Overcoming the problems of inconsistent international migration data: A

Keywords: immigration, emigration, international migration statistics, harmonisation, Europe

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Surmonter les problèmes d'incohérences des données sur les migrations internationales : une nouvelle méthode appliquée aux flux en Europe

Les comparaisons entre pays des caractéristiques des migrations internationales s"avèrent difficiles et confuses du fait des différences de définitions et de méthodes de mesure. Les chiffres de l"émigration fournis par les pays de d"origine des migrants différent souvent des chiffres recueillis par les pays d"accueil. Cet article propose une méthode destinée à rendre cohérentes les estimations des flux migratoires en se référant à une définition spécifique de la durée de séjour. Cette méthodologie tient compte à la fois des différences de définitions et des conséquences des erreurs de mesure dues, par exemple, au sous-enregistrement et aux fluctuations de l"échantillonage. Plus spécifiquement, les différences entre les deux séries de données rapportées sont corrigées en estimant un ensemble de facteurs d"ajustement des données pour chaque pays d"immigration et d"émigration. Les données ajustées tiennent compte de tous les cas particuliers dans lesquels les schémas origine-destination ne correspondent pas aux schémas généraux. Cette nouvelle méthode d"harmonisation des données des flux migratoires, basée sur les travaux antérieurs de [START_REF] Poulain | Confrontation des Statistiques de migrations intra-européennes: Vers plus d"harmonisation?[END_REF][START_REF] Poulain | International migration within Europe: towards more complete and reliable data?[END_REF], est appliquée aux mouvements migratoires entre 19 pays européens de 2002 à 2007. Les résultats présentent des séries fiables et cohérentes de flux migratoires internationaux qui peuvent être utilisées pour comprendre les changements récents dans les schémas migratoires, pour réaliser des projections de population, et pour développer des politiques migratoires à partir d"informations plus sûres.

Mots-clés : immigration, émigration, statistiques de migrations internationales, harmonisation, Europe

Introduction

Our understanding of the mechanisms and patterns of international migration over time are impeded both by the lack of data and by inconsistencies in the measurement and collection of the data that are available. In fact, it is well known that the patterns of migration vary significantly depending on which country is reporting the data [START_REF] Kupiszewska | Comparability of statistics on international migration flows in the European Union[END_REF][START_REF] Nowok | Statistics on international migration flows[END_REF][START_REF] Zlotnik | The concept of international migration as reflected in data collection systems[END_REF]. Considering that international migration is the main factor contributing to population growth in Europe, this is very unfortunate. In response to the problem of inconsistent migration data, we have developed a methodology for harmonising the data available to us from countries in Europe. More specifically, we make use of doublycounted information obtained from migrant sending and migrant receiving countries to estimate adjustment factors necessary for producing a consistent set of migration flows. These estimated flows are benchmarked to a particular definition.

Harmonisation of migration data is required for the development of policies on immigration [START_REF] Kraier | The Evolution of EU Migration Policy and Implications for Data Collection[END_REF]. Differences in both the concepts and techniques used to measure migration make any international comparison of migration difficult. There has been a lot of work on data issues and migration definitions, for example see [START_REF] Champion | International migration and demographic change in the developed world[END_REF], [START_REF] Kelly | Improving the Comparability of International Migration Statistics: Contribution by the Conference of European Statisticians from 1971 to Date[END_REF], [START_REF] Kraly | Efforts to improve international migration statistics: A historical perspective[END_REF], [START_REF] Poulain | Confrontation des Statistiques de migrations intra-européennes: Vers plus d"harmonisation?[END_REF], Raymer and Willekens (2008), United Nations (2002) and [START_REF] Willekens | Monitoring international migration flows in Europe: Towards a statistical data base combining data from different sources[END_REF][START_REF] Willekens | Modeling approaches to the indirect estimation of migration flows: From entropy to EM[END_REF]. Several international institutes such as the International Labour Organization, the Organisation for Economic Co-operation and Development, the United Nations and the European Commission have all invested heavily in the harmonisation of international migration data, but without much success or progression [START_REF] Bilsborrow | International migration statistics: Guidelines for improving data collection systems[END_REF]Herm, 2006a;[START_REF] Fassmann | European migration: Historical overview and statistical problems[END_REF]. In fact, the situation today in terms of migration definitions and measurement is not much better than it was, say, 20 years ago.

Recently, some renewed efforts have been made to improve the migration data situation in Europe. In 2007, the European Parliament adopted a new regulation on migration statistics. This regulation provides clear definitions of immigration and emigration (Official Journal of the European Union, 2007), and lists the migration data that must be supplied to Eurostat, the statistical office of the European Union (EU), by Member States. However, this regulation leaves the Member States free to decide how they will provide these data, including the use of estimation methods [START_REF] Fassmann | European migration: Historical overview and statistical problems[END_REF]. The methodology presented in this paper should help national statistical offices to improve and harmonize the data they currently provide to international organisations, such as Eurostat.

The migration definition set out in the 2007 Regulation corresponds to the definition recommended by the United Nations (1998), where an international migrant is defined as "a person who moves to a country other than that of his or her usual residence for a period of at least a year." One problem affecting the implementation of this definition is that some countries are unable to identify their nationals who have left [START_REF] Fassmann | European migration: Historical overview and statistical problems[END_REF]. Furthermore, many European countries exclude the immigration of nationals from the published statistics, as they are not considered to be "migrants". Another important obstacle has to do with the recommended duration of residence in the country of destination. It may take up to two years to identify all persons who have stayed at least one year, as they may arrive anytime during the annual time period of interest. This means that the publication of migration statistics based on the actual duration of stay may be delayed for some time. To provide statistics to the user community in a quicker fashion, many countries simply count those migrants who have stayed for at least three months, which leads to higher numbers than if the one-year criterion was applied. Other countries use the intended duration of stay as the criterion [START_REF] Fassmann | European migration: Historical overview and statistical problems[END_REF]. Many European countries do not have reliable statistics on emigration. This is mainly caused by the fact that migrants have little incentive to report their move to the administration of the country they have emigrated from. Moreover, it is difficult to count persons leaving the country because they are no longer present in the country collecting the data. In this situation, comparisons of sending country data with receiving country data provide important information on the degree of underestimation found in reported emigration flows (UNECE, 2009). In fact, the analysis of the so-called "double-entry matrix" of migration flows produced by UNECE since the early 1970s, and more recently by Eurostat, has been found to be very useful and informative. [START_REF] Kelly | Improving the Comparability of International Migration Statistics: Contribution by the Conference of European Statisticians from 1971 to Date[END_REF] and [START_REF] Poulain | International migration within Europe: towards more complete and reliable data?[END_REF], for example, have used the information contained in this matrix to assess the degree of harmonisation amongst reported data. In doing so, the possibility that very narrow or loose definitions of migration may be used for reported immigration statistics must be taken into account, which results in lower or higher levels of migration flows, respectively, in relation to, say, the United Nations" recommended one-year definition (UNECE, 2009).

The aim of this paper is to illustrate how reliable estimates of harmonized migration statistics may be obtained from a set of origin-destination flows, where two reported flows are available for each particular flow, i.e., from receiving and sending countries. The new method that we present is based on earlier efforts by [START_REF] Poulain | Confrontation des Statistiques de migrations intra-européennes: Vers plus d"harmonisation?[END_REF][START_REF] Poulain | International migration within Europe: towards more complete and reliable data?[END_REF], and is applied to reported flows between 19 European countries from 2002 and 2007. Note, however, that this paper does not consider flows outside the 19 country system, or those that are missing. [START_REF] Raymer | Obtaining an overall picture of population movement in the European Union[END_REF] describes a method for estimating missing migration flow data.

Comparability of international migration data

The reliability of migration statistics can be measured by how well they correspond to a particular country"s definition or concept of migration. However, as definitions differ across countries, reliability does not guarantee comparability. Moreover, under-registration, undercoverage and accuracy of the collection system also affect the measurement of migration [START_REF] Bilsborrow | International migration statistics: Guidelines for improving data collection systems[END_REF][START_REF] Nowok | Statistics on international migration flows[END_REF]. First, there may be under-registration of migrants. This may be the case if the data depend on declarations by the migrants themselves.

The willingness to report changes in places of residence varies both between countries and between groups of migrants. In general, migrants have more incentive to report their arrival than their departure, as there are usually direct benefits in doing so (e.g., access to social services). Therefore, immigration statistics are generally considered more reliable than emigration statistics [START_REF] Thierry | How the UN recommendations and the forthcoming EU regulation on international migration statistics are fulfilled in the 25 EU countries[END_REF]UNECE, 2009). Second, there may be undercoverage. This measurement category refers to the non-inclusion of particular migrant groups . Here, the differences are most often caused by the absence or inclusion of nationals, students, asylum seekers or irregular (illegal) migrants in the data. In general, asylum seekers are included only when they have been granted refugee status and received a temporary or permanent residence permit. However, in some instances, they are registered at an earlier stage of the asylum process. In other instances, even recognised refugees are not included.

Irregular migrants are generally not included in migration statistics, as they are especially difficult to measure (for obvious reasons). In fact, Spain is the only EU country that includes irregular migrants in the official statistics. Finally, data based on sample surveys may be unreliable due to sampling errors. Furthermore, unless the sample size is very large, the data are likely to show irregularities in the patterns across ages or in the distribution of origins or destinations over time, as flows of migrants represent a relatively small proportion of the overall population being surveyed.

The main sources of the differences in the definitions used by EU countries to measure migration are the concepts of place of residence and duration of stay [START_REF] Zlotnik | The concept of international migration as reflected in data collection systems[END_REF][START_REF] Bilsborrow | International migration statistics: Guidelines for improving data collection systems[END_REF][START_REF] Kupiszewska | Comparability of statistics on international migration flows in the European Union[END_REF]. The de jure (legal) approach to residence implies that in order to become a resident, a migrant must comply with certain regulations, which tend to differ between nationals and foreigners, and among foreigners, between EU-and non-EU-nationals. For example, it is not uncommon for emigrants to be registered in their country of citizenship (origin) even after several years of living abroad [START_REF] Thierry | How the UN recommendations and the forthcoming EU regulation on international migration statistics are fulfilled in the 25 EU countries[END_REF]. Thus, having a place of residence does not necessary imply a presence in that country. The de facto (actual) approach is connected with physical presence in a country, usually for a specified minimum period of time. To prevent the delay caused by measuring actual duration of stay, most European countries use the intended duration of stay instead [START_REF] Nowok | Statistics on international migration flows[END_REF]. Alternatively, the intended duration of stay may be used to provide provisional statistics, which are updated at a later point with the actual duration of stay statistics. Another group of countries measure "permanent" change of residence only (e.g. Poland and Slovakia), which is very restrictive and tends to produce flow levels that are much lower relative to other definitions. The duration of stay criterion used by the majority of EU countries is between three months and one year. Only three countries (Cyprus, Sweden and UK) apply strictly the one-year criterion for immigration, as well as for emigration and for both nationals and non-nationals [START_REF] Thierry | How the UN recommendations and the forthcoming EU regulation on international migration statistics are fulfilled in the 25 EU countries[END_REF]. In fact, some countries do not take duration of stay into account at all. Germany is such an example, where everybody taking up a residence is counted as a migrant.

Because of differences in definition, coverage, registration and accuracy of the collection mechanism, the origin-destination matrix of migration flows between European countries based on immigration data reported by the countries of origin tends to differ from the matrix reported by the countries of destination. With respect to definitions, the differences are expected to be systematic over time. For example, the German definition is wider than the Dutch definition which, in turn, is wider than that of Sweden. In fact, Germany reports higher figures than the Netherlands, and the figures of the Netherlands are higher than those reported by Sweden [START_REF] Kupiszewska | Comparability of statistics on international migration flows in the European Union[END_REF]. A comparison of the size of these reported flows provides information on the effects of differences in definition on the size of migration flows [START_REF] Bilsborrow | International migration statistics: Guidelines for improving data collection systems[END_REF]UNECE, 2009). However, as mentioned above, not all differences can be explained by differences in definition. In some cases, countries report relatively large percentages of unknown countries of origin or destination. Furthermore, sudden jumps in observations may be caused by changes in definitions or by changes in the registration method.

Data on immigration and emigration flows by country of origin and destination are usually presented in an origin-destination matrix with off diagonal entries containing the number of people moving from any origin i to any destination j in a given calendar year. For this study, we have collected migration data for the 19 countries set out in Table 1. As each flow can be reported by both sending and receiving countries, two migration tables may be produced. Such data are set out in Table 2 flows reported by the countries of destination and the lower table contains the flows reported by the countries of origin. Clearly, there are large differences between the two sets of reported numbers (see, e.g., Spain to the United Kingdom or Poland to Germany).

-----Tables 1 and2 about here -----

Method

The differences between reported immigration and emigration numbers are useful for improving and harmonizing the migration data. If reported emigration numbers for a given country turn out to be systematically lower than the corresponding immigration numbers reported by the countries of destination, this suggests that the reported emigration numbers are too low. Adjusting these numbers in an upward direction moves them closer to the actual numbers. The same applies to reported immigration numbers. For each country we can estimate one adjustment factor for immigration and one for emigration in such a way that the adjusted immigration and emigration numbers are closer to each other than the reported numbers. To prevent arbitrary judgments biasing the results, we believe the estimation of adjustment factors for immigration and emigration flows should be estimated simultaneously.

Moreover, it should be noted that immigration is not necessarily recorded more accurately than emigration. In some situations, sending country data may be considered better [START_REF] Nowok | Statistics on international migration flows[END_REF]. [START_REF] Poulain | Confrontation des Statistiques de migrations intra-européennes: Vers plus d"harmonisation?[END_REF][START_REF] Poulain | International migration within Europe: towards more complete and reliable data?[END_REF] was the first to develop a method to adjust reported immigration and emigration numbers for the purpose of obtaining a consistent set of migration flows.

"Correction factors" were estimated by minimizing the sum of squares 2 , ) (

ij i j i ij j E I ,
where I ij denotes migration from country i to country j reported by the receiving country j, E ij denotes the same flow reported by the sending country i, j is the adjustment factor for all immigration to country j and i is the adjustment factor for all emigration from country i. [START_REF] Poulain | Estimation of flows within the intra-EU migration matrix[END_REF] refined this method by dividing the squared differences by the sum of the reported numbers, i.e.,

) /( ) ( 2 , ij ij ij i j i ij j E I E I . ( 1
)
This refinement prevents flows from (or to) large countries from biasing the estimates.

Various constraints have been tried by Poulain and colleagues [START_REF] Abel | International Migration Flow Table Estimation[END_REF]. For instance, following the iterative approach to harmonizing migration flows suggested by van der Erf and van der Gaag (2007), [START_REF] Poulain | Estimation of flows within the intra-EU migration matrix[END_REF] proposed that the estimates should be normalized to Swedish immigration data, as they are generally considered to be highly reliable and in agreement with the UN recommended measure, as well as with the new EU regulation [START_REF] Herm | Country Report Sweden[END_REF]). The parameters j and i may be estimated by solving a system of linear equations, which result from applying the method of Lagrange multipliers.

Multiplying [START_REF] Poulain | Estimation of flows within the intra-EU migration matrix[END_REF] applied their correction method first to countries with relatively reliable data to prevent countries with less reliable data influencing the overall patterns. Here, the main concern is that the less reliable data have origin-destination patterns that are not consistent with the actual patterns. Thus, less reliable flows were adjusted in a hierarchical fashion, i.e., by using the harmonised reliable data as a basis.

There are several limitations in the model described above. First, the reported numbers included in the denominator of Equation ( 1) are known to be incorrect [START_REF] Abel | International Migration Flow Table Estimation[END_REF]. Second, the row and column totals of the two estimated matrices are not equal. As a result, the row and column totals of the average harmonised migration matrix do not correspond to the row and column totals estimated using the adjustment factors. Finally, the method can only be applied to a limited set of countries with reasonably reliable data. This implies that the estimates of the adjustment factors depend on the selection of countries, which may not reflect the broader patterns of interest. For these reasons, we have revised Poulain"s method in two important ways. First, the row-sums and column-sums of the two estimated matrices are set to be equal. Second, we introduce additional constraints on individual cells in the migration matrices, so that more countries (with less reliable data) may be included.

The adjustment factors for our method can be estimated by solving a system of linear equations and imposing a constraint. If we have a N x N receiving country and an equivalent N x N sending country matrix, the adjustment factors for receiving country, j , and the adjustment factors for sending country data, i , can be estimated by:

j ij i j ij j E I ˆ for i = 1,…, N; i ≠ j (2) i ij i i ij j E I ˆ for j = 1, ..., N; i ≠ j (3)
Equation ( 2) states that for each country the emigration total estimated on the basis of the adjusted matrix of flows reported by receiving countries equals the emigration total estimated on the basis of the adjusted matrix of flows reported by sending countries. Equation (3) does the same for immigration totals.

Equations ( 2) and ( 3) can be written as a homogeneous system of 2N linear equations with 2N unknowns, i.e., 0 ... ˆ1 1

1 13 3 12 2 j j N N E I I I (4) …. 0 ... ˆ1 1 2 2 1 1 j Nj N NN N N N E I I I 0 ... ˆ1 31 3 21 2 1 1 N N i i E E E I … 0 ... ˆ1 1 2 2 1 1 NN N N N i iN N E E E I
This system has an infinite number of solutions for j and i . For each set of values of j ˆ and i ˆ that solve this system, j k ˆ and i k ˆ are solutions as well. In order to find a unique solution one restriction needs to be imposed. In accordance with [START_REF] Poulain | Estimation of flows within the intra-EU migration matrix[END_REF], we assume that the adjustment factor for Swedish immigration is equal to one, since Sweden uses a definition of migration that is consistent with the new EU regulation and the quality of Swedish immigration data is considered to be adequate. This also means that the resulting estimates are harmonised in line with the new European regulation.

The basic assumption underlying our estimation procedure (as described above) is that the distributions of reported immigration by country of origin and reported emigration by country of destination correspond to the distribution of actual migration flows under the harmonised definition. This implies that the reported emigration of country A is x% higher or lower than the actual number (based on the standard definition) for all countries of destination. The same assumption applies to receiving country numbers. However, as we find in the next section, the estimated receiving country flows by country of origin and the estimated sending country flows by country of destination are not always consistent with each other. In a number of cases, specific origin-destination flows have to be considered separately.

For that reason, we introduce additional constraints, corresponding to particular origindestination flows that differ from the remaining flows.

Let us assume that the estimated receiving country migration flow from country p to q, pq q I ˆ, differs substantially from the estimated sending country flow, or pq ˆ changes the estimates of q ˆ or p ˆ. This also means that the row and column totals of both estimated migration matrices no longer tally. Therefore, we adjust the system of linear equations ( 2) and ( 3) by adding constraints on individual cells of the matrices. If we assume that the emigration number reported by country p needs to be adjusted, Equations ( 2) and ( 3) can be rewritten as

j ij pq ij i j ij j D E I ) 1 ( ˆ* for i = 1,…, N; i ≠ j (5) i ij pq ij i i ij j D E I ) 1 ( ˆ*
for j = 1, ..., N; i ≠ j (6)

where D ij = 1 if i = p and j = q, D ij = 0 otherwise, and * ˆpq = pq ˆ-1.

The equations including pq I and pq E in the system of equations ( 4) can be rewritten as follows:

0 ... ... ... ... ˆ1 1 1 pN p pq p pq p p pN N pq q p E E E I I I (7) 0 ... ... ˆ1 1 Nq N pq p pq q i iq q E E E I
In contrast with Equation (4), these are non-linear equations, because they include the term pq p pq E ˆ. The values of the coefficients can be estimated by an iterative procedure. The model can be extended in a straightforward way to include additional constraints. However, for any particular country, the number of constraints should not be too high, as this reduces the available information to estimate and .

Data

The sending and receiving country migration data have been provided by the national statistical institutes of the EU Member States in response to annual rounds of data collection conducted jointly by five international organizations and coordinated by Eurostat [START_REF] Kupiszewska | Comparability of statistics on international migration flows in the European Union[END_REF]. As concerns Europe, Eurostat processes and disseminates data received from 37 countries on their website (epp.eurostat.ec.europa.eu). Data sources used by EU member states to produce migration statistics are very diverse [START_REF] Kupiszewska | Comparability of statistics on international migration flows in the European Union[END_REF][START_REF] Nowok | Statistics on international migration flows[END_REF]. The major types of sources are population registration systems, statistical forms, other administrative registers related to foreigners (such as alien registers, residence permit registers and registers of asylum seekers), sample surveys and censuses. Thirteen EU countries use a population register as the source of migration statistics.

Alien registers and residence permit registers are used in seven countries, sometimes in addition to population registers. These registers only provide information on the migration of non-nationals. Cyprus and the UK rely on passenger surveys conducted at the borders, while

Portugal and Ireland rely on household surveys. Greece, France and Portugal do not have any data on migration by nationals. Some countries derive their emigration statistics from data on residence permits by assuming a migrant has left the country when a residence permit has expired. Moreover, they often assume that the country of next residence is the country of their citizenship. The result, we believe, is an overestimation of actual emigration to those particular countries. Finally, several countries include in their so-called "administrative corrections" emigration that has not been declared, which cannot be disaggregated by country of next residence.

Data on immigration by country of previous residence or emigration by country of next residence are not always available or complete [START_REF] Nowok | Statistics on international migration flows[END_REF]. Thus the sending country and receiving country matrices, when combined into a double-entry matrix may be incomplete. For some countries, a large share of emigrants have an unknown country of destination: around 75% in Slovenia, 40% in Luxembourg, 35% in Austria, 31% in the Netherlands and 39% in Spain, for example. Fortunately, the estimation of adjustment factors takes this into account.

In the next section we present our harmonised estimates of migration between 19

European countries that provide data on both immigration by country of origin and emigration by country of destination for the calendar years 2002-2007. The reported data contains both nationals and non-nationals. Table 1 provides a list of the countries. Although there are some data for Ireland, Portugal and Romania, these have not been used because they cover only a part of the migration flows (e.g. only foreigners or nationals). For Iceland, Italy, and

Luxembourg, data for one or more years in the period 2002-2007 are missing. For these countries, the adjustment factors are estimated for averages over the available years.

Results

The results presented in this section are obtained by applying the estimation method described in Section 3. that receiving country data should not always be considered better than sending country data.

Consider, for example, the flows from Poland to Germany in Tables 2a and2b. Here, Germany received an average of 136,927 migrants from Poland, whereas Poland reported that they only sent an average of 14,417. This difference could be explained by the duration criteria used by these countries, with Germany having a very loose definition (instant) and

Poland having a very restrictive definition (permanent). So, in comparison with the harmonised definition of a one year period, Germany"s reported number is considered too high and Poland"s too low.

The estimated adjustment factors are set out in Table 3. We indicated above that in order to estimate the adjustment factors a restriction was introduced, i.e. the adjustment factor for Swedish immigration is set equal to one. For 16 of the 19 countries, the E ij adjustment factor exceeds one, indicating that sending country numbers tend to be underestimated.

However, Table 3 also shows that I ij numbers seem to be underestimated in the majority of countries as well. This may seem contradictory since for 11 of the 19 countries the reported immigration totals exceed the corresponding emigration numbers reported by the sending countries. This is because the reported receiving country numbers should be compared with the adjusted sending country numbers rather than the reported numbers. For example, the immigration total reported by the UK (107,897) exceeds the reported emigration from sending countries to the UK (52,567). The reported emigration to the UK includes 5,219 emigrants from Poland to the UK. However, since the reported emigration from Poland is too low (the adjustment factor equals 18.31, see Table 3) the reported emigration from Poland to the UK is adjusted from 5,219 to 55,506. Moreover, the adjustment factor for Spanish emigration data equals 4.32, so the reported emigration from Spain to UK is adjusted from 3,430 to 16,792.

For several other countries, emigration to the UK is adjusted upwards as well. As a consequence, the adjusted emigration numbers to the UK exceed the total of immigration reported by the UK and thus the reported immigration is adjusted upwards as well. Note that the adjustment factors for immigration for most countries are closer to one than the adjustment factors for emigration, which indicates that the reported immigration numbers are more accurate than the emigration numbers.

-----Table 3 about here -----Multiplying the reported numbers in Table 2a by the adjustment factors for receiving country data and the reported numbers in Table 2b by the adjustment factors for sending country data results in two tables for which the row and column totals are equal (not presented here for space reasons). The differences between the cells in these two matrices are considerably smaller than those in Table 2. In fact, the root mean squared error (RMSE) is reduced from 8966 to 2131. In other words, the differences between the two reported migration flow tables are reduced by 77%. However, we still found some substantial differences in the two estimated migration flow tables. For example, the migration from Poland to Germany estimated on the basis of German immigration data equals 141,035, whereas the estimate based on Polish emigration data is equal to 153,399. These differences reflect the fact that the distribution of reported Polish emigration by country of destination is not consistent with the share of immigration from Poland in the total reported immigration numbers of other countries. As a result, the estimate of the migration flow from Poland to Germany based on Polish data exceeds that based on German data, whereas for most other countries, the adjusted Polish emigration numbers are lower than the corresponding adjusted immigration numbers. This means that one substantial inconsistency in the estimates is likely to influence the estimates of other migration flows. To prevent such inconsistencies from affecting the overall estimates, we have added constraints to individual cells (flows) in the model.

The introduction of constraints to individual cells in the matrix allows us to consider special cases, such as the Poland to Germany flow described above. In total, we found six migration flows where the estimates differed by more than 10,000. Specifically, these flows were Poland to Germany, Poland to UK, Germany to Poland, Germany to UK, Czech

Republic to Slovakia and UK to Poland. After identifying the flows with large differences, we then had to decide whether the constraint should be applied to the numbers of the receiving country or of the sending country. Since we believe that reported emigration numbers are generally considered to be less reliable than reported immigration numbers, we apply the constraints to the sending country data, except for the Germany to Poland and UK to Poland flows (i.e., Poland"s immigration data is considered to be of lower quality that the corresponding emigration data reported by both Germany and the UK).

The adjustment factors taking into account the six constraints on individual flows are set out in Table 4. The coefficients (Lagrange multipliers) for the Poland to Germany and Poland to UK flows are both equal to 0.42. This raises the adjustment factor for emigration from Poland from 10.64 (Table 3) to 18.31 (Table 4), while at the same time, the adjustment factor for Polish emigration to Germany and the UK falls to 7.69 (i.e., 18.31 x 0.42). For Polish immigration, the adjustment factor becomes smaller. The high adjustment factor for Polish receiving data was mainly a consequence of the big difference between the two figures for migration from Germany to Poland. Including a constraint for this flow raises the adjustment factor for Poland"s reported flow from Germany by a factor of 1.74 (i.e., the adjustment factor of 14.25 is multiplied by 1.74 to get 24.80). In contrast, the adjustment factor for Poland"s reported flow from the UK falls to 10.40 (i.e., 14.25 x 0.37). For the Czech Republic, the reported emigration numbers are considerably lower than the corresponding reported immigration numbers with one big exception: the number of emigrants reported to Slovakia is relatively large. Clearly, the emigration flows from the Czech Republic to all other countries need to be adjusted by a different factor than the emigration flow to Slovakia.

-----Table 4 about here -----

The adjustment factors in Table 4 illustrate how substantial improvements in the estimated adjustment factors can be made by introducing constraints on specific "problem" flows in the matrix. For example, the inclusion of a constraint for the migration flow from the Czech Republic to Slovakia lowered the adjustment factor for Slovakia"s receiving migration data from 18.90 to 8.34. Another example is German"s receiving data. Here, the adjustment factor is reduced from 1.03 to 0.81. This is mainly explained by the reduction of the estimate of Polish emigration to Germany. Since Germany has a wide definition of migration, one would expect the adjustment factor to be below one. Thus the adjustment factors in Table 4 appear more plausible than those set out in Table 3.

The harmonised migration tables that used the additional constraints are set out in Tables 5a and5b. The introduction of these constraints led to a further strong reduction in the differences between both tables, as indicated by the RMSE, which fell from 2131 to 952 or by a further 54%. To obtain a final single set of harmonised flows, we believe it is better to rely on Table 5a than on Table 5b. This table gives more weight to the receiving country data, which we consider more reliable. Poulain, on the other hand, advocated taking the average of the two estimated matrices. This approach implies that the origin-destination patterns in the reported sending country data are as reliable as those in the reported receiving country data.

-----Table 5 about here -----

The average adjustment factors estimated for the period 2002-2007 (Table 4) can be applied to the annual reported migration data to create a time series of harmonised flows. In Figure 1, the estimated total immigration and emigration flows for Germany from and to the other 18 countries in this study are compared. As expected, the estimated numbers are lower than the reported numbers because the definition for Germany is much wider than the harmonised definition. The figure also shows that estimated emigration increases more gradually over time than the reported numbers. In Figure 2, the immigration and emigration flows for the UK are presented. Here, the average levels of the reported and estimated numbers do not differ much, but the estimated flows show a more gradual pattern over time than the reported flows. One reason for the sharp fluctuations in the reported numbers is that they are based on sample surveys.

-----Figures 1 and2 about here -----

Discussion

The aim of this paper has been to obtain a reasonable and consistent set of international migration statistics. For this purpose we have developed a model using statistical information from different countries. The method is based on an idea originally proposed by [START_REF] Poulain | Confrontation des Statistiques de migrations intra-européennes: Vers plus d"harmonisation?[END_REF][START_REF] Poulain | Towards a harmonisation of migration statistics within the European Community[END_REF]. Our method differs from his in three important ways. First, we have estimated a set of adjustment factors for receiving and sending country data in a way that ensures consistency in the two sets of marginal totals. Second, we have introduced additional constraints on special origin-destination cases where the average adjustment factors do not apply. This allows us to include countries with less reliable data in our analysis. Third, instead of calculating the arithmetic average of the two estimated matrices, we believe it is better to use the matrix giving more weight to the reported immigration numbers (i.e. Table 5a). In this way we take advantage of the fact that the information on countries of origin in receiving country data tend to be more reliable than the country of destination information in sending country data. Finally, our estimates are consistent with the harmonised migration definition based on an (intended) minimum duration of stay of 12 months. However, the large differences between European countries cannot be explained by differences in definitions alone. First, these differences cannot explain why emigration flows are more likely to be underestimated than immigration flows. Second, whereas eleven countries employ a duration limit that is shorter than that of the harmonised definition [START_REF] Kupiszewska | Availability of statistical data on migration and migrant population and potential supplementary sources for data estimation[END_REF], only five of these countries have an adjustment factor of immigration below one. The other six countries with durations of six months or shorter have adjustment factors for immigration greater than one. These include Austria, Czech Republic, Italy, Luxembourg, the Netherlands and Slovenia. Thus, to an important extent, the differences must also be caused by problems of coverage. This is confirmed by a study comparing migration statistics between Sweden, Denmark and Belgium which suggests that less than 25% of differences are due to differences in the duration criterion [START_REF] Nowok | Statistics on international migration flows[END_REF]. The effects of differences in definition and coverage may offset each other to some extent. One would expect the under-registration of short term migrants to exceed that of longterm migrants. A wide definition of migration (i.e. a short duration of stay) would lead to a higher reported number of migrants than would be expected on the basis of the harmonised definition. Under-registration, however, would lead to a smaller number. This may explain why the adjustment factors for Germany are not as low as one might expect from applying the very wide definition.

The main reason for the relatively low numbers reported by sending countries is that emigrants do not have strong incentives to report leaving a country. In particular, this applies to EU citizens who can live in another EU country without asking for a residence permit. One solution might be to introduce a removal card system [START_REF] Nowok | Statistics on international migration flows[END_REF]. Here, any person leaving country A would be required to fill in a form to be given to the authorities in country B at arrival. After country B has determined whether or not the person is an international migrant under a harmonised definition, it would then inform country A of the arrival. The Nordic countries have such a system and their immigration and emigration statistics are mutually consistent (Herm, 2006a). However, policy makers tend to be more interested in migrants from outside Europe and asylum seekers than intra-European migrants, and therefore such a system is not likely to have a high priority in the future. As long as such a system is lacking, cross-country comparability of migration statistics can only be achieved by comparing statistics from different countries. To the extent that the differences between countries are caused by differences in definitions and coverage, the differences may be expected to remain systematic over time. The method developed in this paper aims to assess the size of these systematic differences. Table 4 shows that for 10 out of the 19 countries in this study, the adjustment factor for sending country data exceeds two, meaning that reported emigration numbers are underestimated by more than 50% in relation to the one-year duration definition. As a consequence, reported net migration totals may be overstated.

In addition to "correcting" the reported receiving and sending country migration data for differences in definition and coverage, our method contributes to producing estimates that tend to fluctuate less strongly over time. One clear example concerns the UK. Since the UK uses a general purpose passenger survey, the reported flows fluctuate considerably over time.

Moreover, flows to some (smaller) countries may not be observed in some years. We believe our method produces more stable estimates of migration flows for the UK (and other countries relying on sample data). Interestingly, the estimated adjustment factors for the UK are close to one. This implies that the sample survey used for estimating migration to and from the UK provides a reasonably reliable estimate of total migration flows on average, but that the annual estimates are affected by sizeable random fluctuations.

The adjustment factors shown in Table 4 can be used to adjust migration numbers to and from countries not included in the matrix, so that total immigration and emigration numbers and total net migration can be estimated for the 19 countries in this study. Before doing so, one first has to make sure that the share of unknowns in the migration statistics can be distributed evenly across all origins or destinations. If so, the adjustment factors will take this into account. Thus, for estimating total immigration and emigration numbers, the adjustment factors should be applied to total migration numbers excluding unknowns.

The matrix may be extended to include flows with missing data. [START_REF] Raymer | Obtaining an overall picture of population movement in the European Union[END_REF] developed a two-step estimation method for countries with missing data (see also [START_REF] De Beer | Estimates of OD matrix by broad group of citizenship, sex and age, 2002-2007[END_REF][START_REF] Raymer | The MIMOSA model for estimating international migration flows in the European Union[END_REF]. The first step estimates missing immigration and emigration totals based on harmonised migration flows and covariate information. The second step uses the origin-destination interaction patterns of the harmonised migration flows and covariate information to estimate the missing interaction patterns. This estimation step takes into account the fact that migration is relatively high, for example, between neighbouring countries and countries belonging to a similar language group.

Figure 1 .

 1 Figure 1. Reported and estimated immigration from and emigration to 18 European countries,Germany, 2002Germany, -2007

  . Here, the average 2002-2007 values of migration between the 19 European countries set out in Table 1 are presented. The upper table contains

  The final set of estimates are obtained by simply taking the average of

	the two, i.e.,	2 ( / ) ˆij i ij j ij E I n	, where

I ij by j ˆ and E ij by i ˆ produces two sets of migration flow estimates from country i to country j. ij n ˆ denotes the harmonised migration flows. Note,

  Table 2a shows the average values of migration between 19 European countries reported by receiving countries for the years 2002-2007 and Table2bshows the corresponding numbers reported by the sending countries. The countries listed in the row headings refer to origins and those listed in the column headings refer to destinations. A comparison of Tables 2a and 2b reveals large differences between numbers reported by sending and receiving countries. According to the numbers reported by receiving countries,

671,315 migrants per year moved between these 19 countries, whereas the numbers reported by sending countries total 499,105. For 11 countries, the reported receiving country immigration totals are higher than the corresponding sending country totals. For example, Germany reported that 256,221 immigrants arrived from the 18 countries in this study, whereas these countries reported that only 66,905 emigrants moved to Germany. Poland reported that 22,306 persons emigrated to the other 18 countries which, for their part, reported receiving 217,977 immigrants from Poland, suggesting that Polish emigration data are around 10 times too low. For 15 of the 19 countries, the emigration total reported by the sending country is lower than the corresponding totals reported by receiving countries. Keep in mind

  Due to differences in definition, coverage, and registration, the origin-destination matrix of migration flows between European countries based on receiving country data tends to differ from the matrix based on sending country data. Germany has a wide definition of migration, as it does not include a time constraint and thus the reported number may well include short term migrants. In contrast, Poland has a very narrow definition of migration and, as a consequence, the reported numbers are very low. By comparing corresponding reported immigration and emigration flows for 19 European countries, we have assessed to what extent German migration statistics are higher than they would be under a harmonised definition and to what extent Polish migration statistics are lower.

Table 1 .

 1 Finally, work is currently being carried out to integrate harmonisation and estimation of missing data into a single (Bayesian) model that also includes measures of uncertainty and expert judgements. The Integrated Modelling of European Migration (IMEM) project recently funded by New Opportunities for Research Funding Agency Co-operation in Europe List of European countries reporting both immigration flows by country of origin and emigration flows by country of destination, 2002-2007

	Country	Abbreviation
	Austria	AT
	Cyprus	CY
	Czech Republic	CZ
	Germany	DE
	Denmark	DK
	Spain	ES
	Finland	FI
	Iceland	IS
	Italy	IT
	Lithuania	LT
	Luxembourg	LU
	Latvia	LV
	Netherlands	NL
	Norway	NO
	Poland	PL
	Sweden	SE
	Slovenia	SI
	Slovakia	SK
	United Kingdom	UK

(NORFACE) is expected to develop such a model (see http://www.norface.org/migration12.html) over the next couple of years. We hope this study will provide an important foundation for work such as this, and other projects aiming to improve our knowledge and understanding of the complexity of international migration.

Table 2a .

 2a Reported migration by country of destination, averages[2002][2003][2004][2005][2006][2007]

		To
	From	AT	CY	CZ	DE	DK	ES	FI	IS	IT	LT	LU	LV	NL	NO	PL	SE	SI	SK	UK	Total
	AT		41	310 14 257	303	774	109	33	774	17	8	9	559	111	180	307	100	208	1 395 19 496
	CY	22		13	276	23	25	23	1	30	3	0	2	51	15	7	61	2	2	2 533	3 087
	CZ	1 316	118		9 218	262	833	56	42	672	24	4	15	511	116	45	164	6	979	4 109 18 489
	DE	15 447	332	1 362		4 001 15 982	921	255 12 809	490	454	166	9 182	2 268	2 876	3 374	299	446 19 039 89 701
	DK	203	25	46	2 687		964	365	1 413	265	85	11	46	475	2 943	34	5 264	3	21	1 874 16 721
	ES	700	45	71 14 703	1 758		644	68	2 044	252	24	18	3 101	768	119	1 300	8	36 14 581 40 239
	FI	270	21	38	2 173	414	844		45	235	43	3	43	379	799	6	3 204	1	6	684	9 208
	IS	31	0	4	236	1 665	131	50		35	10	0	6	75	373	11	462	1	2	417	3 509
	IT	1 608	49	254 22 196	986	9 320	250	74		82	67	33	1 811	246	309	599	79	109	5 829 43 900
	LT	179	35	47	4 496	1 034	2 274	73	272	378		1	236	302	926	43	574	0	5	2 507 13 380
	LU	67	3	2	2 282	162	123	50	27	213	5		2	161	18	5	90	5	1	682	3 897
	LV	83	104	13	2 155	457	300	87	93	183	175	2		125	233	6	264	0	5	1 227	5 511
	NL	791	70	255 13 681	864	4 762	261	55	905	41	27	20		711	163	979	12	41	6 799 30 436
	NO	98	14	24	1 378	3 148	1 696	845	364	167	87	2	24	453		48	5 098	1	24	1 667 15 135
	PL	5 231	752	1 608 136 927	2 436	8 277	187	2 229	9 045	120	19	45	5 744	4 602		3 718	3	276 36 759 217 977
	SE	489	88	67	3 348	3 313	1 826	3 502	492	379	91	14	54	696	4 917	113		15	20	3 213 22 635
	SI	556	9	17	1 798	46	136	6	9	321	2	1	1	90	14	2	42		16	0	3 064
	SK	3 192	432 14 064 11 148	149	788	22	45	690	4	4	4	465	238	18	110	4		4 584 35 961
	UK	1 222	3 170	506 13 263	3 482 38 674	946	228	4 553	875	39	190	5 820	1 624	1 126	3 114	22	116		78 969
	Total	31 504	5 306 18 702 256 221 24 502 87 725	8 397	5 741 33 695	2 407	682	913 30 000 20 921	5 111 28 723	559	2 311 107 897 671 315
	Source: Eurostat

Table 2b .

 2b Reported migration by country of origin, averages[2002][2003][2004][2005][2006][2007]

		To
	From	AT	CY	CZ	DE	DK	ES	FI	IS	IT	LT	LU	LV	NL	NO	PL	SE	SI	SK	UK	Total
	AT		18	937	6 665	166	429	231	27	1 022	111	45	42	426	87	2 401	388	402	1 778	901 16 076
	CY	6		21	57	6	19	12	0	39	9	2	18	10	2	111	13	0	32	371	724
	CZ	186	13		560	24	35	28	2	112	10	3	7	81	16	583	24	8	9 539	219 11 449
	DE	17 787	271	8 104		3 095 16 807	2 371	287 31 235	2 455	1 686	1 494	9 293	2 122 100 827	3 974	2 004	9 456 17 233 230 499
	DK	228	24	179	2 612		1 669	368	1 347	716	655	138	316	602	2 947	833	5 253	31	95	3 889 21 898
	ES	155	9	57	2 686	157		110	9	1 163	120	87	19	869	159	398	203	10	45	3 430	9 684
	FI	97	23	42	758	400	671		53	203	21	71	27	233	777	63	3 216	4	10	1 175	7 842
	IS	13	2	17	205	1 800	59	48		105	64	37	29	49	482	872	478	25	56	232	4 570
	IT	588	6	67 10 206	149	1 508	136	17		11	218	8	531	121	417	199	151	40	3 508 17 879
	LT	48	8	54	1 269	158	628	87	23	204		18	163	116	199	122	233	3	5	2 638	5 975
	LU	31	3	13	911	99	79	35	19	175	4		4	97	12	23	73	5	11	166	1 760
	LV	18	8	6	302	45	18	46	5	51	138	6		20	34	26	67	1	2	196	987
	NL	616	50	298 10 493	533	3 774	322	54	1 278	54	191	33		731	1 020	900	45	138	7 953 28 482
	NO	69	17	43	709	3 093	789	855	412	146	108	23	69	287		281	5 083	5	61	1 395 13 444
	PL	538	15	63 14 417	111	341	20	46	505	6	23	3	557	127		303	2	10	5 219 22 306
	SE	298	73	104	1 634	3 159	1 348	3 403	413	463	48	127	62	522	4 746	354		27	29	3 905 20 713
	SI	311	3	14	589	5	27	4	1	186	1	24	0	30	5	5	38		6	70	1 319
	SK	177	1	629	255	4	16	1	0	42	0	2	0	13	3	15	8	3		69	1 235
	UK	1 593	4 060	2 692 12 579	1 932 33 431	682	103	5 270	1 074	362	324	5 943	1 993	6 507	2 666	0	1 053		82 264
	Total	22 758	4 600 13 339 66 905 14 933 61 649	8 758	2 818 42 914	4 887	3 062	2 619 19 676 14 561 114 854 23 117	2 724 22 364 52 567 499 105
	Source: Eurostat

Table 3 .

 3 Estimates of adjustment factors for immigrationand emigration, 2002-2007

		Immigration	Emigration
	Austria	1.06	1.74
	Cyprus	1.06	5.29
	Czech Republic	2.14	3.33
	Germany	1.03	0.69
	Denmark	0.74	0.80
	Spain	0.82	4.90
	Finland	1.26	1.22
	Iceland	0.57	0.74
	Italy	1.42	2.92
	Lithuania	2.33	2.45
	Luxembourg	5.65	2.43
	Latvia	2.92	6.22
	Netherlands	0.97	1.25
	Norway	0.84	1.19
	Poland	17.85	10.64
	Sweden	1.00	1.21
	Slovenia	5.18	2.71
	Slovakia	18.90	43.69
	United Kingdom	1.21	1.18

Acknowledgements

This work was supported by a European Commission / Eurostat tender n° 2006/S100 106607 (OJ 27/05/2006) for the supply of statistical services. The authors would like to thank the other team members of the MIMOSA (MIgration MOdelling for Statistical Analyses) project for their comments and suggestions on earlier efforts (see http://mimosa.gedap.be).


Lilia A Chtcheglova
email: lilia.chtcheglova@jku.at

Linda Wildling

Jens Waschke

Detlev Drenckhahn

Peter Hinterdorfer

AFM Functional Imaging on Vascular Endothelial Cells

Keywords: VE-cadherin, F-actin, AFM, TREC VE-cadherin, F-actin, TREC, AFM

Vascular endothelial (VE)-cadherin is predominantly responsible for the mechanical linkage between endothelial cells, where VE-cadherin molecules are clustered and linked through their cytoplasmic domain to the actin-based cytoskeleton. Clustering and linkage of VEcadherin to actin filaments is a dynamic process and changes according to the functional state of the cells. Here nano-mapping of VE-cadherin was performed using simultaneous topography and recognition imaging (TREC) technique onto microvascular endothelial cells from mouse myocardium (MyEnd). The recognition maps revealed prominent "dark" spots (domains or clusters) with the sizes from 10 to 250 nm. These spots arose from a decrease of oscillation amplitude during specific binding between VE-cadherin cis-dimers. They were assigned to characteristic structures of the topography images. After treatment with nocodazole so as to depolymerize microtubules, VE-cadherin domains with a typical ellipsoidal form were still found to be collocalized with cytoskeletal filaments supporting the hypothesis that VE-cadherin is linked to actin filaments. Compared to other conventional techniques such as immunochemistry or single molecule optical microscopy, TREC represents an alternative method to quickly obtain the local distribution of receptors on cell surface with an unprecedented lateral resolution of several nm.

INTRODUCTION

The vascular endothelium forming a first cellular barrier on the inner surface of blood vessels, represents one of the best studied cellular systems where vascular endothelial (VE)-cadherin (7B4/cadherin-5) exerts a relevant role in cell-cell adhesion as well in other important physiological processes such as the control of macromolecular permeability, transmigration of leukocytes, and vascular homeostasis [START_REF] Dejana | The role of adherents junctions and VEcadherin in the control of vascular permeability[END_REF]. VE-cadherin belongs to the wide spread und functional important family of calcium-dependent cell adhesion molecules, cadherins, which are single-pass transmembrane glycol-proteins known to be crucial for calciumdependent, homotypic (or homophilic) cell-cell adhesion [START_REF] Hyafil | Cell-cell interactions in early embryogenesis: a molecular approach to the role of calcium[END_REF][START_REF] Takeichi | Morphogenetic roles of classical cadherins[END_REF][START_REF] Gumbiner | Cell adhesion: the molecular basis of tissue architecture and morphogenesis[END_REF][START_REF] Patel | Cadherin-mediated cell-cell adhesion: sticking together as a family[END_REF]). VE-cadherin is the major adhesion molecule of endothelial adherent junctions and known to be primarily responsible for mechanical linkage between endothelial cells. Recent studies indicate that VE-cadherin-mediated binding is disrupted during TNF-α-induced endothelial barrier breakdown in vivo since a tandem peptide targeting the VE-cadherin adhesive interface blocked the permeability increase in response to TNF-α (Heupel, 2009). It is believed that VE-cadherin molecules are clustered and linked through their cytoplasmic domain to the actin-based cytoskeleton (Figure 1) [START_REF] Hirano | Calcium-dependent cell-cell adhesion molecules (cadherins): subclass specificities and possible involvement of actin bundles[END_REF][START_REF] Yap | Molecular and functional analysis of cadherinbased adherent junctions[END_REF][START_REF] Vincent | VE-cadherin: adhesion at arm's length[END_REF]. This is supported by the findings that depolymerization of actin filaments reduced VE-cadherin-mediated binding and drastically increased permeability in vivo ( [START_REF] Baumgartner | Cadherin function probed by laser tweezer and single molecule fluorescence in vascular endothelial cells[END_REF][START_REF] Waschke | Regulation of actin dynamics is critical for endothelial barrier functions[END_REF]. Therefore, cytoskeletal anchorage of cadherin is thought to be important for the strengthening of cadherin-mediated adhesion [START_REF] Yap | Molecular and functional analysis of cadherinbased adherent junctions[END_REF][START_REF] Kemler | Uvomorulin-catenin complex: cytoplasmic anchorage of a Ca 2+dependent cell adhesion molecule[END_REF][START_REF] Angst | The cadherin super-family: diversity in form and function[END_REF] mediated by EC domains (Schan, 2000), which enable to associate in parallel lateral cis-dimers in physiological Ca 2+ concentration (~ 1.8 mM) [START_REF] Shapiro | Structural basis of cell-cell adhesion by cadherins[END_REF]Nagar, 1996;[START_REF] Brieher | Lateral dimerization is required for the homophilic binding activity of C-cadherin[END_REF][START_REF] Takeda | E-cadherin functions as a cisdimer at the cell-cell adhesive interface in vivo[END_REF][START_REF] Koch | Homophilic adhesion by cadherins[END_REF][START_REF] Baumgartner | Affinity of transinteracting VE-cadherin determined by atomic force microscopy[END_REF] (Figure 1 B). The parallel cis-dimer is appeared to be the basic structural functional unit to promote a homophilic bond between cells [START_REF] Shapiro | Structural basis of cell-cell adhesion by cadherins[END_REF][START_REF] Brieher | Lateral dimerization is required for the homophilic binding activity of C-cadherin[END_REF][START_REF] Takeda | E-cadherin functions as a cisdimer at the cell-cell adhesive interface in vivo[END_REF]Chappuis-Flament, 2001) and these cadherin dimers are assumed to contain one or two binding sites [START_REF] Shapiro | Structural basis of cell-cell adhesion by cadherins[END_REF][START_REF] Yap | The juxtamembrane region of the cadherin cytoplasmic tail supports lateral clustering, adhesive strengthening, and interaction with p120 ctn[END_REF][START_REF] Takeda | E-cadherin functions as a cisdimer at the cell-cell adhesive interface in vivo[END_REF][START_REF] Koch | Homophilic adhesion by cadherins[END_REF]) to form transinteracting antiparallel tetramers or adhesion dimers [START_REF] Koch | Homophilic adhesion by cadherins[END_REF] (Figure 1 C). It was early suggested that by repeating such trans-interactions, linear cell-adhesion zipper, which bridge two adjacent cells, can be formed [START_REF] Shapiro | Structural basis of cell-cell adhesion by cadherins[END_REF]. However, a quite different picture of twodimensional molecular organization of cadherins in desmosomes [START_REF] He | Untagling desmosomal knots with electron tomography[END_REF] and on the free cell surface [START_REF] Iino | Single molecule imaging of green fluorescent proteins in living cells: E-cadherin forms oligomers on the free cell surface[END_REF][START_REF] Baumgartner | Cadherin function probed by laser tweezer and single molecule fluorescence in vascular endothelial cells[END_REF] has been elucidated. Indeed, individual cadherin molecules have the tendency to form discrete groups [START_REF] He | Untagling desmosomal knots with electron tomography[END_REF] or oligomers [START_REF] Iino | Single molecule imaging of green fluorescent proteins in living cells: E-cadherin forms oligomers on the free cell surface[END_REF] or microdomains [START_REF] Baumgartner | Cadherin function probed by laser tweezer and single molecule fluorescence in vascular endothelial cells[END_REF] and it has been consequently proposed that these preformed cadherin blocks represent the basic building structures for the two-dimensional structures of cell-cell junctions. Moreover, the strength of intercellular adhesion depends on both the surface concentration and adhesive affinity (affinity for trans-interaction) of cadherins. The observation that cadherin molecules cluster on the cell surface led to the model that high local concentrations are required for the strong binding between cells. It has been demonstrated that the life time of VE-cadherin trans-interaction is only 550-700 ms which occurs at extremely low affinity (K D ~ 10 3 -10 5 M -1 (Baumgartner, 2000a, b), K D ~ 10 4 M -1 (Baumgartner, 2002a)). Such very weak binding properties require the tethering of cadherins to the cytoskeleton in order to guarantee rapid rebinding after dissociation (Baumgartner, 2002b[START_REF] Baumgartner | Cadherin function probed by laser tweezer and single molecule fluorescence in vascular endothelial cells[END_REF] Without tethering to the cytoskeleton, cadherins would be driven apart by increased lateral mobility (~10-to 20-fold increase, [START_REF] Baumgartner | Cadherin function probed by laser tweezer and single molecule fluorescence in vascular endothelial cells[END_REF] and would require a prolonged time interval for new collision and rebinding. Moreover, such weak binding is partially compensated by a high level of active plasmalemmal VE-cadherin cis-dimers on the cell surface (~ 5x10 3 per 1 µm 2 of cell surface (Baumgartner, 2002a)).

Despite this large body of evidence supporting that VE-cadherin molecules are anchored to actin filaments and that anchorage is crucial for adherent junction stability and maintenance of endothelial barrier functions the exact mechanisms underlying this linkage remain to be elucidated. At least in E-cadherin-based adherent junctions a direct anchorage of the cadherin-catenin complex to actin filaments was revealed not to exist (Shapiro and Weiss, 2009). With single molecule fluorescence it was demonstrated that the size of microdomains enriched in actively trans-interacting VE-cadherin was up to ~ 1 µm 2 and these hot spots depended on an intact actin filament system [START_REF] Baumgartner | Cadherin function probed by laser tweezer and single molecule fluorescence in vascular endothelial cells[END_REF]. However, due to the limited lateral resolution (from few tens to 200 nm), the recognition sites cannot be resolved on the nm scale nor can they be correlated to topography features. With the recent development of simultaneous topography and recognition imaging (TREC) on model systems (Stroh, 2004a(Stroh, , 2004b;;[START_REF] Ebner | Localization of single avidin-biotin interactions using simultaneous topography and molecular recognition imaging[END_REF] and further progress on cells [START_REF] Chtcheglova | Nano-scale dynamic recognition imaging on vascular endothelial cells[END_REF][START_REF] Chtcheglova | Localization of ergtoxin-1 receptors on the voltage sensing domain of hERG K + channel by AFM recognition imaging[END_REF], it has been illustrated the local distribution of VE-cadherin on vascular endothelial cell surface with unprecedented lateral resolution of 5 nm [START_REF] Chtcheglova | Nano-scale dynamic recognition imaging on vascular endothelial cells[END_REF]. Therefore, in the present study we aimed to investigate the local organization of VE-cadherin domains in myocardial microvascular endothelial cells (MyEnd) and to correlate the receptor localization with cell membrane topographical features such as actin filaments.

MATERIALS AND METHODS

Cell culture

A well characterized immortalized microvascular endothelial cell line from mouse myocardium (MyEnd) [START_REF] Baumgartner | Cadherin function probed by laser tweezer and single molecule fluorescence in vascular endothelial cells[END_REF][START_REF] Adamson | Rho and rho kinase modulation of barrier properties: cultured endothelial cells and intact microvessels of rats and mice[END_REF] was used. Cells were grown in Dulbecco´s modified Eagles medium (DMEM), supplemented with 50 U/ml penicillin-G, 50 µg streptomycin, and 10% fetal calf serum (FCS) in a humidified atmosphere (5% CO 2 ) at 37 °C. Cultures were passaged twice a week. For experiments, cells were seeded onto gelatinecoated glass slides (final concentration of gelatine 0.02 %), grown until 70-80 % confluence.

To perform AFM measurements, cells were than gently fixed with glutaraldehyde (EM grade 1, Sigma-Aldrich). The solution of glutaraldehyde monomers was added into the medium (final concentration of glutaraldehyde ~ 0.5%) and cells with fixative were subsequently incubated in a humidified atmosphere at 37 °C overnight. Passages 5-20 were used. For pharmacological treatments of MyEnd cortex, stock solutions of nocodazole (4 mg/ml in DMSO) were prepared. The final concentration of nocodazole was ~ 50 µM. Since DMSO can increase the temperature upon mixing with aqueous solutions, first ~ 100 µl of culture medium and mixed with ~ 8 µl of stock drug solution. After reaching room temperature, this solution was added to the Petri dish containing the grown cells and mixed gently with the culture medium (~ 2 ml) to ensure rapid drug delivery to cells. MyEnd cells were than placed at 37 °C for about 80 min and subsequently gently fixed with glutaraldehyde for further AFM measurements.

AFM tip functionalization with VE-cadherin-Fc molecules via PEG-linker

Attachment of a ligand molecule onto the AFM tip converts it into a biospecific molecular sensor to detect a corresponding receptor on a sample surface. Since poly-ethylene glycol (PEG) chains between AFM tips and ligand molecules are particularly advantageous for use in molecular recognition force spectroscopy (MRFS) [START_REF] Hinterdorfer | Detection and localization of single molecular recognition events using atomic force microscopy[END_REF], they are essentially necessary for TREC measurements [START_REF] Preiner | Simultaneous topography and recognition imaging: physical aspects and optimal imaging conditions[END_REF].

Magnetically coated AFM tips (abbreviated as MAC tips) (Agilent Technologies, Tempe, AZ, USA) were firstly extensively washed in chlorophorm and ethanol, dried with nitrogen and subsequently incubated in ethanolamine-HCl solution (Sigma, 550 mg/ml in dimethylsulfoxide (DMSO)) overnight in order to functionalize the tip surface (Si 3 N 4 ) with amino (-NH 2 ) groups [START_REF] Riener | Simple test for single molecule recognition force microscopy[END_REF] (abbreviated as VE-cadherin-Fc), in which the complete extracellular domain of mouse VEcadherin was fused to the Fc fragment of human IgG (Figure 3) (Baumgartner, 2000a;2000b) is coupled to the free-tangling end (in this study aldehyde residue) of PEG linker [START_REF] Bonanni | Single molecule recognition between cytochrome C 551 and goldimmobilized azurin by force spectroscopy[END_REF] (Figure 2, step III).

AFM topographical and dynamic recognition imaging (TREC)

Both AFM topographical and recognition images were acquired in MAC (magnetic alternating current) mode [START_REF] Han | A magnetically driven oscillating probe microscope for operation in liquids[END_REF] using a PicoPlus AFM (Agilent Technologies, Chandler, USA) with magnetically coated tips having a nominal spring constant of 100 pN/nm with a quality factor Q of ~ 1 in liquid. The imaging of living cells was also performed in contact AFM mode. All images were taken in Hank´s balanced salt solution (HBSS) containing 1.8 mM Ca 2+ at room temperature. The TREC data were obtained by scanning ~ 2x2 µm 2 area of the cell surface with a lateral scan speed of ~ 3.0 µm/sec at 256 or 512 data points per line using a commercially available PicoTREC box (Agilent Technologies, Chandler, USA). In order to block the specific interactions between VE-cadherin-Fcfunctionalized tip and MyEnd cell surface, the calcium chelator, 5 mM of ethylenediaminetetraacetic acid (EDTA) was gently injected into the fluid cell of the AFM during scanning.

The operating principle of TREC can be described as following (Figure 4). The functionalized tip with a ligand molecule via a PEG linker is oscillated close to its resonance frequency (~ 10 kHz). The set-point amplitude is adjusted to a value close to the free amplitude. The free amplitude is adjusted to be less that the extended PEG-linker to provide the proper recognition image with high efficiencies and repeatability [START_REF] Chtcheglova | Nano-scale dynamic recognition imaging on vascular endothelial cells[END_REF][START_REF] Preiner | Simultaneous topography and recognition imaging: physical aspects and optimal imaging conditions[END_REF]. When such a tip-tethered ligand binds to its receptor on the sample surface (i.e., when specific molecular recognition occurs), the PEG linker will be stretched during upward movement of the cantilever. The resulting loss in energy will in turn cause the top peaks of the oscillations to be lowered. The ligand-receptor binding events thus become visible due to a reduction in the oscillation amplitude (i.e. recognition signal), as a result of specific recognition during the lateral scan. In contrast to the conventional MAC mode, which exploits a peak-to-peak value of oscillating amplitude (full amplitude) as a feedback parameter, TREC uses the lower part of the oscillation (called as half-amplitude feedback) to drive a feedback loop for obtaining the topography image, whereas the upper part of the oscillation is used for generation of the recognition image (Figure 4). Moreover, using such sophisticated feedback allows accurate determination of the surface topography [START_REF] Preiner | Simultaneous topography and recognition imaging: physical aspects and optimal imaging conditions[END_REF]. To provide more details, the time-resolved deflection signal of the oscillating cantilever is low-pass filtered to remove the thermal noise, the DC (direct current) is offset levelled and amplified before splitting into the lower (U down ) and upper (U up ) parts of the oscillations. The signal passes a trigger threshold on each path, and the lower peak of each oscillation period is determined by means of sample and hold analysis. Subsequent peaks form a staircase function, which is then filtered and fed into the AFM controller, where U down drives the feedback loop to record the topography image and U up provides the information to establish the corresponding recognition image. Moreover, the utilization of cantilevers with low Q factor (~ 1 in liquid) in combination with a proper chosen driving frequency and amplitude regime enables the that both types of information are unrelated [START_REF] Ebner | Localization of single avidin-biotin interactions using simultaneous topography and molecular recognition imaging[END_REF][START_REF] Preiner | Simultaneous topography and recognition imaging: physical aspects and optimal imaging conditions[END_REF].

Image processing

Topographical images are represented either by a 512 x 512 or 256 x 256 matrixes. The collected AFM raw data (height image) are used as initial data, which were subsequently imported and analyzed into MATLAB Version 7 (MathWorks Inc., Natick, NA). The further line-wise flattening, plane fitting and contrast enhancement have been performed as in [START_REF] Kienberger | Improving the contrast of topographical AFM images by a simple averaging filter[END_REF]. All programs employed in this work can be found on MATLAB fileexchange.

RESULTS AND DISCUSSION

Morphology of MyEnd cells

MyEnd cells grown to subconfluent monolayers and the corresponding AFM topography images (Figure 5) illustrate a characteristic morphology that was previously obtained with light microscope [START_REF] Baumgartner | Cadherin function probed by laser tweezer and single molecule fluorescence in vascular endothelial cells[END_REF]. These cells are organized into whirl-like formations, they are highly elongated (~ 80 or even more µm in length, with tens of µm in diameter), and the cell heights vary from ~ 100 nm at the periphery to ~ 1-2 µm on the nucleus (Figure 5 A,B).

In order to overcome the circumstances for the recognition imaging such as the cell elasticity and the lateral diffusion of receptors (e.g. of VE-cadherin [START_REF] Baumgartner | Cadherin function probed by laser tweezer and single molecule fluorescence in vascular endothelial cells[END_REF]), a fixation procedure as for immunochemistry experiences can be applied. In our studies, the cells were fixed with glutaraldehyde. The fixation procedure makes the soft biological objects stiffer and as a consequence, it generally gives access to high lateral resolution in AFM images as it was observed with proteins (GroES) [START_REF] Mou | High resolution surface structure of E. coli GroES oligomer by atomic force microscopy[END_REF]. However, the common fixation of cells in buffer solution at room temperature causes the smoothing of the cell surface with the loss of most filamentous features, which were seen in AFM pictures of living cells (Figure 5 A) [START_REF] Pesen | Micromechanical architecture of the endothelial cell cortex[END_REF] as well nucleus become visible presumably due to the membrane collapse during dehydration caused by the fixation procedure. When the unpurified solution of glutaraldehyde is used the undesirable formation of globular large features on the cell surface (e.g. polymers of glutaraldehyde) can be detected as well. We found a method to gently fix the cells with the solution of glutaraldehyde containing monomers (EM grade) similar to the procedure described by [START_REF] Oberleithner | Endothelial cell swelling by aldosterone[END_REF]. The prepared stock solution of glutaraldehyde (~ 200 µL, 5% in HBSS) was added and gently mixed with the culture medium (~ 2 ml), the cells were then incubated at 37 ° C as cultured before (for more details see Materials and Methods section). Such method is likely prevent unexpected osmotic and temperature changes in the cell culture medium. As a result, the cell volume as well the filamentous structures of cytoskeleton are mostly preserved (Figure 5 B) that makes possible further AFM investigations at a subcellular level. Figure 5 D, E represent typical AFM images of gently fixed MyEnd cell membrane at high magnification of ~ 5x5 µm 2 . The complex filamentous networks with wide range of forms can be usually observed.

Following treatment with nocodazole to depolymerize microtubules the filamentous structure of the cell cortex was conserved (Figure 5 E).

Nano-mapping of VE-cadherins on gently fixed MyEnd cell surface treated with nocodazole

Since VE-cadherin is cell specific and firmly located at intercellular junctions [START_REF] Lampugnani | Interendothelial junctions: structure, signaling and functional roles[END_REF][START_REF] Baumgartner | Cadherin function probed by laser tweezer and single molecule fluorescence in vascular endothelial cells[END_REF], TREC images were collected on the contact region between adjacent cells with VE-cadherin-Fc-functionalized tip in calcium reach buffer solution (i.e. HBSS containing 1.8 mM Ca 2+ ). As previously observed the topography of a scanned cell surface area (Figure 6 A) demonstrates a complex picture of linear and branched filaments with some globular features. In addition, the enlarged number of filaments with a typical width of ~ 60-70 nm is clearly visible (Figure 6 A).The local roughness was estimated as ~ 24 nm and the lateral resolution as ~ 5 nm. In our first TREC studies on MyEnd cells [START_REF] Chtcheglova | Nano-scale dynamic recognition imaging on vascular endothelial cells[END_REF] we observed, that VE-cadherin forms microdomains with dimensions [START_REF] Chtcheglova | Nano-scale dynamic recognition imaging on vascular endothelial cells[END_REF], the number of single events was significantly decreased. The spots with dimensions of ~ 8-16 nm were identified as single cisdimers taking into account the size of the VE-cadherin cis-dimer (diameter ~ 3 nm) and the free orientation of PEG-linker leading to the specific binding even before/after the binding site position. Nevertheless, the drastical increase in the spot sizes accompanying by practical disappearance of small domains (Figure 7 B) and consequent rise in the number of active cisdimers (more than 6000/µm 2 ) imply the complete clustering of VE-cadherin.

The specificity of VE-cadherin recognition process has been verified by addition of calcium chelator, 5 mM EDTA, in the liquid flow cell in which the sample was imaged.

Indeed, in the absence of Ca 2+ functional VE-cadherin cis-dimers on the tip dissociate into inactive monomers [START_REF] Baumgartner | Affinity of transinteracting VE-cadherin determined by atomic force microscopy[END_REF] (Figure 2 B) that leads to the blocking of specific VE-cadherin trans-binding. This effect results in the disappearance of almost all binding events in the recognition image (Figure 6 B'), whereas no change in the topography image has been observed (Figure 6 B). The resolution of the recognition technique is generally limited by the linker length (here to ~ 8 nm).

The receptor binding sites can properly be assigned to the topographical features for heterogeneous biological surfaces such as cells or membrane fragments. Figure 8 illustrates the superimposition of the recognition map (Figure 6 A') onto the corresponding topographical image (Figure 6 A). This procedure allows revealing the locations of receptors in the topographical image with high lateral resolution and high efficiency. Repeated measurements indicate that the size of VE-cadherin domains ranges from 10 to as much as 250 nm. In addition, these domains can be easily aligned to the filaments seen in topography image (Figure 8). These observations directly illustrate the clustering of VE-cadherin cis-

CONCLUSION

It has been previously reported the potential use of AFM in order to localize and identify of membrane receptors [START_REF] Eppell | Cell-surface receptors and proteins on platelet membranes imaged by scanning force microscopy using immunogold contrast enhancement[END_REF] and ion channels [START_REF] Smith | Localization of amiloridesensitive sodium channels in A6 cells by atomic force microscopy[END_REF]. However, these studies have to rely on the use of immunogold particles or fluorescent labeling that needs a combination of AFM with fluorescence microscopy. Such an approach makes it easier AFM topography imaging, however it certainly limits the imaging resolution to molecular scales (e.g. particle or fluorescent label size) at best. Here and previously [START_REF] Chtcheglova | Nano-scale dynamic recognition imaging on vascular endothelial cells[END_REF] we demonstrated the applicability of AFM based TREC technique to gently fixed endothelial cells to visualize VE-cadherin binding sites by using VE-cadherin-Fc -functionalized AFM tips. The recognition map of VE-cadherins contained "dark" spots due to decrease of oscillation amplitude of AFM tip during specific binding between VE-cadherin cis-dimers. In the present study, VE-cadherins were again not uniformly distributed but located mostly along the F-actin filaments, and organized in microdomains or clusters with dimensions from 10 to 250 nm, which were at least four times smaller that observed by using single molecule optical microscopy [START_REF] Baumgartner | Cadherin function probed by laser tweezer and single molecule fluorescence in vascular endothelial cells[END_REF]. The effect that most VE-cadherin domains were found on the top of filaments (Figure 8) clear demonstrates the anchorage of VE-cadherin to the F-actin filaments. The typical sizes (~ 100 and 180 nm) (Figure 6 B) and ellipsoidal shapes (Figure 7, 8) of spots indicate the complete clustering of VE-cadherin. The specific Ca 2+ dependent VEcadherin trans-interaction was abolished by addition of EDTA that lead to the disappearance of specific domains in recognition images.

In addition, TREC technique offers the advantage that structural information (e.g. topography) and recognition maps can be recorded simultaneously at the same speed as that used for the conventional topographic imaging, typically several minutes per image. Another major improvement of TREC over conventional fluorescence approaches to cells is the spatial and recognition resolution obtained in the present work of ~ 5 and ~ 8 nm, respectively. Therefore, the exploitation of dynamic recognition imaging allows to detect single molecular interactions, and thus visualize, identify, and quantify local receptor binding sites and to assign their locations to the topographical features of the cell surface with several nm accuracy. We strongly believe that the described here TREC methodology can be successfully

PERSPECTIVES

The TREC approach to live cell investigations represents certainly a more challenging task. Some TREC images collected on live vascular endothelial cells with antibody-coated tip have been recently reported ( [START_REF] Vliet | Probing drug-cell interactions[END_REF]. However, in these studies the experimental conditions such as the specificity, efficiency and repeatability of recognition were not described in details. It is important to note several current limitations of this contactbased approach such as scanning rate. For instance, the rates of lateral diffusion and internalization of receptors within the cell membrane should be considered with respect to experimentally attainable scanning rates and resolutions. The potential to induce confusing cell responses by mechanical perturbing of the cell surface and its receptors during scanning should be also recognized. Nevertheless, by taking account these constrains with further improvements of AFM (e.g. resolution and acquisition time) we expect that this dynamic mapping of ligand-receptor interactions at the single cell level will be valid to living cells. Blocking experiments did not affect the membrane topography (B).

  (Figure 2, step I (a)). Next, PEG chains are attached with the amino groups on the tip by amide bond formation, for which, PEG linkers possesses an activated carboxy (-COOH) group in the form of an N-hydroxysuccinimide ester (NHS ester) (Figure2, step II). In the last step, a ligand molecule, a recombinant VE-cadherin

  to ~ 100 nm, which were nonuniformly distributed on the cellular surface.Interestingly, only a few domains (~ 4 from ~ 56 detected) were found directly on the top of filaments and most spots were located near and between filaments, thus indicating the incomplete clustering of VE-cadherin molecules. In this study the corresponding simultaneously recorded recognition maps contain again "dark" spots (Figure6B) (amplitude reduction up to 2 nm) with inhomogeneous distribution. These dark spots reflect the microdomains typically with ellipsoidal form (Figure7 A) and dimensions from ~10 to ~250 nm, with a mean ± SD of 162±55 nm (n=56) for the long axis (Figure7B). A closer look at the recognition spots (Figure 7 A) reveals their characteristic ellipsoidal form and that they consist of one large domain with typical sizes of ~ 80 nm (Figure 7 B) or ~ 180 nm surrounded by few smaller domains (10-20 nm). With comparison to the results observed on the early confluent MyEnd cells

  surface and as well support the hypothesis of VE-cadherin anchorage to the Factin cytoskeleton.

  adherent cells or extracted cellular membranes in order to identify locally different receptor binding sites.

Figure 1 .

 1 Figure 1. A) Scheme of VE-cadherin domain organization. As other cadherins VE-cadherin is characterized by the presence of 5 sequence repeats of ~ 110 amino acids, which form folded Greek-key topology extracellular (EC) domains. The connections between successive domains are rigidified by conserved Ca 2+ -binding sites representing the most significant feature of the repeat sequences. The cytoplasmic domain of VE-cadherin includes the "juxtamembrane region" that binds p120-catenin (p120 ctn ) and the "catenin binding domain" that interacts with β-catenin and plakoglobin. B) In the presence of extracellular Calcium (1.8 mM) the rigid cadherin extracellular domains (shown as grey rods) enable to associate in functional cis-dimers. The calcium binding sites between extracellular domains are shown as stars. C) These active cadherin cis-dimers promote a homophilic bond between adjacent cells by forming a trans-adhesion dimer.

Figure 2 .

 2 Figure 2. Coupling scheme for tethering proteins to AFM tips by using aldehyde-PEG-NHS linker. I) The aminofunctionalization of silicon nitride tips can be performed either with ethanolamine-hydrochloride (a, present work) or in gas phase with 3minopropyltriethoxysilane (APTES) (b). II) After aminofunctionalization a poly(ethelene glycol) (PEG) chain is attached via its amino-reactive terminus (e.g. NHS-ester). III) The aldehyde residues on the free end can be further conjugated to the amino groups of the lysine residues of the protein. Reaction of protein and aldehyde results in the formation of Schiff base, which is subsequently fixed by reduction with NaCNBH 3 .

Figure 3 .

 3 Figure 3. Active (A) and inactive (B) forms of recombinant VE-cadherin cis-dimer, which was attached to the AFM tip via PEG-linker and scanned over MyEnd cell surface (C).

Figure 4 .

 4 Figure 4. Schematic of TREC functioning. The raw cantilever deflection signal is fed into the TREC box, where the maxima (U up ) and the minima (U down ) of each oscillation period are used for the recognition and the topography image, respectively.

Figure 5 .

 5 Figure 5. AFM topography images of MyEnd cells obtained either with contact mode (A) or MAC mode (B-E). A) Living cells. B, D) Gently fixed cells and C, E) cells treated with nocodazole and subsequently gently fixed with glutaraldehyde. Cells were grown either in early subconfluent state (images were taken after 1-2 days after seeding) (A, B and D) or in

Figure 6 .

 6 Figure 6. Simultaneously topography (A) and recognition images (A') recorded on MyEnd cell surface (2x2 µm 2 ) treated with 50 µM of nocodazole for 80 min and subsequently gently fixed with glutaraldehyde. The reduction of oscillating amplitude was used as recognition signal. The recognition efficiency was generally high and remains so on several subsequent rescans. After addition of 5 mM EDTA in the fluid cell the recognition spots (dark red domains) disappeared (B') as the active VE-cadherin-Fc cis-dimers on the AFM tip dissociated in inactive monomers, thus abolishing specific VE-cadherin trans-interaction.

Figure 7 .

 7 Figure 7. A) Example of a typical VE-cadherin domain with ellipsoidal form (a≈65 nm; b≈140 nm) embedded by several (4-5) spots with smaller size of 5 -40 nm. The domain was magnified from the corresponding recognition map (Figure 6 A'). Recognition domains were depicted by threshold analysis (threshold = -1.7 nm) and bordered by white lines. B) Distribution of VE-cadherin size spots obtained on cell surface treated with nocodazole.

Figure 8 .

 8 Figure 8. Locations of VE-cadherin domains (in green) on the MyEnd cellular surface treated with nocodazole (topographical image from Figure 6 A). It is clear seen, that the most domains are detected on the actin filaments.

Figure 2 .Figure 3 .Figure 4 .Figure 5 .Figure 6 .Figure 8 .

 234568 Figure 1. A) Scheme of VE-cadherin domain organization. As other cadherins VE-cadherin is characterized by the presence of 5 sequence repeats of ~ 110 amino acids, which form folded Greek-key topology extracellular (EC) domains. The connections between successive domains are rigidified by conserved Ca2+-binding sites representing the most significant feature of the repeat sequences. The cytoplasmic domain of VE-cadherin includes the "juxtamembrane region" that binds p120-catenin (p120ctn) and the "catenin binding domain" that interacts with β-catenin and plakoglobin. B) In the presence of extracellular Calcium (1.8 mM) the rigid cadherin extracellular domains (shown as grey rods) enable to associate in functional cis-dimers. The calcium binding sites between extracellular domains are shown as stars. C) These active cadherin cis-dimers promote a homophilic bond between adjacent cells by forming a trans-adhesion dimer. 238x92mm (300 x 300 DPI)

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Acknowledgements

This work was supported by European Community (EC) project "Bio-Light-Touch" (FP6-2004-NEST-C-1-028781).

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Journal of Molecular Recognition