubules growing into the bud. The SPB and nucleus were then pulled toward the bud neck, and further microtubule growth from that SPB was mainly oriented toward the bud. After SPB separation and central spindle formation, a temporal delay in the acquisition of cytoplasmic dynein at one of the spindle poles was evident. Stable microtubule interactions with the cell cortex were rarely observed during anaphase, and did not appear to contribute significantly to spindle alignment or elongation into the bud. Alterations of microtubule dynamics, as observed in cells overexpressing dynein-GFP, resulted in eventual spindle misalignment. These studies provide the first mechanistic basis for understanding how spindle orientation and nuclear positioning are established and are indicative of a microtubule-based searching mechanism that requires dynamic microtubules for nuclear migration into the bud.     

Role of bud6p and tea1p in the interaction between actin and microtubules for the establishment of cell polarity in fission yeast

BACKGROUND: In many cell types, microtubules are thought to direct the spatial distribution of F-actin in cell polarity. Schizosaccharomyces pombe cells exhibit a regulated program of polarized cell growth: after cell division, they grow first in a monopolar manner at the old end, and in G2 phase, initiate growth at the previous cell division site (the new end). The role of microtubule ends in cell polarity is highlighted by the finding that the cell polarity factor, tea1p, is present on microtubule plus ends and cell tips [1]. RESULTS: Here, we characterize S. pombe bud6p/fat1p, a homolog of S. cerevisiae Bud6/Aip3. bud6Delta mutant cells have a specific defect in the efficient initiation of growth at the new end and like tea1Delta cells, form T-shaped cells in a cdc11 background. Bud6-GFP localizes to both cell tips and the cytokinesis ring. Maintenance of cell tip localization is dependent upon actin but not microtubules. Bud6-GFP localization is tea1p dependent, and tea1p localization is not bud6p dependent. tea1Delta and bud6Delta cells generally grow in a monopolar manner but exhibit different growth patterns. tea1(Delta)bud6Delta mutants resemble tea1Delta mutants. Tea1p and bud6p coimmunoprecipitate and comigrate in large complexes. CONCLUSIONS: Our studies show that tea1p (a microtubule end-associated factor) and bud6p (an actin-associated factor) function in a common pathway, with bud6p downstream of tea1p. To our knowledge, bud6p is the first protein shown to interact physically with tea1p. These studies delineate a pathway for how microtubule plus ends function to polarize the actin cytoskeleton through actin-associated polarity factors.