Ludivine Martin
email: ludivine.martin@liser.lu

Thuc Uyen Nguyen-Thi

Caroline Mothe
email: caroline.mothe@univ-smb.fr

Human resource practices, perceived employability and turnover intention: Does age matter?

Keywords: Age, HR practices, perceived external employability, turnover intention

This paper investigates the age specificities in the link between employee's perceived external employability and turnover intention and how the use of human resource practices moderates this relationship. Results show that the use of motivation-enhancing HR practices induces a larger retention effect for younger and middle-aged employees than for older ones, whereas the turnover intention effects of flexibility-enhancing HR practices are stronger for the middle-age and older groups than for the younger groups. Moreover, the use of HR practices that stimulate employees' motivation, such as training, participation, voice and teamwork, plays a stronger role in retaining highly employable younger employees, while the use of HR practices that offer flexibility, such as flexible working time, teleworking and work-life balance, enables retaining highly employable older employees.

Introduction

Employees' turnover intention (or intention to quit, Böckerman and Ilmakunnas, 2009) is considered as an important work-related attitude -along with job satisfaction, organizational commitment, perceived organizational support, employee engagement and job involvement.

Turnover intention is shown to be the best predictor of actual turnover (e.g. Böckerman and Ilmakunnas, 2009;Van Breukelen et al., 2004), a subject of utmost importance due to the impending shortage of highly skilled workers, as employees with better skills and abilities will be those who tend to leave, whereas those who remain are the ones who cannot find other jobs.

Retention policy is thus a crucial element of human resource (HR) management, especially the retention of older employees who are the guardians of valuable expertise and knowledge (e.g. Sumbal et al., 2017;Delfgaauw, 2007a).

Employee age has been associated to organizational attachment, motivations and turnover intention. Studies on how to deal with turnover intention across the lifespan have provided inconsistent results. [START_REF] Healy | Age and voluntary turnover: A quantitative review[END_REF], looking at the bivariate link between chronological age and voluntary turnover using meta-analysis, reported that the age-turnover association was near to inexistent. [START_REF] Peltokorpi | Organizational embeddedness, turnover intentions, and voluntary turnover: The moderating effects of employee demographic characteristics and value orientations[END_REF] also reported any association between age as moderator in the relationship between organizational embeddedness and turnover intention. By contrast, conducting a meta-analysis of 49 studies published between 1990 and 2008, [START_REF] Ng | The relationships of age with job attitudes: A meta analysis[END_REF] found evidence that younger employees (under 50) are more likely than their older colleagues to leave their job, this relationship depending on moderators such as racial minority membership, organizational tenure or education level. [START_REF] Finegold | Age Effects on the predictors of technical workers' commitment and willingness to turnover[END_REF] indicated that, for the under-30s, satisfaction with opportunities to develop technical skills and pay linked to individual performance has a stronger negative relationship with the intention to leave their current job than for those over 45, reporting a statistically significant but small effect of age.

A c c e p t e d m a n u s c r i p t

We contribute to existing literature in several ways. First, we shed new light on the topic of subjective employment alternatives and turnover intention, considering the specificities of employees' age. We accordingly propose a first analysis of age-differentiated perceived external employability and turnover intention. Second, to the best of our knowledge, no former research has investigated what specific HR practices fit better with the work attitudes of employees belonging to different age groups, taking into account contextual factors such as perceived external employability. We thus investigate the role of HR practices in moderating the turnover effects of perceived employability among different age groups. Third, we are able to provide robust estimators of employees' turnover intention, taking into account their perceived employability and their use of HR practices. We take advantage of a large dataset of official employee statistics, referring to a sample of 16,896 observations representing the active population of Luxembourg's private labour market and containing a large set of job characteristics, socio-demographic characteristics and firm heterogeneity.

Theoretical background and hypotheses

Age-related changes in expectations and motives

Age may explain changes in employees' work attitudes by affecting their needs, their expectations regarding future prospects, and their values at a particular stage in life. Scholars have suggested explanations for why work-related attitudes, including the intention to quit, change with age. First, rooted in the life-span psychology and the socio-emotional selectivity theories [START_REF] Kanfer | Aging, Adult Development, and Work Motivation[END_REF][START_REF] Kooij | Age and workrelated motives: Results of a meta-analysis[END_REF], younger and older workers may differ in terms of emotional reactions. Changes in individual attitudes may be related to changes in people's subjective well-being and mental health. Older adults may be more likely to maximize positive emotional experiences than negative ones, so as to make the best of the limited time A c c e p t e d m a n u s c r i p t they perceive they have left (Carstensen and Mikels, 2005;[START_REF] Mather | Aging and motivated cognition: The positivity effect in attention and memory[END_REF].

While young adults have been associated with more intense emotional reactions to negative stimuli and adversity at work, older people are likely to be more able to understand and control their emotions (Bruine de Bruin et al., 2014;Chapman and Hayslip, 2006). As a result, older workers are supposed to maintain better work attitudes and to be less likely to search for another job in the face of adverse events or working conditions.

Second, research on decision-making and social relationships across the lifespan has also indicated age-related changes in needs and work values, such as the importance of pay and promotion or work expectations [START_REF] Kanfer | Aging, Adult Development, and Work Motivation[END_REF][START_REF] Ng | The relationships of age with job attitudes: A meta analysis[END_REF]. While the prime-aged might be more oriented towards fulfilling social needs, young individuals might display greater motivation to fulfil their growth needs, such as pursuing more challenging opportunities, having new work goals and developing their career [START_REF] Ebner | Developmental changes in personal goal orientation from young to late adulthood: from striving for gains to maintenance and prevention of losses[END_REF][START_REF] Jans | Organizational Commitment, Career Factors and Career/Life Stage[END_REF]. In addition, older adults in their middle and later career periods, may occupy more attractive positions with higher power and status [START_REF] Kalleberg | Aging, Values, and Rewards: Explaining Age Differences in Job Satisfaction[END_REF], thus may be more likelyrelative to younger colleaguesto strive for stability, as they take on broader organizational roles and quality social relationships with colleagues, family and friends, which offer them fulfilment of their status and affiliation needs. Older adults may therefore lower their work-related expectations and have more realistic job expectations.

Third, linked to cognitive perceptions, older workers may feel that their employability is low because of the employers' stereotypes regarding the decline of job performance with age. 2 Indeed, age stereotypes influence employers' judgments but not only: from workers too. Raemdonck et al. (2017) indicate that activating negative age stereotypes tended to worsen 2 We thank an anonymous reviewer for pointing this important aspect.

A c c e p t e d m a n u s c r i p t memory performance, memory self-efficacy and views of ageing in old people. This means that avoiding negative stereotypes about older workers may have a positive effect on their learning and development and, in turn, their performance.

Relationship between perceived employability and turnover intention

Perceived employability represents the subjective perception employees have about their ease of movement [START_REF] March | Organizations[END_REF] and their job alternatives [START_REF] Mobley | A review and conceptual analysis of the employee turnover process[END_REF]. The employability paradox assumes that employee development is a risk for employer in the form of increased turnover intention (e.g. De Cuyper and De Witte, 2011). Empirical analyses show controversial results. [START_REF] Hom | A meta-analytical structural equation analysis of a model of employee turnover[END_REF] found a positive association between perceived employability and turnover intention, while no evidence was found by Berntson et al. (2010). De Cuyper et al. (2011) however showed that perceived employability and turnover intention become positive related when job resources are low (such as job control and social support from superiors and colleagues). [START_REF] Nelissen | Employee development and voluntary turnover: testing the employability paradox[END_REF], testing the employability paradox, found that perceived external employability induces turnover intention, but only in case of upward career development. Recently, [START_REF] Rodrigues | Evaluating the employability paradox: When does organizational investment in human capital pay off?[END_REF] find that high investment in career development practices reinforces the positive association between perceived employability and organizational attachment and the negative association between employability and turnover intention.

Age-related differences in the link between turnover intention and HR practices

Literature on strategic HR management (Böckerman et al., 2012;White and Bryson, 2013) often refers to HR systems such as motivation-enhancing practices (e.g. communication, teamwork, voice, up-skilling and performance appraisal) and incentive-related practices (e.g. teleworking and work-life balance). These frameworks provide a better understanding of the relationship between HR practices and employees' attitudes: each HR bundle is aimed at different goals in A c c e p t e d m a n u s c r i p t specific contexts [START_REF] Bal | From flexibility human resource management to employee engagement and perceived job performance across the lifespan: A multisample study[END_REF]. We analyse the bundle of HR practices regrouping all those that are aimed at enhancing the work environment and employees' motivation [START_REF] Martin | Do innovative work practices and ICT use motivate employees?[END_REF]): e.g. voice, participation, communication, training and teamwork. In line with [START_REF] Bal | From flexibility human resource management to employee engagement and perceived job performance across the lifespan: A multisample study[END_REF], [START_REF] Heywood | Schedule flexibility, family friendly policies and absence[END_REF] and Stirpe et al. (2017), we also take into account a bundle of HR practices enhancing the flexibility for employees: work-life balance, flexible working time and teleworking.

Strategic HR researchers mostly adopt social exchange theory to explain how various aspects of HR practices affect employees' work attitudes. The idea is that HR practices can directly influence an employee's desire to move [START_REF] March | Organizations[END_REF]: employees who are satisfied with HR practices may have less motivation to leave their job, and hence turnover will be lower. However, according to the job demands-resources model [START_REF] Bakker | The job demands-resources model: State of the art[END_REF][START_REF] Schaufeli | Job demands, job resources, and their relationship with burnout and engagement: a multi-sample study[END_REF], employees' attitudes depend not only on the resources provided by HR practices such as flexibility, promotion, involvement and job control, but also on the demands induced by HR practices, such as stress and work overload, which could affect employees' well-being. Thus, HR practices may also induce adverse effects on employees' attitudes: employees experiencing positive HR practices may also perceive the pressure of increasingly higher performance that could, in turn, have adverse consequences on job strain [START_REF] Ramsay | Employees and high-performance work systems: Testing inside the black box[END_REF] and employees' stress, work pressure and anxiety (Wood et al., 2012). [START_REF] Jensen | High-performance work systems and job control consequences for anxiety, role overload, and turnover intentions[END_REF] examined relationships among HR practices, job control, employee anxiety, role overload and employee turnover intentions. They highlighted several negative consequences on employees' turnover intentions when HR practices are implemented with low levels of job control. Taking into account the "resources" provided by HR practices (e.g. empowerment, discretion and job control) and the "demands" (stress, overload and anxiety), empirical evidence consistently provides some support for positive relationships between HR practices and employees' attitudes such as job satisfaction, organizational commitment, A c c e p t e d m a n u s c r i p t motivations, organizational citizenship behaviour and pride (e.g. [START_REF] Knight | Training and employee mobility in the British private and public sectors[END_REF].

Regarding the role of age in these relationships, the meta-analysis of 83 studies provided by [START_REF] Kooij | The influence of age on the associations between HR practices and both affective commitment and job satisfaction: A meta-analysis[END_REF] underlines that the positive relationships are strengthened for older ages for flexible work schemes and weakened when HR practices relate to individual career development.

Only a few studies have explored the issue of age in relation to turnover intention and HR practices. Stirpe et al. (2017) assess the link between retention rate and HR practices, with the age structure in the workplace as a moderator. Bal and Dorenbosch (2015) also used workplace survey data to analyse the age-related differences in the relationship between HR practices and organizational performance, such as absenteeism and turnover.

In this article, we propose an analysis at the employee level to investigate age-related differences in the relationship between motivational practices and voluntary turnover. Since values, expectations and priorities are likely to change with ageing, as stated in the previous sub-section, we expect that some HR practices are less suitable for older workers [START_REF] Khilji | New evidence in an old debate: Investigating the relationship between HR satisfaction and turnover[END_REF]. Compared with their older colleagues, younger employees with their larger perspective regarding the future pay greater attention to the development of their career and to financial aspects. As the motivation-enhancing HR practices (quality circle, job rotation, participation, voice, teamwork and training) aim to provide opportunities for involvement and career progression, these practices may be more valuable for younger employees and influence their turnover intention more than for older ones. The underlying hypothesis is that the younger employees are more positive about the "resources" provided by motivation-enhancing HR practices and less adversely influenced by the "demands" generated by these practices: Hypothesis 1. Motivation-enhancing HR practices are more valuable for younger employees, in the sense that effects of these practices on turnover intention are stronger for younger employees than for older employees.

A c c e p t e d m a n u s c r i p t

By contrast, as older employees in their later career period may be more aware of the shorter time horizon, they may have more salient concerns about the stabilization and the quality of social relationships with colleagues, family and friends that offer them fulfilment of their social status and affiliation needs. They may therefore lower their work-related expectations and have more realistic job expectations. Accordingly, the use of flexibility-enhancing HR practices aiming at fulfilling these needs and motives may be more suited to retain older employees than younger employees: Hypothesis 2. Flexibility-enhancing HR practices are more valuable for older employees, in the sense that the effects of these practices on turnover intention are stronger for older employees than for younger employees.

HR practices moderating the relationship between employability and turnover intention

HR practices satisfy the employee's needs, thus serving as an indication that the organization values employees' contribution. In turn, employees would respond by tending to remain within the organization [START_REF] Cole | Organizational identity strength, identification, and commitment and their relationships to turnover intention: Does organizational hierarchy matter[END_REF]. If employees feel that their organization is disrespectful towards them, they will express their intention to leave it. Organizational actions are interpreted by employees as symbolic of their organization's commitment to them, which, in turn, contributes to organizational support (Armstrong-Stassen and Ursel, 2009). However, while research has generally assumed that HR practices influence all employees in the same way, employees' motives and needs change with age (e.g. [START_REF] Kooij | Managing aging workers: a mixed methods study on bundles of HR practices for aging workers[END_REF][START_REF] Ng | The relationships of age with job attitudes: A meta analysis[END_REF]Zwick, 2015), suggesting that older workers may react differently to HR practices than their younger colleagues.

In Hypothesis 1, we suggest that HR practices that enhance employees' motivationsuch as job rotation, communication, voice, teamwork, training or quality circleare likely to be A c c e p t e d m a n u s c r i p t more valuable for younger employees, in that they may reduce their turnover intention more than for older employees. In this sub-section, we combine perceived external employability and motivation-enhancing practices in relation to turnover intention. We draw our argument from the unfolding model of turnover [START_REF] Lee | An alternative approach: The unfolding model of voluntary employee turnover[END_REF], highlighting that employees do not just intend to quit without events or "shocks" that force them to evaluate their job. If voluntary turnover leads to a better job with improved earnings or working conditions, employees perceiving themselves as having high employability will consider quitting as an option unless their employer mitigates the adverse turnover effect of job opportunities through appropriate HR practices. Accordingly, we consider whether the adverse turnover effects of perceived external employability for the younger age group could be mitigated by motivation-enhancing HR practices. The underlying hypothesis is that in the case of high ease of movement, the resources generated by these practicessuch as commitment, empowerment and improved career prospectsmay alleviate the adverse effect of employability in such a way that younger employees are less motivated to quit: Hypothesis 3. Motivation-enhancing HR practices mitigate the effects of high-perceived external employability or turnover intentions more for the younger group than for the older one.

In the same vein, we also relate perceived external employability and flexibility-enhancing HR practices to turnover intention. Hypothesis 2 suggests that older employees place more value on flexibility-enhancing HR practices than younger employees do, with the result that older employees are more likely than younger employees to stay with an organization when flexibility-enhancing HR practices are implemented. Here, we again draw our argument from the unfolding model of turnover [START_REF] Lee | An alternative approach: The unfolding model of voluntary employee turnover[END_REF] developed for hypothesis 3, to examine people intending to quit without any events or "shocks" that force them to evaluate A c c e p t e d m a n u s c r i p t their job. The idea is that if voluntary turnover leads to a job with better earnings or working conditions, employees perceiving high employability will consider quitting as an option unless the firm mitigates the adverse turnover effect of job opportunities through appropriate HR practices:

Hypothesis 4. Flexibility-enhancing HR practices mitigate the effects of high-perceived external employability on turnover intentions more for the older group than for the younger one. sector. This method prevents the bias problem linked to the fact that employees with bad working conditions or low job satisfaction were more likely to respond or not to the survey.

Three age groups 3 are used: (1) 16 to 29 (early adulthood) (n = 2,522 -16%); (2) between 30 and 49 (middle adulthood) (n = 11,454 -64%); and (3) age 50 and over (late adulthood) (n = 2,920 -20%). 4 The two first age groups refer to the "younger workers" category.

Variables

Intention to quit

Similar to [START_REF] Delfgaauw | The effect of job satisfaction on job search: Not just whether, but also where[END_REF], voluntary turnover is based on the question: "Have you tried to leave your current job in the last 12 months?" with three possible answers "No, not at all", "Yes, I have been looking around" or "Yes, I have intensively searched". As only less than 6 per cent of the weighted sample gave the third answer, a dummy variable for the intention to quit was constructed and the two last answers grouped together (33 per cent of the weighted sample).

Main variable of interest: Perceived external employability

The employability variable measurement is in line with Berntson et al. (2010) andDe Cuyper et al. (2011): "If you were to lose or leave your present job, do you think it would be difficult for you to find an equivalent job?" with answers on a scale from 1 to 4 (1 = very difficult; 2 = quite difficult; 3 = quite easy; 4 = very easy). Due to a low number of responses for some alternatives, the scale was recoded from 1 to 3. The mean of the employability measurement is 3 We do not have access to chronological age 4 The number of observations relates to the non-weighted number of employees in the sample, whereas the percentages are weighted statistics.

A c c e p t e d m a n u s c r i p t 1.99 with a standard deviation of 0.73. Table 1 presents the cross-tabulations of perceived external employability.

-INSERT TABLE 1 ABOUT HERE -

Independent variables: HRM practices

Several scholars have highlighted the need to simultaneously implement HR practices in order to strengthen their synergistic effects [START_REF] Ostroff | Moving HR to a higher level: HR practices and organizational effectiveness[END_REF], using a "bundle" [START_REF] Huselid | The impact of human resource management practices on turnover, productivity, and corporate financial performance[END_REF]. Bundles of HRM practices generate beneficial interplays of the elements of a system, such that an increase in the use of one practice enlarges the returns earned from increasing another. In line with the literature (e.g. Böckerman et al., 2012;[START_REF] Martin | Do innovative work practices and ICT use motivate employees?[END_REF]White and Bryson, 2013), we take into account 4 practices that enhance employees' motivation: voice, communication, training and teamwork. The bundle MotivationHR is an additive index capturing the intensity to which employers are committed to motivate employees in the workplace, taking the value 0 when none of the practices are implemented and 4 when all practices are available.

Following [START_REF] Bal | From flexibility human resource management to employee engagement and perceived job performance across the lifespan: A multisample study[END_REF], [START_REF] Heywood | Schedule flexibility, family friendly policies and absence[END_REF] and Stirpe et al. (2017), we construct an index referring to personnel policies that favour flexibility including 3 practices: teleworking, flexible work time and work-life balance. This index, FlexibilityHR, is additive, being equal to 0 if any practice is available and 3 if all are present.

Control variables

In line with research on turnover intention [START_REF] Cottini | Adverse workplace conditions, highinvolvement work practices and labor turnover: Evidence from Danish linked employeremployee data[END_REF]Böckerman and Ilmakunnas, 2009), control variables are also introduced: harmful working conditions, individual A c c e p t e d m a n u s c r i p t characteristics (gender, age, education, etc), job characteristics (permanent contract, tenure, occupations, etc.). 5 Appendix 1 gives the definitions of the variables and descriptive statistics. 6 All the variables derive from the same source, implying that our research holds the risk of being contaminated by common method variance. However, as the items for the construction of the variables are derived from different modules of the survey, the risks may be tempered.

Because of the nature of our dependent variable (turnover intention), we carried out a Probit estimation. The estimated marginal effects are presented in Tables 2 and3. As the Chow test is significant (p-value = 0.0015), we accordingly divide the sample into separate age groups in order to capture the age differences in turnover intention in relation to perceived external employability and HR practices.

Results

Table 2 presents results for the entire sample without distinguishing age groups.

-INSERT TABLE 2 ABOUT HERE -

The estimated marginal effect 7 of the interaction term between motivation-enhancing HR practices and employability is negative and significant (Model 3). The interaction term between flexibility-enhancing HR practices and employability is also significant and negative (Model 4). However, the results in Model 5where all the interaction terms are included - 5 The estimates may suffer from the omitted-variable bias such as personality traits that are likely to be linked to voluntary turnover. Unfortunately, we do not have this information in our dataset. 6 We do not report details on control variables nor discuss related research findings because of space limitations. 7 As the interaction terms in a Probit model are tricky to interpret, we interpret only the significances, not the magnitudes. These results are similar to the ones obtained with OLS models. For the sake of the paper's length, we do not report them in the paper indicate that HR practices aimed at motivation no longer mitigate the adverse effect of employability on turnover, as the interaction term is no longer significant.

Next, we address the main issue of this paper, which is to assess the age-related differences in the relationship between HR practices, perceived employability and turnover.

Table 3 reports results for the three age groups: the younger group (under 30), the middle-age group (between 30 and 49) and the older group (50 and above). Model 6 in Table 3 shows the results with only HR practices and employability, after controlling for other explanatory variables and controls. 8 Models 7 to 9 progressively include the two-way interaction terms between HR practices and employability.

In Hypothesis 1, we predicted that motivation-enhancing HR practices are more valuable for younger employees, in that these practices may induce retention effects that are greater for younger employees than for older ones. The results in Table 3 (Models 6 to 9) show that motivation-enhancing HR practices have a significant negative effect on the turnover intention of the younger and the middle-age groups. These practices are not associated with the turnover intentions of older employees. These findings provide clear evidence that there are age-related differences in the turnover effects of motivation-based HR practices. Hypothesis 1 is thus corroborated.

-INSERT TABLE 3 ABOUT HERE -

For Hypothesis 2, results in Table 3 show a significant negative effect of flexibilityenhancing HR practices on turnover intention for all age groups. This finding is somewhat surprising, as previous empirical and theoretical arguments lead us to expect a strong negative 8 Due to lack of space, we do not report results of other explanatory and control variables here. The results are available on request from the corresponding author.

A c c e p t e d m a n u s c r i p t effect for older employees. However, looking at Model 9, after including the interaction terms between HR practices and employability, flexibility-enhancing HR practices are no longer significantly related to the turnover intention of younger employees. That is, HR practices aimed at aiding flexibility have a stronger retention effect for middle-aged and older employees than for younger ones. Consistent with H2, there are age-related differences in the link between these HR practices and turnover intention.

Hypothesis 3 relates to whether motivation-enhancing HR practices mitigate the adverse turnover effects of high-perceived employability more for the younger group than for the older one. The estimated marginal effect of the two-way interaction term is negative and significant among the younger and middle-age groups, while no evidence is found for the older group, indicating that younger and middle age employees benefiting from HR practices such as participation, voice, teamwork or training are more likely than older employees to search for another job. H3 is hence corroborated as motivation-enhancing HR practices mitigate the adverse effect of perceived external employability differently, depending on employee's age.

For Hypothesis 4 (existence of age-related differences between flexibility-enhancing HR practices, employability and turnover intention), we examined whether practices aimed at increasing flexibility can mitigate the negative effect of employability on turnover intention, and to what extent this differs depending on age. Models 7 and 9 show negative and significant interaction terms between flexibility-enhancing HR practices and perceived external employability among middle-age and older employees, while no evidence is found for the younger group. The theoretical arguments developed above support the idea that HR practices such as teleworking, flexible working time or work-life balance are effective with regard to discouraging highly employable workers of older age versus younger ones to voluntary leave an organization. These HR practices are efficient in terms of retaining not only older employees but also middle-age ones. H4 is thus corroborated.

A c c e p t e d m a n u s c r i p t

Discussion and conclusion

The negative age-turnover relationship is well documented in the literature. However, to develop suitably differentiated practices to retain employees of different age groups, we need more accurate results in order understand people's mobility patterns across the lifespan [START_REF] Bal | From flexibility human resource management to employee engagement and perceived job performance across the lifespan: A multisample study[END_REF]. We contribute to existing literature on voluntary turnover by studying the link between turnover intention and perceived employability and the moderating role of HR practices in this employability-turnover link, while taking into account age-related changes in individuals' motives and needs. Our sample was enough large to be divided into sub-samples of age groups, allowing us to investigate turnover patterns related to different age groups.

HR practices differentially affect the turnover intention of younger and older employees. Specifically, motivation-enhancing HR practices induce a larger retention effect for younger and middle-aged employees than for older ones. By contrast, the turnover intention effects of flexibility-enhancing HR practices are stronger for the middle-age and older groups than for the younger groups. In addition, HR practices mitigate the adverse effects of perceived employability on turnover intention differently, depending on age. HR practices that stimulate employees' motivation, such as training, participation, voice and teamwork, play a stronger role in retaining highly employable younger employees, while HR practices that offer flexibility, such as flexible working time, teleworking and work-life balance, play a stronger role in retaining highly employable older employees. These findings are in line with theoretical arguments suggesting that specific HR practices tend to have a more notable retention effect for employee groups that benefit more from them (Stirpe and Zárraga-Oberty, 2017;[START_REF] Heywood | Schedule flexibility, family friendly policies and absence[END_REF]. For example, as motivation-enhancing HR practices provide opportunities for involvement and career progression, these practices are more valuable for younger employees and influence their turnover intention more than for their older colleagues. By contrast, as older A c c e p t e d m a n u s c r i p t employees in their middle and later career periods tend to strive more for stability and social relationships, relative to younger adults, HR practices aimed at offering them better fulfilment of social status and work-life balance discourage them from voluntarily leaving. This article suggests that policies for retaining highly employable staff with better skills and core competences are crucial from an organization's point of view. Hence, in light of the assumption that highly employable people are also high achievers [START_REF] De Cuyper | The management paradox: Employability and organizational commitment and performance[END_REF]Van der Heijde and Van der Heijden, 2006), the most productive employees would be the first to voluntary leave if appropriate HR practices are lacking. Our results strongly highlight the complexity of managing HR as a means to retain employees according to their age. Some HR practices appear to be effective for employees of the middle and older age groups, while other practices appear to be more efficient in terms of reducing voluntary quitting by highly employable younger workers. Managers should therefore pay careful attention to the varying effects of HR practices on retaining employees.

Practical policy conclusions can be drawn from this study which provides evidence that HR practices may have differentiated effects according to the age of the employee. We show that the use of motivation-enhancing HR practices induces a larger retention effect for younger and middle-aged employees than for older ones, whereas the turnover intention effects of flexibility-enhancing HR practices are stronger for the middle-age and older groups. Besides, the use of HR practices that stimulate employees' motivation, such as training, participation, voice and teamwork, plays a stronger role in retaining highly employable younger employees, while the use of HR practices that offer flexibility, such as flexible working time, teleworking and work-life balance, enables retaining highly employable older employees. Such results have important public policy consequences in countries where the state tries to regulate the ageing workforce by providing specific incentives and financial support (in various ways: tax exemption, direct funds, etc.) according to which type of age group they want to help. In most A c c e p t e d m a n u s c r i p t cases, the help of the state will be oriented towards the very young to favor their labor insertion into the market place, or the older ones who could have difficulties finding another job if they leave the company before their age of retirement. Hence, all these public policy issues are tightly linked to the degree of involvement of the state (or local/regional collectivities) into firms' policies.

Yet our study suffers from a number of limitations. Potential measurement error may be important for the interpretation of the estimates. Using cross-sectional survey data, we are not able to account for measurement errors by using techniques such as instrumental variables, structural equation modeling or errors-in-variables modeling. Future research should take the effects of measurement error into account. A second one is linked to the fact that we do not distinguish specific to the job training vs general training. This part of the learning by working on the certain job is the specific human capital. The role of firm-specific vs general human capital does play a role on turnover intention and perceived employability if we extend [START_REF] Kriechel | The role of specific and general human capital after displacement[END_REF]'s results: workers of the more specific job activities are shown to remain longer unemployed and to get lower wages. Hence we believe that such workers have lower turnover intentions as they know that it will be very difficult for them to find another job, especially if they cannot reuse part of their specific human capital gained with their experience. Thus, training aimed at increasing general human capital may favor older workers' employability 9 . While most employers do not invest in older workers and older employees rarely receive on-the-job training (Armstrong-Stassen and Ursel, 2009), theory tells us that employees are reluctant to invest in firm specific skills because such investments may come at the cost of developing general skills, thereby reducing their attractiveness in the labor market 9 We thank an anonymous reviewer for pointing us the different types of training and their potential effect on turnover intentions.

A c c e p t e d m a n u s c r i p t (Coff and Raffiee, 2015). This is why these authors develop a theory that perceived firmspecific human capital may be more important than objective firm-specific human capital in influencing these outcomes pertaining to employee mobility and an investment dilemma. The type of training provided and the difference between objective and perceived firm specific human capital should be considered in future studies. Another avenue for further research is the synergistic effects of individual HR practices on employees' work attitudes or, in a more systemic approach, bundles or systems. Further analyses should also replicate our study in different settings and especially in other countries to ensure the generalizability of our findings. Notes: In each cell, the first entry is the number of observations, the second is the percentage proportion of the row total and the third is the percentage proportion of the column total.

A c c e p t e d m a n u s c r i p t

Figure 1

 1 Figure 1 illustrates the moderating role of HR practices on the relationship between

  A c c e p t e d m a n u s c r i p t Data and methodology Data The data comes from a nationally representative employee survey for Luxembourg conducted in 2013 using the guidelines provided by the MEADOW Consortium (2010). The questionnaire of Working Conditions and Quality of Work Life survey was sent to a stratified random sample of employees ranging from 16 to 65 years of age, who had worked for at least twelve months in any workplace in the private sector with 15 or more employees. The dataset constitutes a large representative sample of 16,896 employees working in the Grand-Duchy of Luxembourg. It covers 68 per cent men and 32 per cent women and representing the active population of Luxembourg's private sector labour market. The employment protection legislation is above the one observed at the Organization for Economic Cooperation and Development (OECD)average and the unemployment rate is around 6 percent. The annual average wage is the highest in Europe. The labor market is characterized by a highly international, multicultural and multilingual working environment. More than half of the active population is cross-border employees from neighboring countries such as Belgium, France, and Germany. As in most of Western European countries, the private sector is characterized by the predominance of services. Hence, the paper gives results on employees' working conditions in a continental Europe service economy and includes not only Luxembourgish employees but also French, Belgian, German, and some other nationalities.The sampling design was based on the principle of random selection. The weights used in all of the following analyses ensure that the distributions, by country of residence, nationality, gender, age, white-and blue-collar workers, economic activity, and size class of the organization in which the employee works, are representative of people at work in the private

  Bal, P.M., & Dorenbosch, L. (2015). Age-related differences in the relations between individualised HRM and organisational performance: a large-scale employer survey, Human Resource Management Journal, 25(1), 41-61.Berntson, E.,Näswall, K., & Sverke, M. (2010). The moderating role of employability in the association between job insecurity and exit, voice, loyalty and neglect. Economic and Industrial Democracy, 32, 215-230. Böckerman, P., & Ilmakunnas, P. (2009). Job disamenities, job satisfaction, quit intentions, and actual separations: Putting the pieces together. Industrial Relations, 48(1), 73-96. Böckerman, P., Bryson, A., & Ilmakunnas, P. (2012). Does high involvement management improve worker wellbeing? Journal of Economic Behavior & Organization, 84(2), 660-680. Böckerman, P., & Ilmakunnas, P. (2020). Do good working conditions make you work longer? Analyzing retirement decisions using linked survey and register data. The Journal of the Economics of Ageing, 17, 1-11. Bruine de Bruin, W., Strough, J., & Parker, A.M. (2014). Getting older isn't all that bad: Better decisions and coping when facing "sunk costs". Psychology and Aging, 29(3), 642-647. Carstensen, L.L., & Mikels, J.A. (2005). At the intersection of emotion and cognition: Aging and the positivity effect. Current Directions in Psychological Science, 14(3), 117-121. Chapman, B.P., & Hayslip, B. (2006). Emotional intelligence in young and middle adulthood: Cross-sectional analysis of latent structure and means. Psychology and Aging, 21, 411-418. Coff, R., & Raffiee, J. (2015). Toward a theory of perceived firm-specific human capital. The Academy of Management Perspectives, 29(3), 326-341.

Table 1 . Employability and turnover intention

 1

	Employability

Table 2 : Marginal effects of HR practices as moderator in the link between employability and turnover intention Turnover intention

 2

		Model 1	Model 2	Model 3	Model 4	Model 5
	Employability	0.034***	0.034***	0.035***	0.032***	0.040***
		(0.006)	(0.006)	(0.006)	(0.005)	(0.007)
	MotivationHR		-0.022***	-0.025***	-0.023***	-0.023***
			(0.005)	(0.005)	(0.005)	(0.005)
	FlexibilityHR		-0.024***	-0.019***	-0.020***	-0.020***
			(0.006)	(0.006)	(0.006)	(0.006)
	MotivationHR*Employability			-0.036*		-0.028
				(0.019)		(0.020)
	FlexibilityHR*Employability				-0.041*	-0.035**
					(0.017)	(0.018)
	Observations	16,896	16,896	16,896	16,896	16,896
	Wald chi-square	2282.74	2345.05	2145.04	2078.85	2198.25
	Pseudo R 2	0.185	0.184	0.198	0.210	0.204
	Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

Table 3 : Marginal effects of HR practices as moderatoring the link between employability and turnover intention according to age

 3

	Turnover intention

Note: Standard deviations are reported in parentheses for non-binary variables.

Acknowledgements

This research is part of the WorkAgeing project supported by the Fonds National de la Recherche, Luxembourg (contract FNR/C16/SC/11344520) and by core funding from LISER from the Ministry of Higher Education and Research of Luxembourg. The authors are grateful to two anonymous reviewers for their valuable comments on previous versions of the paper.

 Stirpe, L., & Zárraga-Oberty, C. (2017). Are high-performance work systems always a valuable retention tool? The roles of workforce feminization and flexible work arrangements.

European Management Journal, 35(1), 128-136. Sumbal, M.S., Tsui, E., See-to, E., & Barendrecht, A. (2017). Knowledge retention and aging workforce in the oil and gas industry: a multi perspective study.


Michal Pásek

Fabien Brette

Adam Nelson

C Pearce

A Qaiser

Georges Christé

Clive H Orchard
email: clive.orchard@bristol.ac.uk

M Pasek

# A Nelson

G Christe

Quantification of t-tubule area and protein distribution in rat cardiac ventricular myocytes

Keywords: cardiac myocyte, t-tubule, electrophysiology, excitation-contraction coupling, capacitance, cholesterol

Introduction

During the cardiac action potential, Ca influx via L-type Ca channels activates ryanodine receptors in adjacent sarcoplasmic reticulum (SR) membrane, causing Ca release from the SR [START_REF] Bers | Cardiac excitation-contraction coupling[END_REF].

In ventricular myocytes Ca influx, and hence Ca release, occurs predominantly at invaginations of the surface membrane called transverse (t-) tubules (Brette & Orchard, 2003). This causes spatial and temporal synchronization of Ca release, and hence synchronized contraction of the cell [START_REF] Wier | Ca 2+ release mechanisms, Ca 2+ sparks, and local control of excitation-contraction coupling in normal heart muscle[END_REF].

Recent work using ventricular myocytes has shown that uncoupling the t-tubules physically and functionally from the surface membrane (detubulation) results in loss of ~32% of cell capacitance (a function of membrane area), but ~87% of L-type Ca current (I Ca ), suggesting a high density of I Ca in the t-tubules [START_REF] Kawai | Excitation-contraction coupling in rat ventricular myocytes after formamide-induced detubulation[END_REF]. However optical measurements suggest that the surface area of the t-tubules is 0.44 μm 2 per μm 3 cell volume [START_REF] Soeller | Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques[END_REF]; normalized to the estimated total surface area/cell volume of a myocyte 100 μm long and 20 μm in diameter (0.68 μm 2 /μm 3 ) this gives a t-tubular membrane fraction of 65% [START_REF] Soeller | Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques[END_REF]. This agrees with the lower capacitance (pF)/ cell volume (pl) ratio determined by [START_REF] Satoh | Surface:volume relationship in cardiac myocytes studied with confocal microscopy and membrane capacitance measurements: speciesdependence and developmental effects[END_REF]6.76 pF/pl in 3 month old rats, compared to 8.88 pF/pl in 6 month old rats): assuming a membrane capacitance of 1 µF/cm 2 these values give surface area/volume ratios of 0.676 and 0.888 µm 2 /µm 3 , and hence t-tubular fractions of 65% and 50%, respectively. Thus optical measurements suggest that the t-tubule fraction is higher than that obtained by detubulation. The reasons for this discrepancy are unclear.

If the fractional area of the t-tubule membrane is greater than estimated by detubulation, the density of membrane currents in the t-tubules would be lower than previously calculated, although the absolute amounts and relative concentrations would remain the same. This would have important implications for cell function and for the mechanisms trafficking and localizing proteins at the t-tubules.

The present study used a combination of modeling and experimental approaches to investigate the fraction of the cell membrane within the t-tubules, and its effect on the calculated distributions of ion flux pathways.

Methods

Computational methods

The computer model of the rat ventricular myocyte used in the present study has been described previously (Pasek et al., 2006). The model was implemented in MATLAB 6.5 (MathWorks, Inc.) and was based on Pandit's quantitative description [START_REF] Pandit | A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes[END_REF], modified to include a ttubule compartment. The numerical computation of the system of 59 non-linear differential equations was performed using the solver for stiff systems ODE-15s. The model equations were simultaneously solved using a time step adjusted to keep the estimated relative error of inner variables below a threshold value of 0.001. After every change in model equations or parameter values, the model was run for 20 minutes of equivalent cell lifetime to ensure that steady-state was reached. The values of all variables at this time were assigned as starting values before running model trials. The units in which the equations were solved were: mV for membrane voltage, μA for membrane currents, mM for ion concentrations, ml for volumes and s for time.

Cell isolation and t-tubule imaging

Myocytes were isolated from the ventricles of Wistar rat hearts by enzymatic dissociation, and detubulated using formamide, as described previously [START_REF] Brette | Validation of formamide as a detubulation agent in isolated rat cardiac cells[END_REF]. To image the t-tubules the cells were stained with di-8-ANEPPS, and 1 µm optical sections were imaged at 8 bit resolution using a Zeiss Pascal confocal microscope; confocal images of control and detubulated myocytes stained with di-8-ANEPPS have been published previously [START_REF] Brette | Validation of formamide as a detubulation agent in isolated rat cardiac cells[END_REF]. Offset and gain were adjusted to use the entire dynamic range of the microscope. The area within the cell membrane was outlined manually using Zeiss image analysis software, and the contrast and brightness were increased to produce a binary image in which pixels with an intensity greater than the median were set to the maximum value (255) and those below the median value were set to 0.

The total outlined area, and the area occupied by pixels with an intensity of 255 were measured, and used to calculate the percentage of the cell interior occupied by membranes accessible to staining from the extracellular space, which was taken to represent t-tubule membrane. This technique of "thresholding" and pixel counting is similar to that described previously [START_REF] Heinzel | Spatial and temporal inhomogeneities during Ca 2+ release from the sarcoplasmic reticulum in pig ventricular myocytes[END_REF].

Electron Microscopy

Myocytes were fixed in 5% glyceraldehyde and 0.2 mol/l sodium cacodylate buffer (pH 7.2). After centrifugation and washing the cells were embedded in fresh resin and left for 48 hours. Sections for cutting were chosen after staining with methylene blue and visualisation using light microscopy. Thin longitudinal sections were cut on a Diatome diamond knife and collected on copper slotted grids coated in Pioloform film. The grids were stained with uranylacetate (10 minutes) and lead citrate (10 minutes) and viewed in a Philips CM100 transmission electron microscope (TEM). Myocytes were photographed using Kodak 4489 film at a resolution of 4622 pixels x 3831 pixels, and at x6600 magnification so that each μm was equal to 16.5 mm on the printed image. Analysis of these images was performed without knowing whether control or detubulated myocytes were being analysed.

Measurement of specific capacitance of DOPC membranes

Monolayers of dioleoyl phosphatidylcholine (DOPC) and DOPC + cholesterol were prepared as described previously [START_REF] Bizzotto | Continuing electrochemical studies of phospholipid monolayers of dioleoyl phosphatidylcholine at the mercury-electrolyte interface[END_REF][START_REF] Cohen-Atiya | Characterization of n-alkanethiol self-assembled monolayers on mercury by impedance spectroscopy and potentiometric measurements[END_REF][START_REF] Nelson | Phospholipid monolayers of di-oleoyl lecithin at the mercury/water interface[END_REF][START_REF] Whitehouse | Application of electrochemical impedance spectroscopy to the study of dioleoyl phosphatidylcholine monolayers on mercury[END_REF] by spreading 13 μl of a DOPC + cholesterol mixture in pentane (HPLC grade, Fisher Scientific Chemicals Ltd) at the argon-electrolyte interface in an electrochemical cell. A 2.55 mmol/l working solution of DOPC was obtained by dilution of a 63.7 mmol/l stock solution (Avanti Lipids). The cholesterol was prepared as a stock solution of 10.3 mmol/l. Aliquots were taken from the cholesterol stock solution and added to the DOPC working solution to give a specified mole fraction of cholesterol in DOPC. A fresh mercury drop (area = 0.0088 cm 2 ) was coated with the DOPC and cholesterol mixed layer at the argon-electrolyte interface before each series of experiments. Although the DOPC and cholesterol were about four times excess of surface coverage at the argon-water interface, the coverage of the monolayer on the mercury surface subsequent to transfer was always neither less than, nor in excess of, full coverage. This is because the lipid coverage on the electrode is always controlled by the configuration of the carefully prepared electrode capillary and not by the coverage at the argonelectrolyte interface [START_REF] Cohen-Atiya | Characterization of n-alkanethiol self-assembled monolayers on mercury by impedance spectroscopy and potentiometric measurements[END_REF].

The specific capacitance of DOPC monolayers and DOPC monolayers + cholesterol was measured as zero frequency capacitance using electrochemical techniques of impedance: measurements of impedance (Z) versus frequency (f) of the electrode systems using frequencies logarithmically distributed from 65000 to 0.1 Hz, ac amplitude (ΔE) 0.005 V at potential -0.4 V were carried out on the coated electrode systems. The impedance data were transformed to the complex capacitance plane and the complex capacitance axes were expressed as Re Y ω -1 and Im Y ω -1 respectively, using the EXCEL (Microsoft) spreadsheet. For a series RC circuit, the Re Y ω -1 versus Im Yω -1 plot gives a single semi-circle for the RC element, where the capacitor has no frequency dispersion. A monolayer of DOPC behaves as a simple capacitor in a RC circuit appearing as a single semi-circle in the complex capacitance plot. The incorporation of cholesterol into the DOPC monolayer at mole fractions of 0.3 and above gives rise to the occurrence of low frequency relaxations in the complex capacitance plot. The extrapolation of the RC semi-circle to the Im Y ω -1 axis at low frequency gives the zero frequency capacitance (C) of the RC circuit which is the specific capacitance of the monolayer. These methods applied to the specific capacitance of DOPC monolayers are described in detail [START_REF] Whitehouse | Application of electrochemical impedance spectroscopy to the study of dioleoyl phosphatidylcholine monolayers on mercury[END_REF].

Statistics

Data are presented as mean ± sem of n observations. Data were compared using paired or unpaired t-tests as appropriate, and significance taken as P<0.05.

Results

Which estimate of t-tubule membrane area is correct?

Membrane capacitance is a function of membrane area, and decreases by ~32% after detubulation [START_REF] Brette | Validation of formamide as a detubulation agent in isolated rat cardiac cells[END_REF]Brette et al., 2004a;Brette et al., 2004b;Brette & Orchard, 2006b;Brette & Orchard, 2006a;Brette et al., 2006b;[START_REF] Despa | Na/Ca exchange and Na/K-ATPase function are equally concentrated in transverse tubules of rat ventricular myocytes[END_REF][START_REF] Kawai | Excitation-contraction coupling in rat ventricular myocytes after formamide-induced detubulation[END_REF][START_REF] Komukai | K + current distribution in rat subepicardial ventricular myocytes[END_REF][START_REF] Yang | Na + -Ca 2+ exchange activity is localized in the t-tubules of rat ventricular myocytes[END_REF]. This is similar to the fraction of cell membrane estimated to be in the ttubules using electron microscopy [START_REF] Page | Quantitative ultrastructural analysis in cardiac membrane physiology[END_REF]. However structural and sampling distortions can occur during preparation of tissue for electron microscopy, and measurements obtained by filling the t-tubules of a living cell with fluorescent dye [START_REF] Soeller | Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques[END_REF] combined with measurements of surface/volume ratio [START_REF] Satoh | Surface:volume relationship in cardiac myocytes studied with confocal microscopy and membrane capacitance measurements: speciesdependence and developmental effects[END_REF] suggest that >50% of the cell membrane is within the t-tubules [START_REF] Bers | Excitation-contraction coupling and cardiac contractile force 2nd ed[END_REF]. We have used a simple model to explore this discrepancy: we determined the combinations of t-tubule radius, length and density that produce either 32% (the value obtained by detubulation) or 56% (a value computed from optical measurements and the average surface/volume ratio of 0.782 μm 2 /μm 3 from [START_REF] Satoh | Surface:volume relationship in cardiac myocytes studied with confocal microscopy and membrane capacitance measurements: speciesdependence and developmental effects[END_REF]above). We thus determined whether using 32% or 56% gave combinations of these variables that were close to those observed experimentally. To do this, we used the derived relationship: F t /(1-F t ) = 2πr t l t dens t where F t is the fraction of cell membrane within the t-tubules, r t is t-tubule radius, l t is t-tubule length and dens t is t-tubule density, expressed as the number of t-tubule openings per unit area of surface membrane. The planes in figure 1 show solutions to this equation over the range of ttubule radii and densities reported experimentally. These data show that the plane produced using a fractional area of 56 % contains tubular lengths in the range reported for the average length of tubular inter-branch segments (average 6.9 µm; [START_REF] Soeller | Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques[END_REF], whereas a fractional area of 32% produces lengths <4 µm, which is less than half the diameter of a cardiac myocyte and shorter than observed experimentally. These data suggest that a fractional value of 56% may be closer to the actual value than 32%. This raises the question of why the estimated fraction of cell membrane within the t-tubules is different using the two techniques. One possibility is that the optical dye-filling technique overestimates the fraction of membrane in the t-tubules, although the data presented above makes this less likely. Alternatively detubulation may under-estimate the fraction of cell membrane within the t-tubules, either because some t-tubules remain coupled to the surface membrane or because the specific capacitance of the t-tubule membrane is lower than that of the surface membrane, so that a greater fraction of membrane is lost than capacitance. These possibilities are considered further below.

Could incomplete detubulation contribute to the discrepancy?

To address the first of these possibilities, the extent of detubulation was estimated from confocal images of intact and detubulated rat ventricular myocytes stained with the lipophilic dye di-8-ANEPPS and imaged as described in Methods. These cells were from cell isolations used for previously published work, in which detubulation was used to determine the distribution of ion flux pathways between the t-tubule and surface membranes. t-tubule staining was determined by "thresholding" as described in Methods. In 12 control cells, 15.28 ± 2.22% of the cell interior showed such staining; in 8 detubulated cells, the value was 1.17 ± 0.29%, suggesting that following detubulation 7.7% of the t-tubule network remained accessible to the extracellular space. This will contribute to, but is insufficient to account for, the discrepancy between the optical and electrophysiological measurements of t-tubule membrane fraction.

To investigate whether ultrastructural distortion of the t-tubules following detubulation might alter the apparent membrane area, electron microscopy was used to image intact and formamide-treated (detubulated) myocytes. Representative images are shown in figure 2 (left).

Attempts to use prior labelling with lanthanum, as described previously for skeletal muscle (e.g. [START_REF] Voigt | About the T-system in the myofibril-free sarcoplasm of the frog muscle fibre[END_REF], to identify and image the t-tubules, were unsuccessful, and would in any case not penetrate t-tubules that are inaccessible from the extracellular space. Thus spaces in the image were taken to be part of the t-tubular network, an assumption supported by their dimensions and proximity to the Z line (fig. 2, right), which are similar to those reported previously [START_REF] Soeller | Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques[END_REF]), although it is not possible to determine whether they are open to the extracellular space. The EM images in figure 2 show that the gross structure of the cell appears to be well maintained following detubulation, although there are fewer apparent t-tubules in the formamidetreated cell; table 1 shows that the main change following formamide treatment is a decrease in the number of t-tubules per unit area, although the area of each t-tubule appears to be unchanged.

These changes are compatible with previous data showing that following detubulation, the ttubules appear to collapse into the cell to form longitudinal vacuoles rather than maintaining their transverse location at the Z-lines [START_REF] Brette | Validation of formamide as a detubulation agent in isolated rat cardiac cells[END_REF]. These data suggest that neither incomplete detubulation, nor distortion of the remaining t-tubules can account for the discrepancy.

Could low specific capacitance of the t-tubule membrane contribute to the discrepancy?

It has previously been reported that in striated muscle the t-tubule membrane is rich in cholesterol, compared with the surface membrane [START_REF] Rosemblatt | Immunological and biochemical properties of transverse tubule membranes isolated from rabbit skeletal muscle[END_REF][START_REF] Sumnicht | Lipid composition of transverse tubular membranes from normal and dystrophic skeletal muscle[END_REF]. To investigate whether this could reduce the capacitance of the t-tubule membrane sufficiently to account for the discrepancy, we determined the effect of increasing the cholesterol content of a DOPC monolayer, as described in Methods. In the absence of cholesterol, this membrane has a specific capacitance of 1.8 μF/cm 2 , twice that (0.9 μF/cm 2 ) of a bilayer, which in turn is similar to that of the normal cell membrane (1 μF/cm 2 ). Figure 3 shows that increasing the mole fraction of cholesterol in the DOPC monolayer results in a decrease in its specific capacitance, to ~1 μF/cm 2 (0.56 of control); at 0.3-0.4 mole fraction cholesterol. Increasing cholesterol content above 0.4 mole fraction caused no further decrease in specific capacitance; indeed a small increase occurred, concurrent with phase separation [START_REF] Whitehouse | Application of electrochemical impedance spectroscopy to the study of dioleoyl phosphatidylcholine monolayers on mercury[END_REF]. Thus it appears that high cholesterol in the t-tubule membrane could decrease its specific capacitance, resulting in a smaller fractional loss of capacitance than of tubular membrane following detubulation.

Can incomplete detubulation plus low specific capacitance account for the discrepancy?

The data presented above suggest that a combination of incomplete detubulation (7.7% of t-tubules remaining) and reduced specific capacitance of the tubular membrane (due, for example, to high cholesterol) might account for the discrepancy between electrophysiological and optical estimates of the percentage of membrane in the t-tubules. To explore this suggestion quantitatively, we used a previously described biophysically realistic computer model of the rat cardiac myocyte (Pasek et al., 2006) that incorporates a t-tubular compartment constituting 56% of the cell membrane. Using this model we determined the loss of membrane capacitance that would be observed upon detubulation if 7.7% of the t-tubules remained functionally coupled to the surface membrane, and the specific capacitance of the t-tubule membrane was 0.56 that of the surface membrane (i.e. the maximal fractional decrease observed on increasing cholesterol content, and assuming the cholesterol content of the surface membrane to be 0%). Figure 4 (top) shows the percentage loss of capacitance that would occur with different percentage losses of tubular membrane in the model; each black line represents a different t-tubule membrane specific capacitance: reducing ttubule specific capacitance to 0.56 that of the surface membrane and leaving 7.7% of the t-tubule network intact (i.e. ~92% loss of tubular membrane) results in a greater loss of membrane capacitance (~38%) than that observed experimentally (32%). However if the percentage of the cell membrane in the t-tubules is reduced to 49 %, then 32% of membrane capacitance is lost following detubulation (red line). This assumes the maximum measured decrease in specific capacitance of the t-tubule membrane; if the specific capacitance is higher, then the percentage of the cell membrane in the t-tubules would have to be lower to reconcile the capacitance and optical measurements; the lower panel of figure 4 shows the combinations of specific capacitance and percentage of membrane in the t-tubule that satisfy 32% loss of capacitance. This suggests therefore that 49% may be an upper limit, and thus that optical measurements overestimate the percentage of the cell membrane in the t-tubules while the capacitance measurements underestimate it, although it remains possible that other factors contribute to the discrepancy: for example if factors other than cholesterol reduce the specific capacitance of the t-tubule membrane.

However it appears likely that the actual value lies between 49% and 35%, the value obtained from capacitance measurements corrected for incomplete detubulation only; i.e. assuming that the specific capacitance of the t-tubule membrane is the same as that of the surface membrane.

Effect of altered estimates of t-tubular membrane on calculated distribution of ion flux pathways

Incomplete detubulation, or loss of a greater area of membrane than suggested by capacitance measurements, will alter the calculated distribution of ion flux pathways between the t-tubule and surface membranes: incomplete detubulation will result in an underestimate of the fraction of ion flux pathways within the t-tubules, while loss of a greater fraction of membrane than suggested by capacitance measurements will result in a decrease in the calculated density of ion flux pathways in the t-tubules.

We therefore used values that reconcile the optical and electrophysiological measurements of t-tubule area (t-tubule specific capacitance 0.56 µF/cm 2 , 49% of the cell membrane within the ttubules, 7.7% remaining after detubulation, assuming that this is also the fraction electrically coupled to the surface membrane) in the rat ventricular myocyte model described above, to determine the percentage of key membrane currents that would need to be present in the t-tubules to give previously published values determined using detubulation.

Table 2 shows the results of these calculations. The left column shows previously published percentage losses of current following detubulation (and therefore by implication in the t-tubules) corrected, where necessary, for the presence of the 13% of myocytes that show no detubulation [START_REF] Kawai | Excitation-contraction coupling in rat ventricular myocytes after formamide-induced detubulation[END_REF]; it is worth noting that only 13% of I Ca remains after detubulation, putting an upper limit of 13% on the fraction of the t-tubule network remaining, assuming homogeneous current distribution within the t-tubules). The second column shows these values corrected for the presence of 7.7% of the t-tubule network after detubulation. The third column shows the fraction of each ion flux pathway that has to be located within the t-tubules in the model to give the fraction of current determined experimentally by detubulation; these calculations assume that the current measured experimentally is uncontaminated by other currents flowing under the experimental conditions used. These values differ from those in column two because of factors such as ion concentration changes in the restricted diffusion space of the ttubules. The fourth column shows a similar calculation for the fraction of ion flux pathways, but after correction for possible contamination by other currents flowing under the experimental conditions used. Table 3 shows the parameters underlying the densities of ion flux pathways at the t-tubule and surface membranes in the model, calculated from the data in table 2 with the t-tubular fraction of the cell membrane set to 49%. This shows the effect of correcting for current fraction on current density, in particular that computation of current densities from loss of currents following detubulation results in underestimation of densities at the t-tubule membrane and overestimation at the surface membrane. An initial description of the effects of these corrections on the behaviour of the rat ventricular myocyte model is given in the companion paper by Pasek et al. (2007).

Discussion

Consequences of incomplete detubulation and reduced specific capacitance of tubular membrane

Incomplete detubulation will result in a small underestimate of the fraction of the cell membrane, and of the absolute amount of each membrane current, within the t-tubules (table 2). However it will have a negligible effect on the calculated density of the current within the ttubules or on the relative amount of each current, assuming that the currents are homogeneously distributed throughout the t-tubule so that the remaining t-tubule membrane has a similar current composition to that lost during detubulation.

If the specific capacitance of the t-tubule membrane is lower than that of the surface membrane, then a given percentage loss of capacitance represents a greater percentage loss of cell membrane. Thus estimating the t-tubular fraction of the cell membrane from loss of capacitance following detubulation will result in an underestimate. This will have no effect on the absolute or relative current loss following detubulation. However correction for this effect will reduce calculated current density. If the fraction of current calculated to be in the t-tubules (table 2) is similar to the corrected fraction of t-tubule membrane (49%), then the t-tubules may not represent a specialized site in terms of density of these proteins. Nevertheless some currents, including I Ca and I Na/Ca , are clearly localized at the t-tubules to an extent that is difficult to explain in terms other than t-tubular concentration of protein function: >90% of I Ca for example appears to be in the ttubules; this fraction is far higher than the upper estimates of the fraction of cell membrane within the t-tubules. It has been reported that some currents are modulated differently at the t-tubule and surface membranes. I Ca for example, appears to be more tightly regulated by PKA and Ca at the ttubules than at the surface membrane (Brette et al., 2004a). Thus the concentration of protein function at the t-tubules may be due to concentration of the protein, as suggested by immunohistochemical studies, and/or local upregulation of protein function.

These data suggest that the t-tubules show specialisation in either the density and/or regulation of some membrane currents. This has important implications for the trafficking and targeting of membrane proteins; a higher density and better regulation of proteins such as the Ltype Ca channel suggest that this protein is trafficked and/or targeted specifically to the t-tubule membrane where it is able to co-localise with regulatory proteins and RyR. Although the mechanisms underlying the trafficking of the cardiac Ca channel to the cell membrane are starting to be elucidated, the mechanisms by which it is targeted to the t-tubule and co-localised with RyR at an apparently stable stoichiometry (Brette et al., 2006b) are unknown. However it has recently been shown that the α 2 δ subunit of Ca V 2.1 is completely concentrated in cholesterol rich microdomains in the cerebellum, where it co-localises with the α 1 , pore forming, subunit [START_REF] Davies | The calcium channel alpha 2 delta-2 subunit partitions with Ca V 2.1 into lipid rafts in cerebellum: implications for localization and function[END_REF]. A similar mechanism might account for concentration of Cav1.2 in cholesterol rich ttubule membrane: if, as suggested below, cholesterol is found predominantly in the transverse elements of the t-tubule system, this would be consistent with immunohistochemical data showing localization of the Ca channel to the transverse elements (Brette et al., 2006a).

Conversely, a similar density in the t-tubule and surface membranes suggests that the protein is trafficked/targeted to all parts of the cell membrane and not especially to the t-tubules.

However since membrane composition can alter protein function it is also possible that a high cholesterol concentration in the t-tubule membrane may itself alter the function of proteins located in the t-tubule membrane, although a recent study has shown that the cholesterol-depleting agent methyl-β-cyclodextrin has no significant effect on I Ca in rat ventricular myocytes [START_REF] Calaghan | Caveolae modulate excitation-contraction coupling and beta2adrenergic signalling in adult rat ventricular myocytes[END_REF].

Structural changes associated with detubulation

The extent of detubulation was estimated from confocal images of rat ventricular myocytes stained by extracellular application of the lipophilic dye di-8-ANEPPS, using "thresholding" as described previously to exclude background and noise from the analysis. This assumes that the whole ttubule network is stained using di-8-ANEPPS; it is striking, however, that cells stained in this way show marked transverse striations, but little of the longitudinal elements that have been demonstrated using other techniques; the present data suggest, for example, that ~15% of the cell interior shows t-tubular staining using di-8-ANEPPS, whereas the data of [START_REF] Soeller | Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques[END_REF] suggest that the figure should be closer to 30%, if all elements of the t-tubular network shown using their optical method were present. Since di-8-ANEPPS is lipophilic, one possibility is that the lipid (e.g. cholesterol) content of the t-tubule network is higher in the transverse elements.

Even in this case it seems likely that the percentage loss of stained elements of the t-tubules system reflects the percentage loss of the whole network. However if cholesterol decreases specific capacitance but is inhomogenously distributed in the t-tubule network, this will further complicate estimation of the percentage of the cell membrane located within the t-tubules from capacitance measurements.

We also used TEM to investigate cell structure following detubulation; this showed that the cell structure was generally well maintained, although there were fewer t-tubules per unit area of cell. This is compatible with previous work suggesting that during detubulation the t-tubules are detached from, and therefore no longer "held up" by, the surface membrane. As a result they collapse down into their longitudinal elements to form longitudinal vacuoles within the cell [START_REF] Brette | Validation of formamide as a detubulation agent in isolated rat cardiac cells[END_REF]. These changes would also be expected to disrupt dyads within the center of the cell, as suggested previously to account for the lack of sparks in the center of detubulated myocytes [START_REF] Brette | Spatiotemporal characteristics of SR Ca 2+ uptake and release in detubulated rat ventricular myocytes[END_REF].

Effect of cholesterol on membrane capacitance

Previous work suggests that the skeletal t-tubule membrane is rich in cholesterol [START_REF] Rosemblatt | Immunological and biochemical properties of transverse tubule membranes isolated from rabbit skeletal muscle[END_REF][START_REF] Sumnicht | Lipid composition of transverse tubular membranes from normal and dystrophic skeletal muscle[END_REF]; however the composition of the cardiac t-tubule membrane is unknown, although caveolae, specialized areas of the cell membrane rich in cholesterol and sphingolipids, are found in the t-tubules. The contribution of caveolae is normally neglected in geometric estimations of surface area, although they account for 14-21% of the surface and t-tubule membranes [START_REF] Page | Quantitative ultrastructural analysis in cardiac membrane physiology[END_REF], whereas they are taken into account in capacitance measurements. These "little caves", by forming indentations in the t-tubule membrane, may increase its surface area; thus the >50% of the cell membrane within the t-tubules obtained from the optical data of [START_REF] Soeller | Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques[END_REF] by approximating the t-tubules to cylinders may be an underestimate. In the present study we modeled the t-tubules using a specific capacitance 0.56 that of the surface membrane, since this was the maximum reduction of specific capacitance obtained by addition of cholesterol to an artificial membrane. This therefore assumes ~40% cholesterol in the t-tubule membrane and 0% in the surface membrane, although such extreme differences are unlikely. In skeletal muscle it has been reported that the cholesterol fraction of the surface membrane ranges from 0.28 to 0.38 [START_REF] Rosemblatt | Immunological and biochemical properties of transverse tubule membranes isolated from rabbit skeletal muscle[END_REF][START_REF] Sumnicht | Lipid composition of transverse tubular membranes from normal and dystrophic skeletal muscle[END_REF], and that of the t-tubule membrane is double that of the surface membrane, i.e. 0.56 to 0.76; extrapolating from figure 3 these data suggest that at least in skeletal muscle the specific capacitance of the t-tubule membrane may actually be higher than that of the surface membrane.

However the equivalent values for cardiac muscle are unknown, and the different responses to methyl-β-cyclodextrin in the 2 muscle types (below) suggest that they may be different.

Since the cholesterol content of the t-tubule and surface membranes is unlikely to be 40 and 0% respectively, it is likely that the t-tubular fraction of the cell membrane calculated using these values (49%; see above) is an upper limit. This suggests that the optical method of Soeller and Cannell (1999) may overestimate the t-tubular fraction. The reason for this is unclear, but there are two critical factors in the calculation: (i) t-tubule area/cell volume (0.44 µm 2 /µm 3 ); this (and hence t-tubular fraction) could be overestimated in two ways. First, if the dimensions of a typical t-tubule were overestimated by 100 nm in each axis (the maximum for the sampling parameters used), this would increase the apparent t-tubule area/cell volume ratio; however it is unlikely that such an error would be systematic and it would in any case be compensated by an increase in total surface area/volume, so the t-tubule fraction would remain almost unchanged.

Secondly, dye accumulation and the non-ratiometric method used to image fluorescence may lead to overestimation, although the authors provide evidence that such accumulation is unlikely to have been a problem. (ii) total surface area/volume ratio; underestimating this ratio will result in an overestimate of fractional t-tubule area. The total surface area is calculated from measured membrane capacitance, assuming a specific capacitance of 1 µF/cm 2 . However if this assumed value is too high, cell surface area will be underestimated and the fraction of the membrane in the t-tubules will be overestimated: if the specific capacitance of the t-tubule membrane is assumed to be 0.56 μF/cm 2 and the fraction of cell membrane in the t-tubules to be 0.56, then 38% of capacitance will be lost following detubulation (assuming that 8% of the t-tubule network remains attached; fig. 4 above). If the same values are used to convert the capacitance/volume ratios determined by [START_REF] Satoh | Surface:volume relationship in cardiac myocytes studied with confocal microscopy and membrane capacitance measurements: speciesdependence and developmental effects[END_REF] to surface area/volume ratios (0.897 -1.179 cm 2 /cm 3 ), these can be used to calculate the t-tubule membrane fraction from the data of [START_REF] Soeller | Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques[END_REF]; see Introduction) as between 49% and 37%, assuming accurate measurement of cell capacitance, uncontaminated by membrane currents and accurately calculated from the experimental records: it is possible that membrane capacitance is underestimated by integration of the capacitance current [START_REF] Christe | Evaluation of cardiac cell membrane capacitance from the current response to a small pulse. Compared reliability of numerical integration versus fitting an exponential decay[END_REF]. However, a similar relative error is made when measuring the capacitance of intact and detubulated cells, so that their ratio is not significantly altered [START_REF] Christe | Evaluation of cardiac cell membrane capacitance from the current response to a small pulse. Compared reliability of numerical integration versus fitting an exponential decay[END_REF].

Calculation of cell volume is also not straightforward. [START_REF] Soeller | Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques[END_REF] assumed a cylindrical cell 100 µm long x 20 µm diameter to calculate total surface area/volume ratio, and hence a t-tubular membrane fraction of 65% (see Introduction). However an elliptical crosssection provides a volume estimate closest to 3D rendered volume [START_REF] Satoh | Surface:volume relationship in cardiac myocytes studied with confocal microscopy and membrane capacitance measurements: speciesdependence and developmental effects[END_REF], and increases the surface area/volume ratio so that the estimated t-tubular membrane fraction decreases by ~10%. This may still be an upper limit because for an ellipsoid cell the rendered volume is 29% smaller than the computed volume, so that the surface area/volume ratio may be even larger [START_REF] Satoh | Surface:volume relationship in cardiac myocytes studied with confocal microscopy and membrane capacitance measurements: speciesdependence and developmental effects[END_REF]. Although capacitance/volume ratios obtained in adolescent Sprague Dawley rats (6.76 pF/pl; [START_REF] Satoh | Surface:volume relationship in cardiac myocytes studied with confocal microscopy and membrane capacitance measurements: speciesdependence and developmental effects[END_REF] provide values that agree with the surface area/volume ratio calculated by [START_REF] Soeller | Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques[END_REF]see Introduction), this may not be an appropriate reference for measurements in Wistar rats: a recent study reports an average ventricular myocyte volume and capacitance of 23.6 pl and 200 pF respectively in 300g adult Wistar rats [START_REF] Swift | Slow diffusion of K + in the T tubules of rat cardiomyocytes[END_REF], giving a total membrane capacitance/volume ratio of 8.43 pF/pl, close to that of 8.88 pF/pl obtained in adult Sprague Dawley rats [START_REF] Satoh | Surface:volume relationship in cardiac myocytes studied with confocal microscopy and membrane capacitance measurements: speciesdependence and developmental effects[END_REF]. Combined with the t-tubule area/volume ratio of [START_REF] Soeller | Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques[END_REF], this provides a t-tubule fraction of 52%. Interestingly, detubulation of ventricular cells from Sprague Dawley rats results in similar losses of cell capacitance (32%; [START_REF] Despa | Na/Ca exchange and Na/K-ATPase function are equally concentrated in transverse tubules of rat ventricular myocytes[END_REF] as in the Wistar rats used in the present study.

Previous work investigating the effect of cholesterol on membrane capacitance has shown either a decrease, no change, or increase in membrane capacitance. Interestingly a recent study using the cholesterol-depleting agent methyl-β-cyclodextrin showed no change in membrane capacitance or t-tubule structure in rat ventricular myocytes [START_REF] Calaghan | Caveolae modulate excitation-contraction coupling and beta2adrenergic signalling in adult rat ventricular myocytes[END_REF], although previous work has shown that methyl-β-cyclodextrin disrupts the t-tubules in myotubes [START_REF] Pouvreau | Membrane cholesterol modulates dihydropyridine receptor function in mice fetal skeletal muscle cells[END_REF], so that the structure of skeletal and cardiac t-tubules may rely to different extents on cholesterol. It might be expected, however, that insertion of cholesterol in the membrane would increase membrane thickness, and thus decrease capacitance. In the present study we used an artificial monolayer, and showed that cholesterol reduced membrane capacitance. Although a useful experimental system with a capacitance similar to that of the cell membrane, this membrane differs from that in the cell: for example it is a monolayer rather than a bilayer, its composition is simpler than that of the cell membrane, it is not in contact with proteins, and it is exposed to different mechanical stresses.

Nevertheless the present work suggests that the specific capacitance of the t-tubule membrane may be lower than that of the surface membrane, possibly because of a high cholesterol content; correction for such an effect would increase the fraction estimated by detubulation and decrease the fraction calculated from optical measurements, and could therefore help reconcile the estimates of t-tubule membrane fraction obtained using the two methods; the considerations discussed above suggest that the true fraction lies close to 50%: between the values obtained using the two techniques. 3. Parameters determining the density of ion flux pathways in the t-tubular (t-density) and surface (S-density) membranes in the model, showing the effect of correcting for current fraction on current density. The densities before correction are calculated from the fractions of tubular ion currents obtained by detubulation ("loss of current" in table 2); those after correction were obtained after incorporating incomplete detubulation, the effect of ion concentration changes within the t-tubules and the effect of contamination by other currents (right column in table 2). The t-tubular fraction of the cell membrane in the model was set to 49%. mS/cm 2 : maximum conductance/unit surface area; μA/cm 2 : maximum current/unit surface area; cm/s: permeability/unit surface area.

  electron microscopy. Fabien Brette is a Wellcome Trust Fellow. The work described in this study was supported by the British Heart Foundation, by project AV0Z 20760514 from the Institute of Thermomechanics of Czech Academy of Sciences, by project MSM 0021622402 from the Ministry of Education, Youth and Sports of the Czech Republic and by a Junior Fellowship awarded to Dr. Pásek by the Physiological Society.

Figure 1 .

 1 Figure1. The combinations of density of t-tubule openings, mean tubular radius and mean tubular length that can mathematically coexist in a cardiac myocyte with a t-tubular membrane fraction of either 56% (top) or 32% (bottom). The planes are colour coded to distinguish between long (red) and short (blue) tubular lengths. Comparison of these combinations with published values can help determine which estimate of fractional area of tubular membrane may be closest to the true value; see text for further information.

Figure 2 .

 2 Figure 2. Left: representative transmission EM images of control (top) and detubulated (bottom) rat ventricular myocytes. The bars in each panel represent 2 μm. Right: the distribution of distances of putative t-tubules from the nearest Z-line (top) and the distribution of diameters of putative t-tubules (bottom) in control (filled symbols) and detubulated (open circles) myocytes, with Gaussian fits. n = 166 t-tubules in 4 control cells; 86 t-tubules in 2 detubulated cells.

Figure 3 .

 3 Figure 3. The effect of cholesterol on specific capacitance, measured as the zero frequency capacitance of a DOPC monolayer-coated mercury electrode with cholesterol incorporation. Experiments carried out in 100 mmol/l KCl.

Figure 4 .

 4 Figure4. Top: Relation between loss of tubular membrane and loss of total capacitance for different values of specific capacitance of tubular membrane in models with 56 % and 49 % of membrane within t-tubules. The values of specific capacitance in the 56% model are represented by black lines were: 1 [µF/cm 2 ] (full line); 0.89 [µF/cm 2 ] (dashed line); 0.78 [µF/cm 2 ] (dotted line); 0.67 [µF/cm 2 ] (dot-dashed line) and 0.56 [µF/cm 2 ] (dot-dot-dashed line). The value of specific capacitance in the 49% model (red line) was 0.56 [µF/cm 2 ]. 92% represents incomplete detubulation. Bottom: Relation between specific capacitance and percentage of membrane within the t-tubules that satisfies 32% loss of capacitance observed in experiments with incomplete detubulation.

Table 1 .

 1 T-tubule characteristics determined from TEM images of control and detubulated rat ventricular myocytes, obtained as described in Methods. * P<0.05 compared with control myocytes. n = 431 t-tubules in 8 control cells; 166 t-tubules in 6 detubulated cells.

	Number of	t-tubules/μm 2	Average
	t-tubules		t-tubule area
			(μm 2 )

Acknowledgements

The authors would like to thank L.Sadler for helping with the impedance measurements of DOPC/cholesterol monolayers, Dr David Woolley, Ms Debbie Carter and Mrs Gini Tilly for

Experimental data

Fraction from model

Loss of current

Corrected for incomplete detubulation

From uncontaminated current

After accounting for contamination by other currents 2. Use of a biophysically realistic computer model of a rat ventricular myocyte (specific capacitance of the t-tubule membrane 0.56 µF/cm 2 , 49% of the cell membrane within the t-tubules, 7.7% of the t-tubule network remaining after detubulation, and assuming that this fraction is electrically coupled to the surface membrane) to calculate the percentage of each ion flux pathway necessary within the t-tubules (right columns) to give the percentages of membrane current calculated to be within the t-tubules from experimental data obtained by detubulation (left columns). The bracketed numbers by each membrane current refer to the reference from which the experimental data were obtained, as follows: (1) Brette and Orchard, 2006; (2) [START_REF] Kawai | Excitation-contraction coupling in rat ventricular myocytes after formamide-induced detubulation[END_REF] (3) [START_REF] Komukai | K + current distribution in rat subepicardial ventricular myocytes[END_REF] (4) [START_REF] Despa | Na/Ca exchange and Na/K-ATPase function are equally concentrated in transverse tubules of rat ventricular myocytes[END_REF]. See text for further information.