Assad L Baunto
email: assad.abdullahbaunto@worc.oxon.org

Christian Bordes
email: christian.bordes@univ-paris1.fr

Samuel Maveyraud-Tricoire
email: samuel.maveyraud-tricoire@unilim.fr

Philippe Rous
email: philippe.rous@unilim.fr

SAFETY AND EFFICIENCY OF THE FINANCIAL SYSTEM

Keywords: Friedman, GARCH, T-GARCH, Bai-and-Perron technique, band pass filter. JEL classification: E31, E32, E41, E51

This paper aims to provide a unified theoretical framework of the two hypotheses proposed by Friedman: (i). increased variability of money supply results in the decline of income velocity of money and (ii) high inflation leads high variability of inflation which reduces potential output growth. This paper also provides empirical investigation to validate Friedman's hypotheses using Philippine data. The Philippine economy experienced persistently higher and more variable inflation rate and weaker macroeconomic performance relative to other Asian countries, and these characteristics provide ample opportunity to evaluate Friedman's proposals at work. Utilizing original methodologies (e.g. band-pass filter), our findings validate both proposals.

Introduction

Traditionally, inflation in the Philippines has tended to be consistently higher and more variable than in other Asian countries. Historically this feature has often been linked to shocks or disturbances in various areas of the economy, notably the external (which relates to the balance of payments), real (which relates to output or production), and monetary sectors (sharp swings in monetary policy) [Debelle and Lim, 1998;Bangko Sentral ng Pilipinas, 2001]. This last aspect -the origins of shocks in the Philippines monetary sector and their consequences on macroeconomic performance from the mid-eighties until today -is the main subject of this paper. To analyze this question consistently, we propose a theoretical framework incorporating two fundamental relationships enounced in various contributions by Milton Friedman: the first one is relative to the origins to monetary disturbances and emphasizes the role of money supply shocks; the second one is relative to the (negative) consequences of this monetary uncertainty on economic growth. In each case, these two relationships have been the subject of a vast econometric literature where they are examined separately. For each one, while analyzing the Philippines case, we propose an original procedure to conduct an econometric test of its validity.

The paper is organized in the following way: the main stylized facts relative to the macroeconomicinflation and growth -performances and monetary evolution in the Philippines are presented in section 1; the theoretical framework encapsulating the two main relationships relative to the links between monetary disturbances and macroeconomic performance is proposed in section 2 ; section 3 examines the origins of monetary disturbances in the Philippines by using an original procedure; section 4 do the same for their consequences on macroeconomic performance.

Stylized facts in the Philippines

The history of the Philippine economy beginning early 1980s is marked by episodes of instability. Over the span of nearly three decades, the economy experienced three recessions, 1984-85, 1991 and the 1998, which hampered its chances of becoming one of East Asia's miracles.

The 1980s was the most turbulent period of the economy, when annual output growth registered -7.4% in 1984 and -7.2% in 1985, the sharpest contraction ever experienced by the economy since post war. Annual inflation rates recorded double-digit figures over the period 1982-85 and in 1984 it reached an all-time high record of 49.3%.

The conduct of erratic monetary policy can be partly blamed for the large swings in output and inflation. Excessive money creation was a result of central bank's pursuit of multiple objectives including monetary aggregate targeting in conjunction with exchange rate targeting and output-growth targeting [START_REF] Gochoco-Bautista | An Assessment of the Usefulness of Money for Policy in the Philippines[END_REF].

The collapse of the peso in 1983 exacted large losses to the central bank and, eventually, added constraints to meeting its monetary aggregate targets. Central bank's accommodation of chronic public sector deficits and engagement in development financing strained its balance sheet, which contributed to the distortions of monetary policies and restrained achievement of stable domestic price level. According to Gochoco-Bautista, the liabilities of the central bank were serviced by infusing more money in the economy but, with guidance from IMF's country programme, the central bank engaged in open market operations to tame inflationary pressures. [START_REF] Lamberte | Central Banking in the Philippines: Then, Now and the Future[END_REF] assessed that the central bank of the Philippines is unique among its counterparts in Asia as it had been incurring losses over the years before it was overhauled in 1993 and replaced by the Bangko Sentral ng Pilipinas. From 1983 to 1990, cumulative losses of the old central bank reached 143.7 billion pesos.

The balance-of-payment problem in the early 1980s, the political assassination of opposition leader Benigno Aquino in 1983 and the authorities' declaration of a moratorium on repayment of its debts starting 1984 helped pave way for the recession in 1984 and 1985. In response to the economic crisis, government authorities contracted money supply and imposed fiscal austerity that resulted in jacking up the domestic interest rates. The real sector was significantly affected. Restraining liquidity is not entirely a new policy strategy during economic slowdown and, in fact, meeting tight quarterly monetary targets in the 1980s became a common practice every time the economy faced deterioration of balance of payments and high inflation [START_REF] Lim | Philippine Monetary Policies: A Critical Assessment and Search for alternatives[END_REF]. These targets based on monetary base were achieved by influencing required reserve ratio and rediscount rates, and/or resorting to open market operations to buy and sell central bank bills and government securities which often times significantly affected total liquidity and credit in the financial sector.

Meanwhile, the financial scandal in 1981 when a famous businessman absconded his debts leaving several banks and financial companies on their knees, and the mounting debt crisis alerted the authorities to institute reforms in the financial sector. In 1983, the financial sector was deregulated. Expressed as a ratio of gross domestic product, monetary aggregates (M1, M2 and M3) consistently rose beginning 1986 after they were severely affected by the previous economic turmoil, and became relatively stable after the Asian financial crisis in 1998. Towards the latter part of the 1980s, the volume of M2 and M3 nearly equalized as the central bank gradually abolished deposit substitutes which originally formed part of M3.

Just as the economy saw encouraging signs of economic recovery in the second-half of 1980s with inflation rates albeit at double digits but significantly lower relative to previous levels, a mild recession occurred in 1991. Output contracted by 0.6% as the economy braced for moderate devaluation of the peso and oil price shock brought by the Gulf crisis; inflation rose to 19.3% (average inflation over the 1986-1990 period was 8.7%).

Two important events occurred in early 1990s. In 1992, the economy liberalized its foreign exchange market, which allowed domestic and foreign capital to move freely. Capital inflows rose dramatically reaching 10% of total output in 1996 compared to just 3% by end of the previous decade. But it soon dissipated when another crisis blew most economies in East Asia in [START_REF] Bai | Estimating and Testing Linear Models with Multiple Structural Changes[END_REF]. In June 1993, Republic Act No. 7653, otherwise known as the "New Central Bank Act", was issued establishing the Bangko Sentral ng Pilipinas, or BSP, and transforming the old central bank into the Central Bank Board of Liquidators. Compared to the old central bank, BSP is mandated to maintain its independence to prevent time-inconsistency problem, with price stability as its primary objective.

The economy achieved single-digit inflation rates in the mid-1990s onwards, despite high liquidity and large monetary expansion during the period until the East Asian financial crises when BSP periodically raised policy rates and the liquidity reserve ratios to stave off depreciation of the local currency.

The advent of financial deregulation and liberalization allowed the BSP to rethink the usefulness of its existing monetary framework. Under the monetary targeting framework, BSP uses M3 as its intermediate target for monetary policy and base money as its operating target. Whether the BSP can actually achieve the ultimate target of monetary policy-which are inflation, growth and employment-crucially depends on the predictability and stability governing the relationship between these variables and money, and the ability of the BSP to control broader monetary aggregates.

Recognizing the possible impacts of rapid financial innovations introduced in the economy, the BSP carefully assessed its position and modified its approach to monetary policy in 1995 putting greater emphasis on price stability over rigidly observing targets set for monetary aggregates. With hybrid approach (combination of both monetary targeting and inflation targeting) to conducting monetary policy, the BSP closely monitored movements of a wide range of key variables including interest rates, exchange rates, domestic credit and equity prices and a set of demand and supply and external economic indicators. In January 2000, the BSP approved the principle of inflation targeting and officially adopted inflation targeting as its main monetary framework two years hence.

To operationalise inflation targeting, the BSP underscored the following important elements: 1). setting up inflation range targets, with two-year target horizon, using the rate of change of 'headline' consumer price index, 2). making use of sophisticated forward-looking macroeconomic inflation-forecasting model to project future inflation, 3). relying on various monetary policy instruments, e.g. policy rates, to achieve inflation targets, 4). holding periodic meetings-every six weeks-of the Monetary Board, the policy-making body of the BSP to assess macroeconomic conditions and discuss future monetary policy stance, 5). publishing quarterly reports to explain BSP's policy stance and progress in meeting inflation targets, and 6). remaining accountable to the public in case actual inflation deviates from the targets (BSP, 2006).

Average inflation over 2002-06 was 5.3%. According to the official report by the BSP, inflation rates for the first-two years after the official adoption of inflation targeting are below their targets while from 2004 onwards actual inflation rates are slightly above their targets. Supply side factors are blamed for the deviations. Average output growth over the period was 5.2%.

Money and uncertainty: Two Friedmanite proposals

The past two decades and the current one have witnessed a literal flood of econometric literature dealing with main Friedman's proposals on the links between money, inflation and real growth. Expressed in broad terms, the literature has dealt with the two following overlapping proposals:

-Money Supply Volatility Hypothesis: "An exceptional volatility of monetary growth increases the degree of perceive uncertainty an thereby increases the demand for money" [START_REF] Friedman | Lessons from the 1979-82 Monetary Policy Experiment[END_REF]; and

-Inflation Variability and Growth Hypothesis: "Inflation, particularly highly variable inflation, interferes with growth by (a) introducing static into the messages transmitted by the price system, increasing the uncertainty facing individuals and business enterprises, which encourages them to divert attention from productive to protective activities, and (b) inducing governments to adopt such counterproductive false cures as price controls and incomes policy. These adverse effects have sometimes been more than offset by other forces, so that high inflation has not prevented rapid growth". [Friedman, 1980, pp. 55-6] The first hypothesis was a subject of much debate across academic and policy circles when a decline of income velocity of money, derived from the Quantity Theory of Money equation, was observed. Milton [START_REF] Friedman | Monetary Variability: United States and Japan[END_REF][START_REF] Friedman | Lessons from the 1979-82 Monetary Policy Experiment[END_REF] argued that the decline in M1 velocity that began in the United States in 1982 was due to an increase of the variability of the growth rate of money supply. An increase of money supply implies a rise of uncertainty, which leads to a rise of money demand for precautionary reasons and hence to a diminution of investment (as the increase of money demand implies a diminution of demand of financial assets). Ceteris paribus, income velocity should decrease. Hence, an active monetary policy is not accurate as its effects on activity are uncertain and may even be harmful6 .

Earlier accounts supporting Friedman's hypothesis includes [START_REF] Hall | Velocity and Variability of Money Growth: Evidence from Granger-Causality Test[END_REF] who suggested that money growth volatility in the US, proxied by eight-quarter lagged moving standard deviation of money, causes changes in velocity, in Granger sense. Other studies questioned the robustness of the specification of the model used by Hall and Noble and proposed, instead, that there may be other causal influences on velocity due, perhaps, to structural change in the short-run [START_REF] Brocato | Velocity and the Variability of Money Growth: Evidence from Granger-causality Tests[END_REF] including financial deregulation [START_REF] Mehra | Money Growth Volatility and High Nominal Interest Rates[END_REF][START_REF] Mehra | Velocity and the Variability of Money Growth: Evidence from Granger Causality Tests: Comment[END_REF], financial innovation [START_REF] Thornton | Velocity and the Volatility of Unanticipated and Anticipated Money Supply in the United Kingdom[END_REF] and disinflation. The instability of the relationship implies that there exists a shift in the process generating velocity rather than mere variability in the determinants of income velocity [START_REF] Mcmillin | The Velocity of M1 in the 1980s: Evidence from a Multivariate Time Series Model[END_REF]. A more recent assessment of this configuration points to the determinants of velocity driving the instability [START_REF] Chowdhury | The Velocity of US M2 in the 1990s: Some Further Evidence[END_REF].

Attempts that lend support to the hypothesis were found in both developed economies [START_REF] Chowdhury | Velocity and the Variability of Money Growth: Some International Evidence[END_REF][START_REF] Lynch | Velocity and the Variability of Anticipated and Unanticipated Money Growth: A Cross-country Comparison[END_REF][START_REF] Mccornac | Velocity and Money Growth Variability: Evidence from Japan[END_REF] and emerging economies (Baliamoune- [START_REF] Baliamoune-Lutz | Velocity Effects of Increased Variability in Monetary Growth in Egypt: A Test of Friedman's Velocity Hypothesis[END_REF]. In Malaysia, for instance, the hypothesis is found to be robust for M1 and M2 such that much of the volatility of money growth was attributed to the financial liberalisation process [START_REF] Choong | Financial Liberalization, Money Growth Variability and the Changing Characteristics of Money Velocity in Malaysia[END_REF]). But, still others argue in favour of "little general applicability" of the hypothesis [START_REF] Bordes | Friedman's Velocity Hypothesis: Some Evidence for France[END_REF][START_REF] Thornton | Friedman's Money Supply Volatility Hypothesis: Some International Evidence[END_REF][START_REF] Payne | Velocity and Money Growth Variability: Some Further Evidence[END_REF] or no causal relationship at all [START_REF] Arize | Money Growth Volatility and Income Velocity in the United Kingdom[END_REF], at least for the major industrialised economies. Finally, Friedman's hypothesis appears to be moot for narrower definitions of money, for example in UK [START_REF] Thornton | Velocity and the Variability of Monetary Growth in the United Kingdom[END_REF] and Egypt (Baliamoune- [START_REF] Baliamoune-Lutz | Velocity Effects of Increased Variability in Monetary Growth in Egypt: A Test of Friedman's Velocity Hypothesis[END_REF]). In the Philippines, no known work has been done yet on this topic and this motivates the paper.

This study employs a traditional Granger-causality test. However, this paper is different from previous literature, with the exception of Serletis and Shahmoradi (2005), as the variability of money growth is computed using a Generalised Autoregressive Conditional Heteroskedasticity, or GARCH, set up [START_REF] Bollerslev | Generalized Autoregressive Conditional Heteroskedasticity[END_REF]. One particular novelty of the model is that it avoids the ad hoc nature of calculating variability of money growth traditionally used in the literature that is based on moving standard deviation of the series. Instead, the GARCH model generates a stochastic volatility process of money (M1) growth, after controlling for other covariates that have potential influence on the money growth variability, e.g. output growth and interest rate rates (see also Serletis and Shahmoradi, 2005). Its great degree of flexibility allowed this paper to structure the conditional variance to accommodate the effect of high money growth translating into high money growth variability (see figures 1 and 2). Moreover, structural breaks of income velocity of M1 are taken into account as these shifts can imply non-stationarity of the series. If found stationary, after accounting for the breaks in detrending the series, cointegration techniques are not relevant and a simple Granger causality test can be implemented.

The second hypothesis was also carefully scrutinized and related econometric studies undertaken can be classified into the following three surrounding issues. The first one relates to whether high inflation rates might result in more variable inflation and to, subsequently, create more unpredictability in future inflation. However, there appears contradictory evidence of the causal relationship between inflation levels and inflation uncertainty and this leaves macroeconomists uneasy whether the Friedman-Ball [START_REF] Friedman | Nobel lecture: inflation and unemployement[END_REF][START_REF] Ball | How does inflation raise inflation uncertainty?[END_REF] hypothesis really holds (see Davis and Kanago, 2000;Fountas, 2001;Fountas et al., 2002;Grier et al., 2004;Aspergis, 2004;Kontonikas, 2004;[START_REF] Thornton | High and Variable Inflation: Further Evidence on the Friedman Hypothesis[END_REF].

The second issue relates to the welfare loss associated with inflation so that unpredictable future inflation tends to distort the efficient allocation of resources through the price mechanism and, hence, to lower total output. Studies that tested the link between the inflation variability and the output growth include Grier and Perry (2000), Hayford (2000), Fountas et al. (2002), Aspergis (2004) and Grier et al. (2004). Unfortunately, the results found in these studies are not unanimous.

And finally, the last issue investigates the link between the level and the variability of both inflation and growth (refer to Wilson and Culver, 1999;Grier et al., 2004;Wilson, 2006;and Fountas and Karanasos, 2007), which basically addresses the simultaneous feedback between the variables of interest. The results derived are also mixed and depend on the samples and econometric methodologies employed.

In all previous studies that use GARCH models, they appear to support Friedman's second hypothesis. In our case, we attempt to replicate GARCH model but we allow the asymmetric effects of good news and bad news, i.e. Threshold-GARCH or T-GARCH. We also attempt to employ bandpass filter to extract potential real output from its business-cycle component and short-term shocks.

It would be interesting then to examine whether our results that employs T-GARCH square with the findings of these studies.

An unified theoretical framework

The foregoing analysis of the paper is based on the following theoretical framework7 : 3) is an IS curve, where the output gap depends on the real interest rate and of its past values.

t t p t t z y y ε + + ≡ ) 1 ( 2 1 1 ) 2 ( π π σ ξ μ + + = - - t p t p t y y ( ) t t t t t t g z L E i L z + + - - = - - - 1 1 1 ) ( ) ( ) 3 ( θ π ϕ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ∑ ∑ ∑ ∑ = = = = - = = = = Δ - Δ = + + = → Ω + + + = ν ν π π λ λ φ φ β β α α κ σ β ε α ω σ σ ε ε λ π φ κ π 1 1 1 1 , 2 , 2 2 , 2 1 , , , , 0 ) ( ) ( ) 4 ( i i i i i i p i i i q i i i MTLR d t MTLR t m t t t t t t t t t m t L L L L L L L L m m and L L with N z L L * * ) 5 ( π α + = r [ ] [ ] [ ] * * ) 6 ( * m m z E E i MTLR t M l t t z k t t t Δ - Δ + + - + = + + γ γ π π γ α π t t t t v i i i + - + = - * 1 ) 1 ( ) ' 6 ( ρ ρ t t i t y t t w i y p m + - = - κ κ ) 7 ( 1 , 1 0 ) ( ) 8 ( - + = t m y L σ κ κ
Equation ( 4) is a « two-pillar » Phillips curve (Gerlach, 2004 ). It is a standard backward-looking Phillips curve, but with the intercept ( m κ ) depending on the medium term /long run (MTLR) component of money supply growth relative to the MTLR component of real money demand growth.

Equations ( 6) and (6') represent the central bank's behaviour. Equation ( 7) indicates that the desired value of the nominal interest rate for the current period (i*) is determined by monetary authorities according to an Ireland's rule [Ireland, 2004]. Like an inflation target, this rule calls for the Central bank to adjust the short-term nominal interest rate in reaction to deviations of expected inflation and output from their steady-state levels to assure monetary stability in the short-run to medium term. However, this rule also calls for the Central bank to adjust the short-term interest rate to deviations of actual money growth from its medium-term to long run reference value corresponding to the steady state level of nominal money demand. In the case where π γ , the interest rate is determined according to the Friedman's k-percent money supply rule. Equation ( 7) is a Friedman-Meltzer type specification of the demand for money (Nelson, 2002) where it depends negatively on the return rate on its substitutes -equities, bonds, physical capital -and positively on the interest rate on monetary assets.

The model encapsulates the two proposals we are interested in here. First, according to equation ( 7), the income-elasticity of the money demand depends positively on the money supply variability. Second, according to equation (2), inflation uncertainty, due mainly to monetary disturbances, impacts negatively on economic growth as represented by the evolution in the level of potential output. Each of these two proposals is the subject of each of the following sections where the Philippines case is analyzed.

Empirical analysis

Variability of M1 and velocity in the Philippines

Data series used in the foregoing analysis comes from the CEIC database. The money measure employed is M1, consisting of domestic currency in circulation and domestic money banks demand deposits, which is a good proxy of money as medium of exchange. The choice of M1 as our reference of analysis is driven by our curiosity whether there is really cogent evidence in favour of the collapse of Friedman's volatility hypothesis for narrow definitions of money as some previous studies claim. Our full-sample consists of quarterly series from 1982:Q2 to 2006:Q4. Data for M1, nominal and real GDP, and income velocity are adjusted for seasonality using multiplicative moving average. We conducted a series of stationarity test for our data. The model rests upon the stationarity of the series. Where a series is not stationary, the relationships derived in the estimation procedures are spurious [START_REF] Granger | Spurious Regressions in Econometrics[END_REF]. Two criteria to test for non-stationarity are employed: KPSS and DF-GLS. KPSS [START_REF] Kwiatkowski | Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?[END_REF] tests for the null hypothesis of stationary series against the alternative of non-stationarity while the Dickey-Fuller with GLS de-trending [START_REF] Eliot | Efficient Test for an Autoregressive Unit Root[END_REF] tests for the null hypothesis of non-stationarity against the alternative of stationarity. Careful inspection of our data series suggests that, in order to correctly specify our tests, only the drift term should be included in the null and alternative hypotheses for growth rate of M1. On the other hand, both the drift and time trend should be included for the income velocity (log) series. Table 1 displays the results. M1 growth rate is a stationary series using KPSS and DF-GLS criteria. Income velocity is non-stationary using KPSS and DF-GLS. The non-stationarity of log of income velocity of M1 implies that innovations have persistent effects. However, it is also possible that the trend is not correctly specified. In particular, the persistence of a time series is influenced by infrequent permanent shocks due to rare economic events. Ignoring these shifts in the M1 income velocity generating mechanism may at best distort conventional unitroot tests. It may be fitting then to isolate these rare occurrences, or structural breaks, that significantly altered the behaviour of the time series permanently (Perron, 1989). Bordes et al. (2007) show that the velocity of money in the euro area is affected by structural breaks both in the intercept and trend. For example, structural change in the financial system seems to explain the breakdown of money holdings in industrial countries (Tucker, 2006;Ferrero, Nobili and Passiglia, 2007).

Figure 1. M1 growth rate and Income velocity

-16% -8% 0% 8% 16% 24% 1982Q2 1983Q1 1983Q4 1984Q3 1985Q2 1986Q1 1986Q4 1987Q3 1988Q2 1989Q1 1989Q4 1990Q3 1991Q2 1992Q1 1992Q4 1993Q3 1994Q2 1995Q1 1995Q4 1996Q3 1997Q2 1998Q1 1998Q4 1999Q3 2000Q2 2001Q1 2001Q4 2002Q3 2003Q2 2004Q1 2004Q4 2005Q3 2006Q2
Recent technique that endogenously determines multiple structural breaks and corresponding estimates of the break dates was developed by Bai andPeron (1998, 2003). The BP technique considers a partial structural change model such that not all parameters of the model are subject to shifts and, hence, avoids the penalty of losing the number of degrees of freedom, a conventional pitfall of pure structural change model especially when more than one break exist. It is implemented using a sequential algorithm for estimating models with unknown number of structural breaks and yields consistent estimates of the breakpoints. We consider five as the maximum number of break points ( The following is the interpretation for M1 income velocity with constant and trend, where q stands for the number of regressors which can change overtime:

The supF test for 0 versus 1.0000 breaks (scaled by q) is: 0.0000 The supF test for 0 versus 2.0000 breaks (scaled by q) is: 46622.4172

The supF test for 0 versus 3.0000 breaks (scaled by q) is: 668177.2922

Table 2 suggests that significant breaks occurred around 1985, 1988 and 19998 and this likely supports earlier findings on instability of income velocity of money in the economy that led to Bangko Sentral ng Pilipinas' adoption of inflation targeting in place of monetary targeting in 2000 [START_REF] Guinigundo | Inflation Targeting: the Philippine Experience[END_REF] and a breakdown of equilibrium relationship between logs of M1 and price level as a result of the Asian financial crisis [START_REF] Gochoco-Bautista | An Assessment of the Usefulness of Money for Policy in the Philippines[END_REF].

The evidence for log of M1 income velocity (v t ) as an integrated process with broken trends shows a strong non-reversible tendency of the series. It seems therefore appropriate to remove the deterministic component of the variable prior to investigating the stochastic nature it reveals. In detrending the series, the choice of the specification of deterministic trend is crucial since the deterministic component can distort test results for stationarity. Including a single linear trend can impose severe penalty as this assumes a constant growth rate of the series. Hence, we allow the deterministic component of the series to be driven by a simple linear time trend (trend) and we introduce time dummy variables (D i ) that correspond to the three structural breaks identified earlier using the BP procedure and their possible interaction with the time trend:

( )

1 1
, 1, when t {1985Q1, 1988Q2 and 1999Q2} where 0, otherwise

q q t o i i o i i t i i i v D trend D trend e T D α α β β = = = + + + × + ∈ = = ⎧ ⎨ ⎩ ∑ ∑ Eqn (1)
Estimating equation 1 using ordinary least squares permits us to generate a detrended series for log of M1 income velocity ( ˆt v ). Further, the detrended series appears to be stationary (test results not presented here) which allows using it as a valid regressor to analyse Friedman's volatility hypothesis later in this section.

Results in table 3 suggest that the three structural breaks significantly affected both the constant and the velocity trend. Notably, the declining trend velocity which is exhibited by negative effect of the dummy on the slope during the period 1985Q1-1988Q1 reflects growing monetization of the economy (Gochoco-Bautista, 2006). The full impact of financial deepening in the economy on velocity, which introduced financial and technological innovations to enhance transactions including Automated Teller Machines or ATM and IT, towards the latter part of the 1980s may have been offset by relatively high degree of currency substitution [START_REF] Yap | Dollarization: Concepts and Implications for Monetary and Exchange Rate Policy in the Philippines[END_REF] as the economy embraced foreign exchange and capital liberalisation in the early 1990s to attract untapped capital from abroad 9 . Interestingly, currency substitution came into force when the Uniform Currency Act, that recognises the domestic currency or peso as the only legal tender in settling contractual obligations, was abolished in June 1996. It comes as no surprise that structural break in 1988 pulled down only the intercept term and not the slope of trend during the period 1988Q2-1999Q1, probably due to the dominating effect of currency substitution in increasing income velocity of M1. Finally, the effect of the Asian financial crisis in 1998 and the worldwide IT bubble in the early part of 2000s to create temporary supply shocks in the economy may have restrained income velocity to depress the constant by a relatively large amount but not enough to sufficiently reverse the sign of the slope of trend velocity during 1999Q2-2006Q4.

9 Currency substitution may also arise when the economy is plagued by high and variable inflation rate to discourage the use of domestic currency as a medium of exchange. But, according to [START_REF] Yap | Dollarization: Concepts and Implications for Monetary and Exchange Rate Policy in the Philippines[END_REF], given stable macroeconomic conditions in the economy, currency substitution in the Philippines is brought by institutional change, e.g. capital liberalisation. Either way, currency substitution is likely to increase income velocity of money. To calculate the variability of money growth, a GARCH (p,q) model is used. The model assumes that the persistence in the dynamics comes from the conditional second moment of the series. Consider a univariate regression with GARCH (p,q) effects:

( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 0 1 2 2 2 0 1 1 1 1 ~0, + , , t t t t t t t t t t q p i i i i i i i i i m L m X N L L m L L L L L L ν γ γ β ε ε σ σ ω α ε δ σ ω α α δ δ γ γ - = = = = + + + Ω = + + = = = ∑ ∑ ∑ Eq (2)
where m t is money (M1) supply growth; X is a vector of covariates that may have influence on m t such as short-run nominal interest rate and output growth; ε t , error term; Ω t-1, available information set in period t-1; σ t 2 , conditional variance which depends linearly on past squared-error terms and past variances; and i 1 0, 0, 0; , , ,

o i i o i i ω α δ γ γ β ω > ≥ ≥
∀ are parameters to be estimated. Lack of complete data series on T-bill rate (90 days) covering our full sample period confined this research to use weighted average of lending rate of ten Philippine commercial banks as a proxy for short-term nominal interest rate. The use of weighted average of lending rate of ten commercial banks may cast doubts if it really reflects the opportunity cost of holding money. Previous literature points to the existence of undue concentration of banking industry dominated by big players in the market, especially in commercial banking, during the 1970s and 1980s [START_REF] Tan | Interlocking Directorates, Commercial Banks, Other Financial Institutions and Nonfinancial Corporations[END_REF][START_REF] Milo | Analysis of the State of Competition and Market Structure of the Banking and Insurance Sectors[END_REF]. Nevertheless, given this limitation in the model, the interest rate variable used in this paper and the T-bill rate exhibit high and positive correlation where data availability permits. Initial unit-root tests show that interest is a non-stationary process and, hence, the first order difference (which is stationary) is used to control its influence on M1 growth, which is a stationary series. While table 1 cannot ascertain whether real GDP growth rate is a stationary process, equation 2 is implemented by including the level of real GDP growth rate.

The optimal number of lags is obtained by using the Schwarz criterion and, in this case, it is one. Mean equation in equation 2 thus follows an AR(1) process. The conditional variance is determined by a GARCH(1,1) model as a standard model of volatility in the literature and includes contemporaneous M1 growth as one of its regressors, following [START_REF] Thornton | High and Variable Inflation: Further Evidence on the Friedman Hypothesis[END_REF]. From table 4, output growth has the expected positive and significant effect on M1 growth, although only at 10% significance level. Despite interest rate not having the expected sign, it turns out that it is insignificant. While not all of the parameters in the conditional variance are positive, the GARCH component is nevertheless insignificant. Significance of M1 growth in the conditional variance equation implies positive relationship between money growth rate and money growth volatility. We proceed to calculating M1 growth volatility as the estimated conditional variability defined in equation 2. Unit root test is applied to the estimated conditional variability (results not presented here) and confirms that, indeed, it is stationary using DF-GLS criterion.

Using the detrended series of log of M1 income velocity (given by equation 1) and M1 growth volatility (given by equation 2) which are each integrated of order naught, I(0), an ordinary least square can be performed to test whether the parameter has the expected sign (see figure 2). Passing the standard diagnostic tests for normality, autocorrelation and heteroskedasticity, result in table 5 confirms the significantly negative relationship between income velocity and money growth volatility. Finally, before Friedman's hypothesis can be ascertained true in the Philippines, the direction of causality needs to be formally tested. Granger and Sim's tests [START_REF] Granger | Investigating causal relation by econometric and cross-sectional method[END_REF][START_REF] Sims | Money, income and causality[END_REF] are employed to determine the causality in the Granger sense. If volatility of M1 growth Granger-causes income velocity, it means that, conditional on information in lagged income velocity, lagged volatility of money growth does help to forecast contemporaneous income velocity. Of course, the opposite direction is also possible in which case the validity of Friedman's volatility hypothesis is questioned. Our Granger causality test is driven by the Schwarz criterion to determine the optimal number of lags as rejection of the null hypothesis is very sensitive to the number of lags included in the process.

1982Q2 1983Q1 1983Q4 1984Q3 1985Q2 1986Q1 1986Q4 1987Q3 1988Q2 1989Q1 1989Q4 1990Q3 1991Q2 1992Q1 1992Q4 1993Q3 1994Q2 1995Q1 1995Q4 1996Q3 1997Q2 1998Q1 1998Q4 1999Q3 2000Q2 2001Q1 2001Q4 2002Q3 2003Q2 2004Q1 2004Q4 2005Q3
With lag of two quarters, the null hypothesis that velocity does not Granger-cause M1 growth volatility is not rejected at 5% significance (see table 6). On the other hand, with optimal lag of six quarters, the null hypothesis that M1 growth volatility does not Granger-cause income velocity is rejected at 5%. Hence, the Friedman's hypothesis is verified. Note: The optimal number of lags is determined by using the Schwarz (BIC) criterion

Inflation, uncertainty and output growth

Following the theoretical model, the real GDP can be decomposed in a cyclical, a non-cyclical component and an error term: Econometric techniques offer the possibility of extracting cycles that move in given frequency bands (Cf. [START_REF] Hodrick | Postwar Business U.S. Cycles: An Empirical Investigation[END_REF][START_REF] Baxter | Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series[END_REF][START_REF] Christiano | The Band Pass Filter[END_REF].

Broadly, these methods consider that t Y can be estimated in the frequency domain by minimizing the conditional expected mean-squared error:

( ) [ ] T t t Z Z Z Z Y Y E Min ,..., , : 1 2 ≡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ - (2)
t Y ˆis the linear projection of t Y onto every element in the data set, t Z is the component allowed to pass through the filter.

The decomposition of real GDP (RGDP) in potential output, business cycle and short run shocks appears to be particularly accurate to test Friedman's hypothesis. Indeed, as presented in the section 4, the inflation rate is linked to the output gap (and less to potential output). Besides, according to Friedman, the uncertainty due to high inflation may affect potential output (whatever the phase of the business cycle).

Through these common characteristics, each filter-that are the Hodrick-Prescott filter (1997) (Hereafter the HP filter), the Baxter-King filter (1999) (hereafter the BK filter)) and the CF filterpresents singular features. Contrary to the HP filter, the BK and CF filters can be applied as well for business cycles (between 1.5 years to 8 years) than for higher frequencies (short run shocks) and lower frequencies (the long run or potential output). Compared to the BK filter, the CF filter uses all observations of a series while the BK filter does not (Cf. [START_REF] Shelley | The relation between U.S. money growth and inflation: evidence from a band-pass filter[END_REF].

In what follows, in order to appreciate the robustness of our results, we implement all of these filters to our data. We proceed as follows. First, we isolate the business cycle from the potential output. For that, the HP filter is implemented by fixing the value of the smoothing parameter to 1600. For the BK and CF filters, the frequency domain of the business cycle is considered to lie between 6 quarters (1.5 years) to 32 quarters (8 years). The number of lags and leads is equal to 12 for the BK filter. At this stage, the series of RDGP is decomposed as the sum of the cyclical series including the business cycle (and the noise (short run shocks) in the case of the HP filter) and the noncyclical series including the trend (and the noise when using the BK and CF filters). Second, only for the BK and CF filters, we implement a filter to the non-cyclical series with a frequency domain that lies between to 2 quarters to 5 quarters in order to dissociate the short run shocks from the potential output. The series obtained using this methodology are presented in Figure 3. After having extracting the business cycle, the short run shocks series and the potential RGDP, we use a GARCH(p,q) model. The model assumes that the persistence in the dynamics comes from the conditional second moment of the series. Although the GARCH(p,q) conditional variance model is widely used, there are other alternatives to represent the conditional variance of the inflation rate. In the standard GARCH(p,q) model, positive and negative residuals have a symmetric impact on the conditional variance. However it seems relevant to incorporate a threshold element and introduces a Threshold-GARCH (p,q) model, hereafter, TGARCH, that allows for negative residuals to have a different impact on the conditional variance than do positive residuals [START_REF] Glosten | On the Relations between the Expected Value and the Volatility of the Normal Excess Return on Stocks[END_REF]): We use quarterly data of inflation obtained from CEIC database. Our analysis covers the period 1982Q2-2006Q4. Real GDP is seasonally adjusted using the Census X12 method.

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 0 1 2 1 2 2 2 2 , , 1 t -1 1 1 1 1 t-1 0, ×I , , ,
i i i i i i i i i t Z L L N Y L L L L L L L L π π ν π γ γ π γ ε ε σ σ ω α ε β σ δ ε α α β β γ γ ε - - = = = - = + + + Ω → = + + + = = = < ⎧ = ⎨ ⎩ ∑ ∑ ∑ (
As the series 2 ,t π σ is built from estimated coefficients, the question of the robustness of the results relating to the Granger causality test arises. One can test robustness using the following protocol (repeated 1000 times):

First, with the estimated vectors of coefficients (CV) and the standard deviations vectors of these coefficients (SDV), we build a new vector of coefficients (BVC) as:

( ) ( )

) (i RSDV i CV i BVC + =
Where CV(i) is the i th component of CV. RSDV(i) is obtained by multiplying the i th component of SDV by a uniform random number (that lies between -2 and 2).

Second, BVC is used to calculate a new series of the conditional variances of inflation.

Third, with this new series, we implement a Granger causality test10 on the variables of inflation, conditional variances of inflation and on potential output growth.

The results of the TGARCH models (Table 7) show that the mean equations of inflation rate is quite similar whatever filter is used for extracting the series of business cycle: in all cases, lag inflation rate and lag output gap are both highly significant and positive11 . Hence, as expected, a positive output gap is correlated with an increase of inflation. The conditional variance equation of inflation rate (that is the uncertainty of inflation) gives less clear results. When using the CF and BK filters, negative inflationary shocks significantly result in the reduction of inflation uncertainty, which appears to confirm Friedman's hypothesis. However, even if the coefficient related to the impact of negative inflationary shocks is negative with business cycle derived from the HP filter, the coefficient is not significant at a 10% level. In order to implement Granger causality tests, we build a VAR model for each potential output corresponding to the use of a particular filter (Table 8). Whatever filter used to estimate potential output, the lag inflation rate is positively and highly significantly linked with the uncertainty of inflation rate (calculating as the conditional variance of the TGARCH model) in accordance with the Friedman's hypothesis. Furthermore, in all cases, we obtain a negative link between inflation rate and potential output growth. One reason of this negative link is that an increase of productivity diminishes costs of production and at the same time increases potential output. Contrary to the Friedman's hypothesis, the link between the uncertainty of inflation and the potential output is not significant and even positive when using the HP filter. The Granger causality tests show that, for whatever filter used, there is a causality between inflation and uncertainty of inflation. According to the VAR results, this link is positive, which coincides Friedman's second hypothesis (Table 9). More precisely, there is bi-causality when the CF filter is used and to a less extent the HP filter (as unidirectional causality running from inflation rate to inflation uncertainty is obtained in 34.5% of the cases). But, when the BK filter is used, a unidirectional causality from inflation rate to uncertainty is obtained.

Surprisingly, even if the coefficients linking inflation uncertainty and potential output growth in the VAR equations are not significant (but negative as the Friedman's theory suggests), bi-causality between inflation uncertainty and potential output growth, in Granger sense, is obtained when the CF and HP filters are employed. With the BK filter, however, there is no significant causality between these two aggregates. Since the main difference between the BK filter and the other ones is that the first 12 lags and last 12 leads are not taken into account, we can presume that these results are due to the tails of the sample. In particular, the period between 1982 and 1985, omitted by the BK filter, was the period of high inflation; hence, as Friedman suggested, the periods of high inflation seem to significantly and negatively influence potential output growth.

Conclusion

Using data from the Philippines, this paper provides strong evidence in favor of Friedman's proposals on uncertainties in money supply and inflation, and economic growth. Taking into account possible structural breaks in velocity, our study shows that high variability of money growth is linked with a diminution in the income velocity of narrow definitions of money. Moreover, high level of inflation Granger causes a higher variability of inflation, which, to a certain extent, Granger causes a diminution of the potential output.

Hence, the higher level of inflation that characterized the Philippines relative to other East Asian economies seems to be one of the main explanations of shocks in the 1980's and the 1990's. This further explains the weaker macroeconomic performance of the economy during this period.

  we determine the location of the breaks by computing the global minimum of the sum-of-squared residuals. We identify the optimal number of breaks both through the Akaike Information and Schwarz (BIC) criteria. The amount of trimming is specified as dates are based on minimised sum of squares. ** (*) indicates significance at 1% (resp. 5%) level.

Figure 2 .

 2 Figure 2. Conditional variability of M1 growth and income velocity (log, detrended)

  Conditional variability of M1 growth rateLog velocity with no break and no trend

Figure 3 :

 3 Figure 3: Potential output and business cycle

  otherwise. If the asymmetry parameter δ is negative then negative inflationary shocks result in the reduction of inflation uncertainty.

  κ

	Equation (
	where: y is the actual value of real GDP; t z is the output gap; p t y is the potential value of real GDP;
	t i is the nominal interest rate; t E is the conditional expectation calculated at date t; t π is the
	inflation rate; t g denotes a goods demand-side shock; t ε denotes a supply-side shock; t p is the
	price level; t m denotes the money supply; t w denotes a money demand shock (all of the variables,
	except for the interest rate, are expressed as logarithms);	MTLR t m Δ	and	d t m , Δ	MTLR	denote,
	respectively, the medium-term/long run (MTLR) components of money supply and money demand
	growth.	* Δ summarizes the excess of MTLR nominal money growth over MTLR real money m
	demand growth

Table 1 . KPSS and DF-GLS unit root tests

 1

	Variables	KPSS	DF-GL
	Income velocity of M1 (log)
	With drift and time trend	0.149**	-2.502
	With drift but no time trend	1.237***	-0.638
	M1 growth rate
	With drift and time trend	0.056	-7.929***
	With drift but no time trend	0.087	-1.700*
	Interest rate differentials
	With drift and time trend	0.035	-6.710***
	With drift but no time trend	0.047	-6.623***
	Output growth
	With drift and time trend	0.117	-2.606
	With drift but no time trend	0.412*	-0.819
	Income velocity of M1 (log)
	With drift and time trend	0.149**	-2.502
	With drift but no time trend

Note: ***, **, * respectively indicates rejection of the null at 1%, 5% and 10% significance levels.

Table 3 . Coefficient estimates (detrending)

 3

	Variables	Coefficient
	Constant	0.1737***
	Dummy1985Q1 (D 1 )	0.5799***
	Dummy1988Q2 (D 2 )	-0.2122**
	Dummy1999Q2 (D 3 )	-0.7572***
	Time trend (trend)	0.0134***
	D 1 x trend	-0.0358***
	D 2 x trend	0.0123***
	D 3 x trend	0.0100***
	Note: ***, **, *

respectively indicates rejection of the null at 1%, 5% and 10% significance levels.

Table 4 . GARCH(1,1) model of M1 growth volatility

 4

	Variables	Coefficient
	I. Mean Equation
	Constant	0.0297***
	Interest rate (1 st	0.0044
	difference)
	Output growth	0.1596*
	M1 growth (-1)	0.0471
	II. Conditional Variance Equation
	Constant	0.0005**
	Residual (-1) or ε 2 t-1	0.5317**
	GARCH (-1) or σ 2 t-1	-0.0530
	M1 growth	0.0097***
	Note: ***, **, *

respectively indicates rejection of the null at 1%, 5% and 10% significance levels.

Table 5 . OLS for M1 income velocity (detrended)

 5

	Variables	Coefficient
	Constant	0.0099**
	M1 growth	-5.7842***
	volatility
	Adjusted R²	0.1122
	F-stat	13.0129***
	Jarque-Bera	4.7287*
	Breusch-	0.9546
	Godfrey
	White	39.9240***

Note: *

**, **, * respectively indicates rejection of the null at 1%, 5% and 10% significance levels.

Table 6 . Granger-causality test Variables Optimal number of lags Likelihood ratio H0 at a 5% level

 6

	Log velocity (detrended
	and debreaked) Granger causes variability of M1	2	0.13	No reject
	Variability of M1 Granger
	causes log velocity	6	29.95	Reject
	(detrended)

Table 7 : TGARCH equations Variables CF coefficients BK coefficients HP coefficients

 7

	I. Mean Equation (π)
	Constant (γ 0 )	3.62***	6.11***	4.70***
	π(-1)			0.52***	0.32***	0.46***
	z(-2)			0.60**	0.78***	0.91***
	II. Conditional Variance Equation (σ π )
	Constant (ω)	18.29**	15.82*	16.23***
	ε 2	t-1			0.51	0.08	0.28
	σ 2	π, t -1			0.38***	0.40	0.47**
	ε	2 -1 I × t	t	1 -	-0.77*	-0.59***	-0.68
				Note: ***, **, *

respectively indicates rejection of the null at 1%, 5% and 10% significance levels.

Table 8

 8

														: VAR models
								CF filter						BK filter					HP filter
					σ	2	π, t -1	Π	y	P	σ	2	π, t -1	Π	y	P	σ	2	π, t -1	Π	y	P
	σ	2	π, t -1	0.27***	-0.01	-0.002	0.36***	0.08	-0.003	0.26	-0.003	-0.000003
					(0.11)	(0.01)	(0.002)	(0.12)	(0.16)	(0.02)	(0.11)	(0.03)	(0.00008)
	σ	2	π, t -2	0.13***	-0.02***	-0.001	0.03	-0.08	-0.01	0.13	-0.04	0.00006
					-0.05	-0.01	(0.001)	(0.07)	(0.09)	(0.01)	(0.05)	(0.01)	(0.00004)
	π (-1)	11.34***	0.31***	-0.01	1.42***	0.24	-0.002	6.46***	0.29***	0.0002
					(0.74)	(0.10)	(0.01)	(0.12)	(0.15)	(0.02)	(0.39)	(0.10)	(0.0003)
	π (-2)	-2.70	0.55***	0.00	-0.97***	0.16	-0.01	-1.11	0.35	0.0005
					(1.45)	(0.20)	(0.03)	(0.20)	(0.26)	(0.03)	(0.80)	(0.20)	(0.0006)
	y	P (-1)	4.98	-1.50***	1.26***	0.52	-1.69**	1.05***	84.82***	-11.54**	1.94***
					(4.36)	(0.59)	(0.09)	(0.67)	(0.86)	(0.09)	(24.92)	(6.30)	(0.02)
	y	P (-2)	-3.00	0.29	-0.59***	-1.26*	1.10	-0.79***	-82.53**	9.53	-0.95***
					(4.32)	(0.59)	(0.09)	(0.65)	(0.83)	(0.09)	(24.24)	(6.13)	(0.02)
	C			-44.63*** 7.06***	1.22***	11.01***	7.20*	2.82***	-33.01*** 11.81***	0.01**
					(14.15)	(1.92)	(0.28)	(3.03)	(3.90)	(0.43)	(9.76)	(2.47)	(0.01)
	Adjusted R-squared	0.84	0.48	0.79	0.78	0.12	0.73	0.81	0.34	0.99

Note: under brackets stand standard deviations. ***, **, * respectively indicates rejection of the null at 1%, 5% and 10% significance levels.

Table 9 : Granger causality tests

 9

			CF filter
		σ π Granger causes π	σ π does not Granger cause π			y P Granger causes σ π	y Granger cause P does not σ π
	π Granger causes σ π	88.50%	11.50%	σ π Granger causes y P	93.50%	5.40%
	π does not			σ π does not
	Granger cause	0%	0%	Granger cause	0.00%	1.10%
	σ π			y	P
			BK filter
		σ π Granger causes π	σ π does not Granger cause π			y P Granger causes σ π	y Granger cause P does not σ π
	π Granger causes σ π	6.80%	85.70%	σ π Granger causes y P	0.20%	8.30%
	π does not			σ π does not
	Granger cause	0%	0%	Granger cause	0.30%	85.10%
	σ π			y P
			HP filter
		σ π Granger causes π	σ π does not Granger cause π			y causes σ π P Granger	y P does not Granger cause σ π
	π Granger causes σ π	65.5 %	34.5 %	σ π Granger causes y P	79.4 %	3.3 %
	π does not			σ π does not
	Granger cause	0 %	0 %	Granger cause	11.3 %	6 %
	σ π			y P

From a theoretical point of view, the Friedman's hypothesis is based on the fact that the income effect is higher than the substitution effect. The substitution effect occurs when an increase of the variability of money growth rate implies a rise of demand for foreign currency, considered as a perfect substitute of money. When substitution effect dominates, income velocity increases.

This is an extension of the model proposed byBordes and Clerc (2007).

Following Wang (2006), the BIC criterion is preferred to the AIC criterion.

The number of lags is equal to 2. This procedure was also implemented with respectively 4 and 6 lags. As results are not really different, they are not presented in this paper but are available on request.

The number of lags is determined by an analysis of cross correlations.

This conference was organized with the support of the EU Euro-Philippines Network on Banking and Finance, Safety and Soundness of the Financial System (Asialink/ASIE/B7-3010/2005/105-139), coordinated by the University of Limoges (www.upd.edu.ph/~cba/asialink). ASIA-LINK is a Programme of the European Commission that seeks to promote regional and multilateral networking among higher education institutions in Europe and developing economies in Asia. The contents of this paper are the sole responsibility of the authors and can under


domain: chim sdv

text:
Francesco Rota Sperti

Thibaut Charbonnier

Pauline Lejault

Joanna Zell

Claire Bernhard

Ibai E Valverde
email: ibai.valverde@u-bourgogne.fr

David Monchaud
email: david.monchaud@cnrs.fr

Biomimetic, smart and multivalent ligands for G-quadruplex isolation and bioorthogonal imaging

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

The principle of template-assembled synthetic proteins (TASP) [START_REF] Mutter | A Chemical Approach to Protein Design-Template-Assembled Synthetic Proteins (TASP)[END_REF][START_REF] Mutter | Template Assembled Synthetic Proteins (TASP) as Functional Mimetics of Proteins[END_REF] was developed by Mutter to tackle the complicated issue of how to control the folding of polypeptides into protein-like functional macromolecules. Inspired by this principle, Sherman reported on templateassembled synthetic G-quartets (TASQ) 3 as a model system of how discrete G-quartets can be assembled intramolecularly. To this end, four guanine residues were covalently linked to a template resulting in a conformationally dynamic suprastructure, the guanines being either independent of each other (the so-called 'open' conformation of TASQ) or assembled into a G-quartet (via the formation of 8 hydrogen bonds, the 'closed' conformation).

The first prototypes of TASQ were built on a lipophilic template (Cram's bowl-shape cavitands [START_REF] Cram | Host-guest complexation. 65. Hemicarcerands that encapsulate hydrocarbons with molecular weights greater than two hundred[END_REF] with long alkyl chains) for studying the cation (Na + , K + , Sr 2+ ) chelation properties of discrete, synthetic G-quartets in organic media (CHCl3). [START_REF] Nikan | Template-assembled synthetic G-quartets (TASQs)[END_REF][START_REF] Nikan | Cation-Complexation Behavior of Template-Assembled Synthetic G-Quartets[END_REF][START_REF] Nikan | Crystal Structure of a Template-Assembled Synthetic G-Quadruplex[END_REF] Soon after, water-soluble TASQs were developed, hinging on hydrophilic templates such as the polyazamacrocyclic DOTA for the DOTASQ, [START_REF] Stefan | DOTASQ as a prototype of nature-inspired G-quadruplex ligand[END_REF] the cyclodecapeptide RAFT (regioselectively addressable functionalized template, initially introduced by Mutter for the synthesis of TASP) [START_REF] Mutter | Template Assembled Synthetic Proteins (TASP) as Functional Mimetics of Proteins[END_REF][START_REF] Dumy | Solution structure of regioselectively addressable functionalized templates: an NMR and restrained molecular dynamics investigation[END_REF][START_REF] Dumy | A convenient synthesis of cyclic peptides as regioselectively addressable functionalized templates (RAFT)[END_REF] for the RAFT-G4, [START_REF] Murat | The Use of a Peptidic Scaffold for the Formation of Stable Guanine Tetrads: Control of a H-bonded Pattern in Water[END_REF] as well as cavitands with phosphate appendages. [START_REF] Nikan | Synthesis of a water-soluble triazole-linked cavitandguanosine conjugate[END_REF][START_REF] Bare | Synthesis of a Single G-Quartet Platform in Water[END_REF] This opened new possibilities for biodirected applications such as the design of biomimetic G-quadruplex ligands (or G4ligands, [START_REF] Neidle | Quadruplex Nucleic Acids as Novel Therapeutic Targets[END_REF] vide infra) or of molecular platforms to evaluate the G-quartet interacting properties of G4-ligands. [START_REF] Bare | Synthesis of a Single G-Quartet Platform in Water[END_REF][START_REF] Murat | Template-Assembled Synthetic G-Quadruplex (TASQ): A Useful System for Investigating the Interactions of Ligands with Constrained Quadruplex Topologies[END_REF] We have been particularly interested in fine-tuning the chemical scaffold of water-soluble TASQ in order to optimize their properties as biomimetic G4-ligands. The main binding site of a small-molecule within the G4 architecture is the external, accessible G-quartet. [START_REF] Haider | A structural analysis of G-quadruplex/ligand interactions[END_REF] Since a G4 is more stable if it has more constitutive G-quartets, [START_REF] Mergny | Following G-quartet formation by UV-spectroscopy[END_REF] we set out to synthesize TASQ to interact with G4s according to such a biomimetic, like-likes-like interaction between a native G4 quartet and the synthetic TASQ quartet. By doing so, we have gradually modified the chemical nature of TASQ from the first biomimetic G4-ligand (DOTASQ, [START_REF] Stefan | DOTASQ as a prototype of nature-inspired G-quadruplex ligand[END_REF][START_REF] Stefan | Deciphering the DNAzyme Activity of Multimeric Quadruplexes: Insights into Their Actual Role in the Telomerase Activity Evaluation Assay[END_REF] and PorphySQ) [START_REF] Xu | Porphyrin-templated synthetic G-quartet (PorphySQ): a second prototype of Gquartet-based G-quadruplex ligand[END_REF] to the first smart G4-ligands PNA DOTASQ [START_REF] Haudecoeur | A Model of Smart G-Quadruplex Ligand[END_REF][START_REF] Haudecoeur | Multitasking Water-Soluble Synthetic G-Quartets: From Preferential RNA-Quadruplex Interaction to Biocatalytic Activity[END_REF] (Figure 1) and PNA PorphySQ, [START_REF] Laguerre | Porphyrin-Based Design of Bioinspired Multitarget Quadruplex Ligands[END_REF] whose closed conformation is triggered only by interaction with G4s), twice-as-smart G4-ligands PyroTASQ [START_REF] Laguerre | A Twice-As-Smart Synthetic G-Quartet: PyroTASQ Is Both a Smart Quadruplex Ligand and a Smart Fluorescent Probe[END_REF][START_REF] Zhou | Computational understanding and experimental characterization of twice-as-smart quadruplex ligands as chemical sensors of bacterial nucleotide second messengers[END_REF] and N-TASQ, [START_REF] Laguerre | Visualization of RNA-quadruplexes in live cells[END_REF][START_REF] Laguerre | Direct visualization of both DNA and RNA quadruplexes in human cells via an uncommon spectroscopic mechanism[END_REF] smart ligands and smart probes, used to detect G4s in vitro and in cella, and the multivalent G4-ligand BioTASQ [START_REF] Yang | Transcriptome-wide identification of transient RNA G-quadruplexes in human cells[END_REF][START_REF] Renard | Small-molecule affinity capture of DNA/RNA quadruplexes and their identification in vitro and in vivo through the G4RP protocol[END_REF] (Figure 1), used as molecular bait for isolating G4 from human cells and identifying them by sequencing.

A critical bottleneck in the development of TASQ resides in their chemical accessibility.

Despite their relatively short synthesis, some technical pitfalls preclude efficient large-scale synthesis. We thus decided to revisit the synthesis of TASQ and report herein on the synthesis of both cyclen-template synthetic G-quartet (CyTASQ) and its biotinylated counterpart BioCyTASQ (Figure 1), whose design was inspired by that of the reference compound PNA DOTASQ and BioTASQ, [START_REF] Haudecoeur | A Model of Smart G-Quadruplex Ligand[END_REF][START_REF] Yang | Transcriptome-wide identification of transient RNA G-quadruplexes in human cells[END_REF][START_REF] Renard | Small-molecule affinity capture of DNA/RNA quadruplexes and their identification in vitro and in vivo through the G4RP protocol[END_REF] but with a simpler chemical scaffold and less time-consuming chemical accessibility.

Design & synthesis of CyTASQ and BioCyTASQ. These two new TASQs were designed to keep the global structural organization of PNA DOTASQ and BioTASQ (Figures 1 and2), changing the topologically constrained amide linkers for more flexible alkyl linkers of similar length (in terms of number of atoms). This replacement, although conceptually simple, results in a more straightforward accessibility to the final TASQ with increased overall chemical yields (from 0.6% to 6% for BioTASQ and BioCyTASQ, respectively, Figure 2). Briefly, the starting material for the synthesis of CyTASQ is the commercially available cyclen while that of BioCyTASQ is a biotinylated aminomethylcyclen (biotin-AMC), [START_REF] Yang | Transcriptome-wide identification of transient RNA G-quadruplexes in human cells[END_REF][START_REF] Renard | Small-molecule affinity capture of DNA/RNA quadruplexes and their identification in vitro and in vivo through the G4RP protocol[END_REF] prepared in one step (39% chemical yield) from AMC. [START_REF] Rousselin | Efficient Synthesis of New C-Functionalized Macrocyclic Polyamines[END_REF] These polyazamacrocycles were reacted with an excess (8 mol. equiv.) of 5-(Boc-amino)pentyl mesylate (prepared in two steps from the commercially available 5-amino-1-pentanol, 56% yield) in presence of potassium carbonate (K2CO3) in acetonitrile (ACN) to lead to compounds 1 (47% yield) and 2 (62% yield).

These intermediates were deprotected with trifluoroactetic acid (TFA) to afford compounds 3 and 4 (100% yield), which were subsequently coupled with an excess (4.4 mol. equiv.) of Boc-PNA G-OH monomers (prepared in one step from the commercially available Boc-PNA G(Z)-OH, 72%) in presence of N,N,Nʹ,Nʹ-tetramethyl-O-(N-succinimidyl)uronium tetrafluoroborate (TSTU) and diisopropylethylamine (DIPEA) to afford the protected TASQs 5 (6% yield) and 6 (25% yield). The final compounds, CyTASQ and BioCyTASQ, were obtained after a last, quantitative deprotection step (TFA).

Evaluation of G4-interacting properties of CyTASQ and BioCyTASQ in vitro.

The apparent affinity of TASQs for different DNA/RNA sequences was evaluated via the firmly established FRET-melting assay (Figure 3A). [START_REF] Renciuk | A FRET-based screening assay for nucleic acid ligands[END_REF][START_REF] De Cian | Fluorescence-based melting assays for studying quadruplex ligands[END_REF] Doubly labelled biologically relevant G4-forming DNA/RNA sequences 31 (0.2 µM) were heated from 20 to 90 °C in presence of TASQs (1.0 µM).

The sequences used were the human telomeric-mimicking F-21-T (FAM-d[ 5' G3(T2AG3)3 3' ]-TAMRA; FAM for fluorescein amidite, TAMRA for tetramethylrhodamine), the Myc promotermimicking F-Myc-T (FAM-d[ 5' GAG3TG4AG3TG4A2G 3' ]-TAMRA), the human telomeric transcript F-TERRA-T (FAM-r[ 5' G3(U2AG3)3 3' ]-TAMRA) and the 5'-UTR of the mRNA coding for VEGF (F-VEGF-T, FAM-r[ 5' G2AG2AG4AG2AG2A 3' ]-TAMRA), along with F-duplex-T as a control (the hairpin-forming FAM-d[ 5' (TA)2GC(TA)2T6(TA)2GC(TA)2 3' ]-TAMRA).

As seen in figure 3A, the thermal stabilization of the DNA/RNA sequences was delayed in presence of all TASQs, but with a wide range of effects, with mid-transition temperatures (DT1/2, in °C) ranging from 1.0 and 21.8 °C. Interestingly, the chemical simplification of the G arms (CyTASQ versus PNA DOTASQ and BioCyTASQ versus BioTASQ) affects the TASQ G4stabilizing properties differently: on one hand, the stabilizations induced by PNA DOTASQ (black bars, DT1/2 between 12.0 and 21.2 °C) are systematically higher than that of CyTASQ (brown bars, DT1/2 = 5.2 -10.0 °C); whereas on the other hand, the BioTASQ stabilization values (gray bars, DT1/2 = 1.0 -2.7 °C) are systematically lower than that of BioCyTASQ (red bars, DT1/2 = 4.7 -10.0 °C), being comparable to that of CyTASQ. This could be interpreted in terms of flexibility of the G arms: arms with a greater flexibility may be detrimental for the nonbiotinylated TASQs (CyTASQ versus PNA DOTASQ), implying that the amide connection in the arms of PNA DOTASQ somehow pre-organizes its external G-quartet for a better G4 recognition (presumably via internal H-bonding, Figure 3B). [START_REF] Stefan | DOTASQ as a prototype of nature-inspired G-quadruplex ligand[END_REF] However, this flexibility improves the performances of biotinylated TASQs (BioCyTASQ versus BioTASQ) by decreasing the propensity of the biotin tag to intramolecularly interact with one of the G arms of the TASQ, known to perturb their association with G4 and initially thought to be a biotin/guanine interaction. [START_REF] Renard | Small-molecule affinity capture of DNA/RNA quadruplexes and their identification in vitro and in vivo through the G4RP protocol[END_REF] These new results suggest that the interaction might occur between the biotin and the amide connector of the G arm neighboring the cyclen (Figure 3B), which seems to be less sterically constrained. CyTASQ and BioCyTASQ are thus less structurally preorganized than PNA DOTASQ (lower apparent affinity) but also less internally poisoned than BioTASQ (higher apparent affinity). These results also show that TASQs do not interact with duplex-DNA (see the control with F-duplex-T, with DT1/2 < 0.5 °C), highlighting a G4 specificity that was confirmed by competitive FRET-melting assays performed with F-Myc-T and F-TERRA-T (0.2 µM) in presence of Bio(Cy)TASQ (1.0 µM) and an excess (3 and 10 µM) of an unlabelled duplex-DNA competitor ds17 (d[ 5' C2AGT2CGTAGTA2C3 3' ]/d[ 5' G3T2ACTACGA2CTG2 3' ]). The new TASQs are highly G4specific (Figure 3C) with a maintained stabilization of >92% for CyTASQ and >98% for BioCyTASQ. The high affinity and exquisite selectivity of the biotinylated BioCyTASQ makes it well suited to be used as a molecular bait for fishing G4s out of nucleic acids mixtures.

Evaluation of G4-capture properties of CyTASQ and BioCyTASQ in vitro.

The ability of the biotinylated TASQs to pull down G4s was assessed via an optimized version of the 'pull-down' or 'affinity capture' protocol developed for the BioTASQ (Figure 4A). [START_REF] Renard | Small-molecule affinity capture of DNA/RNA quadruplexes and their identification in vitro and in vivo through the G4RP protocol[END_REF] FAM-labelled G4forming DNA/RNA sequences (1 µM) were incubated for 2 h with either BioTASQ or BioCyTASQ (10 µM) in presence of streptavidin-coated magnetic beads in TrisHCl buffer (20mM, pH 7.2) containing 1 mM KCl, 99 mM LiCl and 10 mM MgCl2 (the Mg 2+ being found to decrease the random electrostatic interactions between DNA and TASQs). The G4-forming sequences used were the human telomeric-mimicking F-22AG (FAM-d[ 5' AG3(T2AG3)3 3' ]), a section of the promoters of MYC (FAM-d[ 5' GAG3TG4AG3TG4A2G 3' ]) and SRC genes (FAMd[ 5' G3AG3AG3CTG5 3' ]), and F-duplex as a control (FAM-d[ 5' (TA)2GC(TA)2T6(TA)2GC(TA)2 3' ]). The FAM-G4/Bio(Cy)TASQ/beads assemblies were isolated (magnetic immobilization), the supernatant removed and the FAM-G4 resuspended in solution after a thermal denaturation step (10 min at 90 °C). The capture/release efficiency of TASQ was quantified by the FAM emission of the resulting solution, normalized to the controls performed without TASQ.

Both BioTASQ and BioCyTASQ efficiently captured G4s in solution (Figures 4B-E). This could be assessed by both the decrease of the FAM intensity of the supernatant, which reflects the pull-down per se (with a pull-down efficiency as low as -98 % as compared to the control, i.e., experiments performed without TASQ, normalized to 100%, panel C) and the increase of the

Evaluation of G4-interacting properties of CyTASQ and BioCyTASQ in cella.

The biotin appendage of Bio(Cy)TASQ can also be used for optical imaging. Inspired by pretargeted imaging and therapy strategies involving biotin-and/or streptavidin-antibody conjugates, [START_REF] Sakahara | Avidin-biotin system for delivery of diagnostic agents[END_REF][START_REF] Lesch | Avidin-biotin technology in targeted therapy[END_REF][START_REF] Altai | Pretargeted imaging and therapy[END_REF] we used Bio(Cy)TASQ for imaging G4s in human cancer cells (MCF7) based on the highly specific interaction between the biotin appendage of TASQ and a Cy3-labelled streptavidin (SA-Cy3). Two strategies were implemented, with a systematic comparison of the properties of BioTASQ and BioCyTASQ: a post-fixation or a live-cell labelling strategy. In the first strategy, MCF7 cells are fixed (MeOH) then incubated sequentially with Bio(Cy)TASQ (1 µM, 1 h), SA-Cy3 (1 µg/mL) and DAPI (2.5 µg/mL) (Figure 5A). In the second strategy, MCF7 cells are treated live with Bio(Cy)TASQ (1 µM, 24 h; IC50 >100 µM) before fixation (MeOH), and sequential SA-Cy3 and DAPI labelling (Figure 5B). Both strategies are intended to provide complementary outputs as the former leads to a snapshot of G4 landscapes as captured by chemical fixation while the latter highlights cellular sites where TASQs accumulate in live cells. In both instances, BioCyTASQ provided a brighter response than BioTASQ (Figure 5, the images were collected under strictly identical experimental setups). Post-fixation labelling led to a rather diffuse labelling in the cytoplasm along with stronger labelling in perinuclear regions (yellow arrows), nucleoli (white arrows) and non-nucleoli nucleoplasmic sites (red arrows). Live-cell labelling provided a similar perinuclear/nucleoli/nuclear distribution (yellow/white/red arrows) but with higher contrast, highlighting G4 foci in a more precise manner, with abundant G4-RNA sites, mostly found in ribosome sites (nucleoli (white arrows) and rough endoplasmic reticulum (yellow arrows)) and sparser G4-DNA sites (located in the nucleoplasm (red arrows)). These results are fully in line with the direct G4 labelling pattern provided by N-TASQ. [START_REF] Laguerre | Visualization of RNA-quadruplexes in live cells[END_REF][START_REF] Laguerre | Direct visualization of both DNA and RNA quadruplexes in human cells via an uncommon spectroscopic mechanism[END_REF][START_REF] Moruno-Manchon | Smallmolecule G-quadruplex stabilizers reveal a novel pathway of autophagy regulation in neurons[END_REF][START_REF] Lejault | Regulation of autophagy by DNA G-quadruplexes[END_REF] We observe that the live-cell treatment shows a similar staining pattern to post-fixation labelling, indicating the G4 landscape is not redistributed by TASQ treatment. Live cell imaging is more accurate because the ligand's target is not chemically altered by fixation. This approach should thus be preferred to investigate G4 biology with TASQs. To the best of our knowledge, this is the first description of a pretargeted imaging strategy based on the biotin/avidin system applied to visualize G4s in human cells.

Conclusion

The panel of strategies now available for gaining insights into G4 landscapes within human cells encompasses optical imaging [START_REF] Umar | G-Quadruplex-Based Fluorescent Turn-On Ligands and Aptamers: From Development to Applications[END_REF][START_REF] Monchaud | Quadruplex detection in human cells[END_REF] and sequencing methods. [START_REF] Kwok | G-quadruplexes: prediction, characterization, and biological application[END_REF][START_REF] Spiegel | The structure and function of DNA G-quadruplexes[END_REF] These strategies rely on exquisitely efficient and specific molecular tools to either label G4 sites within cells (e.g., direct labelling with G4 probes or indirect labelling via bioorthogonal chemistry) [START_REF] Umar | G-Quadruplex-Based Fluorescent Turn-On Ligands and Aptamers: From Development to Applications[END_REF][START_REF] Monchaud | Quadruplex detection in human cells[END_REF][START_REF] Raguseo | Chemical-biology approaches to probe DNA and RNA G-quadruplex structures in the genome[END_REF][START_REF] Cañeque | Visualizing biologically active small molecules in cells using click chemistry[END_REF] or stabilize G4s in vitro to cause polymerase stalling which is used as a next-generation sequencing readout (e.g., pyridostatin in G4-seq [START_REF] Chambers | High-throughput sequencing of DNA G-quadruplex structures in the human genome[END_REF] and rG4-seq 44 protocols). [START_REF] Kwok | G-quadruplexes: prediction, characterization, and biological application[END_REF][START_REF] Spiegel | The structure and function of DNA G-quadruplexes[END_REF][START_REF] Kwok | Detecting RNA G-Quadruplexes (rG4s) in the Transcriptome[END_REF] In light of the number of potential G4-forming sequences in the human genome and transcriptome, [START_REF] Chambers | High-throughput sequencing of DNA G-quadruplex structures in the human genome[END_REF][START_REF] Todd | Highly prevalent putative quadruplex sequence motifs in human DNA[END_REF][START_REF] Huppert | Prevalence of quadruplexes in the human genome[END_REF][START_REF] Bedrat | Re-evaluation of G-quadruplex propensity with G4Hunter[END_REF][START_REF] Hänsel-Hertsch | G-quadruplex structures mark human regulatory chromatin[END_REF][START_REF] Hänsel-Hertsch | Genome-wide mapping of endogenous G-quadruplex DNA structures by chromatin immunoprecipitation and highthroughput sequencing[END_REF][START_REF] Hänsel-Hertsch | Landscape of G-quadruplex DNA structural regions in breast cancer[END_REF][START_REF] Zheng | Detection of genomic G-quadruplexes in living cells using a small artificial protein[END_REF] and the biological processes they might be involved in, [START_REF] Varshney | The regulation and functions of DNA and RNA G-quadruplexes[END_REF][START_REF] Rhodes | G-quadruplexes and their regulatory roles in biology[END_REF][START_REF] Kim | The interplay between G-quadruplex and transcription[END_REF][START_REF] Del Mundo | Modulation of DNA structure formation using small molecules[END_REF][START_REF] Maizels | G4-associated human diseases[END_REF] the task can seem daunting; however, this offers a virtually unlimited playground for chemical biology investigation, as every new tool and approach could provide alternative and/or complementary information helping to further decipher the complex biology of G4s.

Here, we continue to exploit the potential of biomimetic and smart G4 ligands, demonstrating the versatility of biotinylated TASQs to both isolate G4s by pull-down affinity capture, implementable in cells by G4RP-seq for instance, and visualize G4s via an original streptavidin/biotin pretargeted imaging approach, found to be a reliable alternative to in situ click chemistry. [START_REF] Cañeque | Visualizing biologically active small molecules in cells using click chemistry[END_REF] We address the problem of poor chemical accessibility of TASQs via the design and synthesis of the new generation TASQs rereferred to as CyTASQ and BioCyTASQ, which can now be produced on scales and timescales compatible with a broader use. The in vitro validation provided here lends further credence to the strategic relevance of TASQs as multivalent molecular tools to investigate G4s in cella endowing them with new functionalities that continue to demonstrate the versatility of their applications.

Methods

Synthesis of CyTASQ. Compound 1:

To a solution of cyclen (30 mg, 0.20 mmol, 1.0 equiv.) in acetonitrile (1.16 mL) was added 5-((tert-butoxycarbonyl)amino)pentyl methanesulfonate (400 mg, 1.40 mmol, 7.0 equiv.) and K2CO3 (191 mg, 1.40 mmol, 7.0 equiv.) and the solution was stirred until complete conversion of the starting material (48h, monitoring by RP-HPLC).

The crude mixture was filtered, and concentrated under vacuum. The residue was then purified by silica gel column chromatography (CH2Cl2/MeOH (90:10)). After evaporation of the solvents, compound 1 was obtained (74.2 mg, 0.08 mmol, 47 % yield). [START_REF] Mutter | A Chemical Approach to Protein Design-Template-Assembled Synthetic Proteins (TASP)[END_REF]

Synthesis of BioCyTASQ. Compound 2:

To a solution of biotin (514.7 mg, 2.10 mmol, 0.8 equiv.) and DIPEA (949 μL, 5.40 mmol, 2.0 equiv.) in DMF (10 mL) was added TSTU (900 mg, 3.00 mmol, 1.1 equiv.) and the solution was stirred at RT until the complete activation of the carboxylic acid, assessed via HPLC-MS monitoring. The solution was then added dropwise (1 mL/3 h) to a solution of AMC (546 mg, 2.70 mmol, 1.0 equiv.) in DMF (20 mL) and the reaction was carefully monitored by HPLC-MS. Upon completion, TFA (500 μL) was added and the solution was concentrated under vacuum and the resulting residue purified by RP-HPLC in a H2O/can + 0.1% TFA mixture (gradient of 2 to 100 % over 50 minutes). After evaporation of the solvents, compound 2 was obtained (926 mg, 1.04 mmol, 39% yield). [START_REF] Mutter | A Chemical Approach to Protein Design-Template-Assembled Synthetic Proteins (TASP)[END_REF] H NMR: (500 MHz, D2O) δ 4.60 (dd, J = 7.9, 4.9 Hz, 1H), 4.41 (dd, J = 8.0, 4.5 Hz, 1H), 3.51 -2.73 (m, 20H), 2.30 (t, J = 7.3 Hz, 2H), 1.78 -1.50 (m, 4H), 1.48 -1.29 (m, 4H) (signals of intracyclic amines and amide are missing due to proton solvent exchange). [START_REF] Neidle | Quadruplex Nucleic Acids as Novel Therapeutic Targets[END_REF] To a solution of compound 2 (283.2 mg, 0.32 mmol, 1.0 equiv.) in acetonitrile (4 mL) was added 5-((tert-butoxycarbonyl)amino)pentyl methanesulfonate (720 mg, 2.56 mmol, 8.0 equiv.) and K2CO3 (472 mg, 3.42 mmol, 10.0 equiv.) and the solution was stirred at 50°C for 56 h. Another aliquot of 5-((tert-butoxycarbonyl)amino)pentyl methanesulfonate (392 mg, 1.40 mmol, 4.0 equiv.) was added and further stirred for 16 h. The crude mixture was filtered and concentrated under vacuum and the residue was purified by HPLC in a H2O/ACN + 0.1% TFA mixture (gradient of 30 to 100 % over 40 min). Compound 4 was obtained (232.5 mg, 0,20 mmol, 62% yield). [START_REF] Mutter | A Chemical Approach to Protein Design-Template-Assembled Synthetic Proteins (TASP)[END_REF] [M+H] + 1168.09 m/z = (calcd. for C59H114N11O10S: 1168.68). Compound 6: Boc-PNA G-OH (245 mg, 0.63 mmol, 4.8 equiv.), TSTU (191 mg, 0.63 mmol, 4.8 equiv.) were dissolved in DMF (1.5 mL) and DIPEA was added (99 μL, 0.63 mmol, 4.8 equiv.). After the complete activation of the carboxylic acid (HPLC-MS monitoring), a solution of compound 5 (100 mg, 0.13 mmol, 1.0 equiv.) and DIPEA (44 μL, 0.26 mmol, 2.0 equiv.) in DMF (1.5 mL) was added. The mixture was stirred at RT overnight. The solution was then concentrated under vacuum and the residue was purified by RP-HPLC in a H2O/ACN + 0.1% TFA mixture (gradient of 15 to 65 % over 50 minutes). After evaporation of the solvents, compound 6 was obtained (77.8 mg, 0.03 mmol, 25% yield). [START_REF] Mutter | A Chemical Approach to Protein Design-Template-Assembled Synthetic Proteins (TASP)[END_REF] H NMR: (500 MHz, DMSO-d6) δ 10.8 (m, 2H), 8.3-7.9 (m, 7H),7.70 (s, 3H), 7.1 (s, 2H), 6.8 (s, 1H), 6.5 (m, 5H), 6.4 (m, 2H),5.0 (s, 4H),4.9 (m, 2H), 4.4 (m, 4H), 3.9-3.8 (m, 32H), FRET-melting assays. FRET-melting experiments were performed in a 96-well format using a Mx3005P qPCR machine (Agilent) equipped with FAM filters (lex = 492 nm; lem = 516 nm) in 100 μL (final volume) of 10 mM lithium cacodylate buffer (pH 7.2) plus 10 mM KCl/90 mM LiCl (F21T, F-duplex-T) or plus 1 mM KCl/99 mM LiCl (F-Myc-T, F-Terra-T, F-VEGF-T) with 0.2 μM of labeled oligonucleotide and 1 µM of TASQ. Competitive experiments were carried out with labeled oligonucleotide (0.2 μM), 1 µM TASQ and increasing amounts (0, 15 and 50 equiv.) of the unlabeled competitor ds17. After an initial equilibration step (25°C, 30 s), a stepwise increase of 1°C every 30s for 65 cycles to reach 90°C was performed, and measurements were made after each cycle. Final data were analyzed with Excel (Microsoft Corp.) and OriginPro®9.1 (OriginLab Corp.). The emission of FAM was normalized (0 to 1), and T1/2 was defined as the temperature for which the normalized emission is 0.5; DT1/2 values are means of 3 experiments.

Pull-down assay. The streptavidin MagneSphere® beads (Promega) were washed 3 times with TrisHCl buffer containing 1 mM KCl, 99 mM LiCl and 10 mM MgCl2. Bio(Cy)TASQ (10 µM) was mixed with 5'-labeled oligonucleotides (F-ON, 1 µM), i.e., F-Myc, F-SRC, F-22AG and F-duplex, MagneSphere® beads (32 µg) in the same TrisHCl buffer (320 µL final volume) and stirred for 2 h at 25 °C. The beads were immobilized (magnet) and the supernatant removed (fluorescence analysis 1). The solid residue was resuspended in 320 µL of TBS 1X buffer, heated for 10 min at 90 °C (gentle stirring 800 r.p.m.) and then centrifuged for 2 min at 8900 rpm. The supernatant was taken up for analysis (magnet immobilization), after being distributed in 3 wells (100 µL each) of a 96-well plate, using a ClarioStar® machine (BMG Labtech) equipped with FAM filters (lex = 492 nm; lem = 516 nm) (fluorescence analysis 2). Competitive experiments were carried out with labeled oligonucleotide (1 μM), 10 µM TASQ and in the presence of the unlabeled competitor ds12 (20 mol. equiv.). Data were analyzed with Excel (Microsoft Corp.) and OriginPro®9.1 (OriginLab Corp.); normalized FAM emission values are means of 3 measurements, according to the following methodology: i-fluorescence analysis 1: each analysis originated in 3 different experiments, performed as triplicates: a/ 3 control wells in which the F-ON was alone, whose FAM emission was normalized to 100; b/ 3 wells in which F-ON was mixed with beads, in order to quantify the non-specific F-ON/bead binding; and c/ 3 wells in which F-ON and Bio(Cy)TASQ were mixed with beads, in order to quantify the specific F-ON/Bio(Cy)TASQ/bead binding. ii-fluorescence analysis 2: each analysis originated in 2 different experiments, performed as triplicates: a/ 3 control wells comprising solutions that resulted from experiments performed with F-ON and beads, in order to quantify the non-specific F-ON/bead binding, the FAM emission of the solution was normalized to 1; and b/ 3 wells comprising solutions that resulted from experiments performed with F-ON, Bio(Cy)TASQ and beads, in order to quantify the actual Bio(Cy)TASQ capture capability when compared to the control experiments.

Cell culture and imaging. MCF7 cells were routinely cultured in 75 cm 2 tissue culture flasks (Nunc) at 37 °C in a humidified, 5% CO2 atmosphere in Dulbecco's Modified Eagle Medium (DMEM) supplemented with 10% fetal bovine serum (FBS, Gibco) and 1% Penicillin-Streptomycin (Pen-Strep: 5.0 U.mL -1 Pen/5.0 µg.mL -1 Strep, Gibco) mixture. Cells were subcultured twice a week using standard protocols. Round coverslips (12 mm) were sterilised with 70% ethanol before cell seeding. MCF7 cells were seeded at a density of 6.10 4 cells per coverslip on chambered coverslips (24 well-plate) and allowed to recover for 24 h. In the case of live-cell labelling, cells were incubated with Bio(Cy)TASQ (1 µM, 24h) at 37 °C, washed once with PBS 1X and fixed and permeabilized with ice cold MeOH for 10 min at room temperature.

In the case of post-fixation labeling, seeded cells were fixed and washed with PBS 1X (3x), then incubated with 1 µM Bio(Cy)TASQ for 1 h at 25°C, washed with PBS 1X (3 x 5 min), then incubated for 1 h at 25°C in a light-tight box with Streptavidin-Cy3 (1 µg/mL) and washed with PBS 1X (3 x 5 min) and once with H2O. Cells were mounted onto glass microscope slides with Fluoromount-G (Southern Biotech) containing DAPI (2.5 µg/mL). The cells were imaged with a Leica TCS SP8 confocal laser-scanning microscope with a 63X oil objective, collected through the following channels: DAPI (excitation: 340-380 nm; emission: < 425 nm), GFP (excitation: 450-490 nm; emission: 500-550 nm) and Cy3 (excitation: 518-562 nm; emission: > 580 nm).

Images were processed with ImageJ (https://fiji.sc). [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF]

Figure 1 .

 1 Figure 1. Structures of the DOTA-based PNA DOTASQ and BioTASQ and the cyclen-based CyTASQ and BioCyTASQ.

Figure 2 .

 2 Figure 2. Chemical synthesis of CyTASQ and BioCyTASQ.

Figure 3 .

 3 Figure 3. A. Schematic representation of the FRET-melting assay (upper panel) and results collected with doubly labelled G4s (DNA: F-21-T, F-Myc-T; RNA: F-VEGF-T, F-TERRA-T) and a duplex as a control (F-duplex-T) in the presence of TASQ ( PNA DOTASQ in black, CyTASQ in brown, BioTASQ in gray and BioCyTASQ in red). B. Schematic representation of possible intramolecular H-bond between the biotin appendage and the amide linkage of both PNA DOTASQ and BioTASQ arms. C. Competitive FRET-melting experiments performed with doubly labelled G4-DNA (F-Myc-T) or G4-RNA (F-TERRA-T) in presence of TASQ (CyTASQ in brown, BioCyTASQ in red) and increasing amounts of unlabelled duplex-DNA competitor (ds17, 15 and 50 molar equiv.).

FAM

  intensity after releasing the beads content by a thermal denaturation step (with a release enrichment up to 52-fold as compared to the control, i.e., experiments performed without TASQ, normalized to 1, panel D). The results obtained again demonstrate the improved performances of BioCyTASQ (red bars) in comparison with BioTASQ (gray bars) during the elution step (9-versus 44-, 29-versus 38-and 14-versus 52-fold enrichment for F-Myc, F-22AG and F-SRC, respectively). Again, these results also show that TASQs are specific for G4s (see the control with F-duplex, with 2-and 3-fold enrichment), a specificity further confirmed by competitive pull-down experiments performed with F-Myc, F-22AG and F-SRC (1 µM) in presence of Bio(Cy)CyTASQ (10 µM) and an excess (20 µM) of an unlabelled duplex-DNA competitor ds12 (the self-complementary strands d[ 5' CGCGA2T2CGCG 3' ]), in which the pulldown efficiency is maintained at >82% for BioTASQ and >103% for BioCyTASQ (Figure 4E).

Figure 4 .

 4 Figure 4. A. Schematic representation (A) and results (B) of the in vitro G4 pull-down protocol performed with FAM-labelled oligonucleotides (the G4s F-Myc, F-22AG and F-SRC; the hairpin F-duplex) and either BioTASQ or BioCyTASQ, quantified by either the decrease of the fluorescence of the supernatant (step 1, C) or the increase of the fluorescence during the elution (step 2, D). Competitive pull-down experiments (E) performed with F-Myc, F-22AG and F-SRC, Bio(Cy)TASQ and the unlabelled duplex competitor ds12 (20 mol. equiv.).

Figure 5 .

 5 Figure 5. Schematic representation (and images) of the Bio(Cy)TASQ-based, two-step strategies implemented to label G4s in MCF7 cells, either (A) post-fixation labelling or (B) live-cell incubation. Images are collected in the range of 518-562 nm for SA-Cy3 (yellow) and < 425 nm for DAPI (blue channel); scale bar 10 µm; yellow, white and red arrows indicate G4 foci found in perinuclear regions, nucleoli and nucleoplasm, respectively.

  H NMR (500 MHz, CDCl3): δ 4.81 (br s, 4H), 3.10 (dt, J = 6.3, 6.3 Hz, 8H), 2.89-2.73 (m, 16H), 2.08 (s, 3H), 1.54-1.49 (m, 17H), 1.43 (s, 36H), 1.31 (m, 9H). ESI-MS: [M+H] + m/z = 913.95 (calcd. for C48H97N8O8: 913.74). Compound 3: compound 1 was stirred in 2 mL of TFA for 1 hour. After evaporation of the TFA, compound 3 was obtained (78.5 mg, 0.08 mmol, 100 % yield). Compound 5: Boc-PNA G-OH (160 mg, 0.40 mmol, 4.5 equiv.) and TSTU (118 mg, 0.40 mmol, 4.5 equiv.) were dissolved in DMF (1 mL) and DIPEA was added (54 µL, 0.36 mmol, 4.0 equiv.). After 1 h, a solution of compound 3 (45 mg, 0.09 mmol, 1.0 equiv.) and DIPEA (54 µL, 0.36 mol, 4.0 equiv.) in DMF (1 mL) was added and the mixture was stirred at RT for 3 d. The solution was then concentrated under vacuum and purified by RP-HPLC in a H2O/ACN + 0.1% TFA mixture (gradient of 5 to 40 % over 20 min). After evaporation of the solvents, the compound 5 was obtained (12.3 mg, 0.01 mmol, 6 % yield). 1 H NMR (500 MHz, DMSO-d6) δ 10.94 (s, 4H), 8.31 (m, 1.3H), 8.14 (m, 0.7H), 8.02-7.78 (m, 7H), 7.03-7.01 (m, 2H), 6.76-6.55 (m, 9H), 5.08-5.00 (m, 5H), 4.88-4.84 (m, 3H), 4.19 (br s, 0.5H), 4.12 (br s, 2.5H), 3.97 (br s, 0.5H), 3.92 (br s, 0.5H), 3.87 (m, 4.5H), 3.72 (br s, 0.5H), 3.54-3.7 (m, 5H), 3.29-2.95 (m, 34H), 2.86-2.71 (m, 8H), 1.51-1.36 (m, 50H), 1.27-1.14 (m, 10H). ESI-MS: [M+H] + m/z = 2079.17259 (calcd. for C92H149N36O20: 2079.17434). CyTASQ: compound 5 was dissolved in 1 mL of TFA and stirred for 1 hour. The complete deprotection was assessed by HPLC-MS (H2O/ACN + 0.1% TFA mixture (gradient of 5 to 100 % over 7 min); retention time = 0.44 min; [M+2H] 2+ m/z = 840.0; calcd. for: C72H117N36O12 [M+2H] 2+ m/z = 839.9). TFA was removed under reduced pressure, the residue lyophilized and used immediately, without further purification.

  H NMR: (500 MHz, DMSO-d6) δ 8.01 (s, 1H), 7.84 (s, 2H), 7.70 (s, 1H), 6.80 (d, J = 14.5 Hz, 3H), 6.40 (s, 2H), 4.32 (dd, J = 7.8, 4.9 Hz, 1H), 4.21 -4.14 (m, 1H), 4.13 (dd, J = 7.8, 4.9Hz, 1H), 3.40 -3.34 (m, 5H), 3.16 (d, J = 7.5 Hz, 2H), 3.09 (dt, J = 10.0, 5.3 Hz, 1H), 3.05 (s, 13H), 2.92 (tt, J = 10.6, 5.6 Hz, 8H), 2.80 (tt, J = 13.1, 5.7 Hz, 3H), 2.71 (s, 4H), 2.13 -2.06 (m, 2H), 1.66 (tt, J = 14.1, 7.0 Hz, 2H), 1.54 (s, 11H), 1.53 (t, J = 11.4 Hz, 1H), 1.37 (d, J = 2.2 Hz, 39H), 1.30 (s, 9H), 1.28 (d, J = 7.8 Hz, 2H). 13 C NMR: (126 MHz, DMSO-d6) δ 162.9, 158.5, 158.2, 155.8, 117.5, 115.1, 77.5, 70.6, 70.3, 61.2, 59.4, 55.6, 36.7, 30.8, 29.1, 28.4, 28.3, 22.4. MALDI:

3. 5

 5 (m, 8H), 3.3 (m, 10H), 3.2 (m, 5H), 3.1 (m, 13H), 2.9 (m, 2H), 2.6 (m, 2H), 2.1 (m, 3H), 1.6 (m, 11H), 1.5 (s, 36H), 1.3 (m, 13H). ESI-HRMS: [M+H+Na] 2+ m/z = 1178.63633 (calc. for [C103H166N39O22SNa] 2+ : = 1178.63519). BioCyTASQ: compound 6 was dissolved in 1 mL of TFA and stirred for 1 hour. The complete deprotection was assessed by HPLC-MS (H2O/ACN + 0.1% TFA mixture (gradient of 5 to 100 % over 7 min); retention time = 0.38 min; [M+2H] 2+ m/z = 967.5; calcd. for C83H134N39O14S: [M+2H] 2+ m/z = 967.6). TFA was removed under reduced pressure, the residue lyophilized and used immediately, without further purification.

  C NMR: (126 MHz, D2O) δ 177.7, 165.4, 117.4, 115.1, 62.1, 60.3, 55.4, 51.9, 46.3, 44.3, 44.2, 44.0, 42.6, 42.1, 39.6, 39.1, 39.1, 35.3, 28.0, 27.9, 27.7, 24.8, 16.2. ESI-MS: [M+H] + m/z = 428.3 (calcd. for C19H38N7O2S: 428.6). Compound 4:

Acknowledgments

The authors thank the Centre National de la Recherche Scientifique (CNRS), the Agence Nationale de la Recherche (ANR-17-CE17-0010-01; ANR-18-CE07-0017-03), the Université de Bourgogne, Conseil Régional de Bourgogne and the European Union (PO FEDER-FSE Bourgogne 2014/2020 programs) and the INSERM Plan Cancer 2014-2019 (n° 19CP117-00) for financial support. Souheila Amor and Katerina Duskova are warmly thanked for their help in the pretargeted imaging protocols; Christine Arnould (INARe Dijon) and DImaCell (Dispositif Inter-régional d'Imagerie Cellulaire) for the help with and access to the microscopes.