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Theory of rapid force spectroscopy
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Nature Communications volume 5, Article number: 4463 (2014) Cite this article
Optical spectroscopy
In dynamic force spectroscopy, single (bio-)molecular bonds are actively broken to assess their range and strength. At low loading rates, the experimentally measured statistical distributions of rupture forces can be analysed using Kramers' theory of spontaneous unbinding. The essentially deterministic unbinding events induced by the extreme forces employed to speed up full-scale molecular simulations have been interpreted in mechanical terms, instead. Here we start from a rigorous probabilistic model of bond dynamics to develop a unified systematic theory that provides exact closed-form expressions for the rupture force distributions and mean unbinding forces, for slow and fast loading protocols. Comparing them with Brownian dynamics simulations, we find them to work well also at intermediate pulling forces. This renders them an ideal companion to Bayesian methods of data analysis, yielding an accurate tool for analysing and comparing force spectroscopy data from a wide range of experiments and simulations.
In the realm of soft matter, structural stability often hinges on delicate intermolecular bonds that are easily broken apart through external forces. The resulting malleability is characteristic of biological matter on practically all scales from single proteins1,2,3 over mesoscale cellular scaffold structures4 and individual cells5 to whole tissues6. Thanks to the development of a variety of nanomanipulation methods, intermolecular interactions can nowadays be investigated on a single-molecule level using a number of techniques commonly referred to as 'dynamic force spectroscopy'7,8,9,10,11,12, allowing the experimentalist to isolate single binding sites and probe their strength by quickly and reliably inducing hundreds or thousands of unbinding events. The wealth of stochastic unbinding trajectories thus obtained is routinely analysed through a schematic but effective description of molecular bonds in terms of the attraction range xb and the activation energy of the binding potential. To extract quantitatively useful predictions from this simple model, any theory of unbinding kinetics needs to provide a reasonable approximation to the underlying molecular dynamics. At the relatively low loading rates that were conventionally realized in experiments, any transient effects arising from the finite relaxation time of the bond itself can be neglected. This has allowed for the development of a range of analytical theories of forced bond breaking that greatly facilitate the analysis and interpretation of dynamic force spectroscopy data13,14,15,16,17,18. In contrast, detailed molecular dynamics simulations2 usually operate in the opposite limit of very high loading rates, where bond breaking becomes essentially deterministic19. Recently, also single-molecule assays are increasingly resolving the hitherto elusive rapid dynamics of bond breaking and accompanying macromolecular conformational changes, for example, in protein unfolding upon rapid loading20, or taut DNA recoil21 and supercoiling22. This provides a strong incentive to also push the existing theories to higher loading rates. Moreover, in spite of the experimental progress and improved computational abilities23, matching the loading rates used in experimental and simulation studies remains challenging20, making the development of a unified analytical theory of dynamic force spectroscopy, covering both fast and slow loading rates, all the more desirable.
To this end, we derive in the following a probabilistic theory of dynamic force spectroscopy in the spirit of Bell24, Evans & Ritchie13 and Dudko, Hummer & Szabo14 that becomes exact at high external forces (or, equivalently, high loading rates) and reduces to established results at low loading rates. We provide explicit, closed-form analytical results for the most common experimental loading protocols. They agree with exact numerical simulations of the microscopic bond model for all loading rates, save for a narrow region at the crossover from diffusion-dominated to deterministic dynamics. This makes them an ideal companion to Bayesian methods25 and a natural choice for the analysis of spectroscopy experiments and simulations alike. Moreover, we show that these results constitute the lowest-order approximation to a rigorous mathematical formulation of escape kinetics, which opens the way of their systematic extension to higher precision.
Molecular binding and unbinding transitions lie at the heart of every chemical reaction and have thus been thoroughly investigated long before the advent of single-molecule manipulation techniques. In 1940, Kramers laid down a comprehensive, analytically tractable theory of chemical reaction rates26 that has since then become synonymous with reaction rate theory and can still be considered state of the art for most applications. The basic idea is that a molecular bond corresponds to a local free energy minimum and thus remains stable under weak perturbations. Its thermal fluctuations can be represented, within an effective picture, by those of a Brownian particle trapped in some one-dimensional binding potential U(x), with the 'reaction coordinate' x typically corresponding to the distance between two binding partners. The function U(x) should have a stable minimum at x=0, surrounded by a region of attraction extending to some finite coordinate xb>0 beyond which U(x) either vanishes or turns repulsive. As soon as the particle has left the basin of attraction, x(t)>xb, the bond can be considered broken. Excluding the possibility of quantum-mechanical tunnelling, which is negligible on a macromolecular scale, the dissociation process is a tug of war between thermal and potential forces. The thermal forces drive the bond coordinate x diffusively out of the bound state and the deterministic force F(x)=−U′(x) drags it back to the origin. On a probabilistic level, the dissociation rate of an ensemble of initially bound particles can then be deduced from an associated Fokker–Planck equation27, a partial differential equation for the time-dependent distribution of particles that is mathematically exact, but cannot be solved in closed form without the help of further simplifying assumptions. In most cases of practical interest, the activation energy is large compared with the thermal energy scale, >>kBT. Dissociation then becomes a rare event, leaving sufficient time for any transients caused by the fast microscopic bond dynamics to die out. In the steady-state situation that ensues, an accurate analytical solution of the Fokker–Planck equation is possible26, yielding a time-independent unbinding rate k that scales exponentially in the activation energy, k∝exp(− /kBT).
This provides a natural starting point for the analysis of force-induced bond rupture. An external pulling force F acting along the reaction coordinate x 'tilts' the internal binding potential U, which lowers the effective free energy barrier and increases the unbinding rate. Within the Bell model24, the reaction distance xb is assumed to remain fixed under the external force, such that the force-dependent unbinding rate immediately follows as k(F)=k(0)exp(Fxb/kBT). However, reaction rates are not measured directly in single-molecule experiments, where actual unbinding times may follow a broad statistical distribution. Also, external forces are usually not constant in time. In a typical experiment, molecular bonds are pulled apart using retracting actuators such as AFM cantilevers that exhibit Hookean stretching behaviour and therefore exert forces growing linearly with their retraction distance. Assuming an external force F(t) that steadily increases in time, Evans & Ritchie13 derived from the force-dependent unbinding rate k(F) a general expression for the experimentally measured distribution p(F) of rupture forces,
Here, the force dependence of the loading rate is optional, but can be used to take into account nonlinear loading protocols or nonlinearly elastic force transducers such as polymer linkers28,29. For a power-law binding potential and a cusp-shaped binding potential of finite range, Evans & Ritchie were furthermore able to improve upon the phenomenological Bell model by accounting for force-induced shifts in the reaction distance xb. Focusing on a linearly increasing external force, Dudko, Hummer & Szabo later derived analytic results for cusp-shaped19 and linear-cubic30 binding potentials. These could finally be condensed into a uniform expression for the rupture force distribution and its first two moments that contained a new fit parameter to smoothly interpolate between different potential shapes14,15. A recent crop of theories further fleshed out the free energy landscape by taking into account the force fluctuations pertaining to stiff actuators16,17,18 (that is, actuators with a spring constant ). These theories nowadays provide the standard tools used to convert rupture force histograms obtained from force spectroscopy experiments into estimates of the underlying binding potentials.
From a dynamical point of view, these approaches still rely on a strong separation between the short timescale of internal bond dynamics and the long timescale of bond dissociation. Although this approximation is well justified in the original Kramers theory26 of a force-free bond, it is bound to break down as soon as the external loading becomes rapid enough to effectively flatten out the energy barrier before rupture occurs. In that case, unbinding becomes essentially deterministic as the bond is swept away ballistically by the external force. As shown by Hummer & Szabo19 for a harmonic cusp potential, one can accurately predict the mean rupture force at high loading rates by neglecting stochastic fluctuations altogether and afterwards obtain a global approximation to the mean rupture force by manually interpolating between the high-force result and a conventional theory that accounts for the low-rate regime.
In the following, we derive a probabilistic theory of forced unbinding that includes fluctuations even at high pulling speeds and becomes exact both in the limits of high and low loading rates. Already the leading order results of this theory surpass previous work; moreover, it provides a systematic route for further improvement. We start with the same cusp-shaped binding potential as Hummer & Szabo,
Formally, the potential becomes negatively infinite at x=xb, corresponding to an absorbing boundary condition (thus ignoring rebinding events, which quickly become negligible under external load1). Although it can be argued14 that a linear-cubic potential constitutes a more faithful approximation to many real binding potentials, we will show in the following that the practical difference between both models is often insignificant; what we lose in generality is more than made up for by what we gain in terms of analytical tractability.
To set the stage, we first summarize some basic definitions. The time-dependent probability W(x, t)dx to find any particle in the ensemble between x and x+dx follows from the Fokker–Planck equation27
Here, D denotes the diffusion coefficient and V(x, t) an external pulling force potential that may either represent some prescribed force protocol F(t)≡ −∂xV(x, t) or a moving external spring, if V(x, t)≡κ[x−y(t)]2/2. The spatially integrated distribution
is the proportion of bound particles or 'survival function' at any given time t. A constant survival function S(t)=const corresponds to zero escape events and thus a vanishing unbinding rate k=0. Likewise, a positive escape rate k>0 amounts to an exponentially decaying survival function S(t)=S(0)exp(−kt). In the general case, S(t) may be neither constant nor exponential, but an arbitrarily complex function of time. However, it is always monotonously decaying and nonnegative and thus defines a (potentially time-dependent) generalized unbinding rate k(t),
In principle, we could now solve equation (3a) (or an equivalent integral formulation31,32) numerically33 to obtain the time-dependent probability distribution W(x, t), calculate the survival probability S(t) via equation (4) and feed the result into equation (5) to precisely compute the unbinding rate k(t) for a known set of model parameters ( , xb, D). This procedure is, however, too computationally intensive for the inverse problem of obtaining , xb and D from experimental data. To arrive at an analytical approximation to the unbinding rate that is quickly evaluated on a computer, we write down a first approximation to W by ignoring the absorbing boundary,
With the external driving potential V(x, t) in equation (3c), which is at most parabolic, WG is strictly Gaussian for any localized initial distribution WG(x, t=0)=δ(x−x0). It is easily evaluated analytically,
where follows from a purely deterministic equation of motion,
C(t) denotes the positional autocorrelation function,
and χ the relative change in the system's overall spring constant introduced by the external actuator; that is, χ=1 for external fields or soft springs , otherwise.
Going back to the time-dependent escape rate equation (5), we note that the computation of (t) via equation (4) would be needlessly complicated. Since escape events can only take place at the absorbing boundary xb, the outflow of bound particles into the unbound state is equivalent to the probability flux j(xb, t)= − (t) across xb. It only depends on local properties of the probability distribution W, via the continuity equation
Replacing W by WG in equation (10) defines the corresponding approximate flux jG, survival function , and escape rate kG(t)=jG(xb, t)/SG(t).
Note that the Gaussian expressions become asymptotically exact for pulling forces greater than the critical force needed to flatten out the energy barrier, F>>Fc=2 /xb (corresponding to high loading rates in a constant-rate experiment), due to an essentially ballistic decay of the bound state. Intuitively, the probability density WG does not have time to 'sense' (and react to) the presence of the absorbing boundary before it is pulled across xb by the deterministic drift term A(x, t)WG(x, t). For the escape rate, we thus find the exact asymptotic limit
The situation is slightly more complicated for slow loading, where deterministic driving and stochastic dynamics interfere. Consider first the limiting case of a freely diffusing particle, that is, if the binding potential, the external forcing and the absorbing boundary condition are neglected. There is a purely diffusive net flux at the position xb, half of which is randomly backscattered (see Fig. 1). It is suggestive that inserting a perfect absorber at x=xb would suppress the backscattering and therefore double the diffusive flux across xb. Adding the deterministic drift back in, we get
Figure 1: Flux into an absorber at xb.
(a), Given some statistical distribution W(x, t) of particles, these particles can be driven across the position xb, either ballistically by external forces (jdrift) or diffusively through random thermal noise (jdiff.). (b) Inserting an absorber at xb effectively eliminates diffusive backscattering, thus doubling the diffusive contribution to the resultant probability flux j* into xb.
This expression for the flux can indeed be understood as the first-order approximation to an exact theory, as discussed in the Methods section. There we also show that j*(xb, t) provides an asymptotically exact expression for the escape rate at low loading rates,
We now observe that the additional factor of two in front of the diffusive component in j* compared with jG is irrelevant for the limit of large pulling rates, which is dominated by the deterministic drift term A(xb, t)WG(xb, t), suggesting that equation (11) still holds with jG replaced by j*. Moreover, note that for high energy barriers >>kBT and low pulling rates , the Gaussian survival probability SG(t) remains close to 1 since WG extends only negligibly beyond xb for all relevant times t, that is,
Our two asymptotic results can therefore be combined into the unified approximation
which is exact both in the limits of low and high loading rates. Together with equation (1), this yields the rupture force distribution
Evaluating p(F) in its general form equation (16) still requires some computational effort, since it depends in a potentially complicated way on experimental details such as the driving protocol, the initial distribution of particles within the bound state and the stiffness of the force actuator. However, for the common case of a linearly increasing pulling force F= t (exerted by an external field or a soft spring with stiffness ) we obtain the closed analytical result
where k0 is the associated force-free Kramers rate for the cusp potential,
and is the force-dependent coordinate of the maximum of WG(x,F),
In the limit of small loading rates we obtain and equation (17) reduces to the expression derived by Dudko, Hummer & Szabo (DHS) in ref. 14 for ν=1/2. In the Methods section, we provide a compilation of analogous results for stiff force transducers, arbitrary driving protocols or arbitrary initial conditions W(x, t=0) (Table 1), as well as a closed expression for the mean rupture force ‹F›.
Table 1 Analytical approximations to the rupture force distribution p(F).
Some remarks about the comparison of data and theory may be useful, here. First, note that, in any case, a comparison of data and theory for the distribution p(F) is substantially more informative than merely fitting ‹F›. Yet, every analytical approximation to the true rupture force distribution depends on at least three different parameters (binding energy , attraction range xb and diffusivity D). Direct fits of experimentally obtained rupture force histograms are therefore prone to get trapped in some local optimum in parameter space, thus often missing the best possible solution. One way to obtain more reliable results is to first aggregate several data sets obtained under different loading rates and subsequently perform a 'global' fit using a single set of parameters only. Conventionally, this is done by either performing a least-squares fit of several histograms at once or by fitting the mean rupture force as a function of loading rate13,14,15,19. Both approaches can be improved upon systematically using a maximum-likelihood approach25 that, instead of optimizing for some arbitrary measure of fit quality (such as the squared residual), employs Bayesian analysis to select those model parameters most likely to underlie the given rupture force histograms. Compared with conventional fitting methods, the maximum-likelihood approach straightforwardly extends to heterogeneous data sets encompassing different linker stiffnesses or loading protocols. Moreover, it has proven significantly more robust with respect to small ensemble sizes25, a potentially crucial advantage in the analysis of real-world experiments. In general, the larger the range of applicability of a given theory of force spectroscopy, the better the results obtained using the maximum-likelihood approach. This fact should work to our advantage, as our model covers a much wider range of loading rates than the predominant Bell–Evans 'standard model'13 and its recent extensions by DHS14 and others16,17,18. In the remainder and in the Supplementary Note 1, we illustrate the data fitting procedure with some examples and provide some practical tools and protocols for optimized data analysis.
Application to simulation data
Although our theory becomes exact in the limits of high and low external loading rates, the quality of our approximation at finite loading rates is a priori unclear. To assess the practical applicability of our method, we have thus generated synthetic rupture force distributions using Brownian Dynamics simulations of the underlying microscopic bond model (see Methods). As Fig. 2 exemplifies, our theory is as good as the approach by Hummer & Szabo19 in capturing the mean rupture force ‹F› as a function of loading rate. Moreover, whereas the Hummer–Szabo model builds on an athermal treatment of the underlying microscopic equation of motion, we fully account for thermal fluctuations. These can be significant even within the 'ballistic' regime , as Fig. 3 and the experimental data by Rico et al.20 show. Hence, our approach allows us to perform a complete and systematic Bayesian analysis (see Methods and ref. 25) of rupture force histograms (as opposed to mean rupture forces), thus making full use of the available experimental data. As apparent from Fig. 3, our approximation still breaks down at intermediate loading rates, because, in our formalism, we do not actually absorb particles as they cross the absorbing boundary at xb but merely count them. After leaving the potential well, they build up a 'phantom population' that may later produce an unphysical backflow into the bound state. In principle, this deficiency could be rectified, at least for the cusp potential, by extending the systematic integral equation approach outlined in the Methods to higher orders. Yet, the range of applicability of equation (16) already covers the vast majority of unbinding events. By simply truncating p(F) after its first zero crossing, we obtain an analytical expression for the rupture force distribution that works well at all loading rates, except for a narrow range close to a critical value .
Figure 2: Mean rupture force ‹F› as a function of loading rate.
Circles: ‹F› as determined from our numerical simulations (see Fig. 3). Crosses: best DHS15 fit (=9.49 × kBT, xb=1.01 nm, D=574 nm2 s−1). Triangles: best Hummer–Szabo19 fit ( =10.2 × kBT, xb=1.0 nm, D=1015, nm2 s−1). Squares: ‹F› determined from p(F) (see Methods section), using the fit parameters obtained in Fig. 3. Pentagons: asymptotic analytical approximation equation (40) to ‹F›, using the fit parameters obtained in Fig. 3. Inset shows the same data in double-logarithmic coordinates. The mean rupture force converges onto the Hummer–Szabo19 asymptote 1/2 at large loading rates, , and onto the logarithmic DHS asymptote ‹F›~[ln ]1/2 (ref. 14) at intermediate loading rates, (dashed red lines, shifted upwards for better visibility). In the limit →0, external forces are too small to induce rupture, yielding as the measured rupture force the force at the time of spontaneous unbinding, ‹F›~ /k0. For our choice of system parameters, the best currently available experimental setup20 would already be able to access the ballistic regime where ‹F› increases with 1/2.
Figure 3: Analytical theory compared with simulations.
Using a single set of model parameters, our theory (equation (17), solid lines) provides an accurate global approximation to both slow (a) and fast (c) external force protocols (as compared with the intramolecular relaxation timescale, in our case), apart from a narrow range (b) close to a critical loading rate ( c≈105 pN s−1 for our choice of parameters). The 'experimental' rupture force histograms have been generated by direct stochastic integration (see Methods section), using =10 × kBT, T=300 K, xb=1 nm, D=1,000 nm2 s−1 and =1…1011 pN s−1. Our best-fit parameters obtained with equation (17) are =10.15 × kBT, xb=0.98 nm, D=976 nm2 s−1. Since the mean rupture force varies by orders of magnitude at large loading rates, we use double-logarithmic scaling for >107 pN s−1 (c).
Although we find the derivation of an analytical, global approximation to the rupture force distribution p(F) satisfying in itself, its practical utility lies first and foremost in the accurate and efficient analysis of experimental unbinding data. To estimate how well our model stacks up against the prevailing methods of data analysis, we have thus analysed numerically obtained rupture force histograms, see Supplementary Fig. 1. We considered both the cusp-shaped potential and a linear-cubic binding potential (Supplementary Figs 2 and 3), using local and global (maximum-likelihood) fits both of equation (16) and of the rupture force distributions derived by DHS14 and Maitra & Arya17 (as well as a 'cusp-optimized' counterpart to their results, detailed in Supplementary Note 2) for soft and stiff linkers, respectively. Furthermore, we emulated conventional experimental procedures by fitting the mean rupture force F, using both the analytical expressions derived by Friddle15, associated to the DHS-model14, and Maitra & Arya17, as well as the numerical interpolation formula derived by Hummer & Szabo19. In the Supplementary Note 1, the interested reader will find a comprehensive discussion of all these approaches, the gist of which is as follows. At high loading rates, unsurprisingly, our theory proves superior to existing probabilistic theories13,14,16,17. More importantly, however, the combination of the maximum-likelihood analysis and our globally valid approximation is powerful enough to compete with the best conventional models even for a linear-cubic binding potential while requiring neither prior knowledge of the potential shape nor additional fit parameters. The only other global model to date, the numerical interpolation formula obtained by Hummer & Szabo, yields similarly good results as our own approach if supplied with sufficient data, although the increased computational cost of numerical integration leads to longer fitting times. Using a smaller range of loading rates (that is, 3–6 decades in instead of 12), the higher information content of our full-histogram description can produce significantly better results. Moreover, as our approach inherits the greater generality and robustness of the Bayesian maximum-likelihood analysis, this gap is bound to widen with small ensemble sizes or heterogeneous data sets. Since the maximum-likelihood method is somewhat more difficult to implement in practice than traditional methods, we wrote (and provide for free use) a ready-made Mathematica notebook that covers some of the most common force spectroscopy setups, see Supplementary Data 1.
Our theory provides an analytically tractable generic model of dynamic force spectroscopy that reproduces previously known, accurate results14,17 at low loading rates and improves upon the results derived by Hummer & Szabo for high loading rates19 by including stochastic fluctuations. It provides excellent results also at intermediate loading rates, thus constituting an ideal companion to Bayesian methods of data analysis. Apart from serving as a systematic and convenient replacement for current theories of force spectroscopy, our approach may prove crucial to the analysis of future high-speed force spectroscopy setups and full-scale MD simulations. Finally, we note that at low enough loading rates, the effect of a polymeric force transducer onto the resultant rupture force distributions can be approximated by choosing F(t) and (t) accordingly28,29. At higher loading rates, the dynamics of force propagation within the polymer21,34,35 may become relevant, which could be an interesting subject for future theoretical developments based on our theory.
Alternative derivation of equation (12b)
The (non-Gaussian) probability distribution function W(x, t) is, in the presence of an absorbing boundary at x=xb, in general not analytically tractable. However, it is related to its Gaussian counterpart WG(x, t) in a simple manner32,33,
where j(x, t) is the associated probability flux, satisfying the continuity equation
with the boundary conditions W(x, t)|x→−∞=W(xb, t)=0. The Gaussian distribution WG(x, t) and flux jG(x, t) also satisfy the continuity equation (21a) for WG(x, t)|x→±∞=0. Alternatively36, the absorbing boundary condition in equation (20b) can be interpreted as a sink term σ(x, t)<0 ∀t, resulting in the modified equation
where W(x, t)|x→±∞=0. Using the fact that the flux vanishes at infinity, j(x→−∞, t)=0, we integrate equation (21a) to obtain
or equivalently, (t)=−j(xb, t).
Taking the time derivative of equation (20a) gives
which can be compared with equation (21a), leading to
Inserting this expression into equation (21b) and then integrating over the interval (−∞, xb] results in
We now want to determine the sink term, σ(x,t). We shall therefore make the ansatz
which, by introducing the effective flux ψ(xb, t)=jG(xb, t)+g(t)WG(x, t), reduces equation (25) to
Equation (27) was originally derived by Buonocore et al. in ref. 37, where it was noted that the function g(t) can be uniquely determined using
a criterion that follows from the fact that for all t,
Solving equation (28), we obtain g(t)= −A(xb, t)/2 (ref. 38)38 and thus
Formally, equation (27) can be solved iteratively,
where 0<τn<τn−1<⋯<τ1<t and j(xb, τn) vanishes as n→∞. Truncating the above result after the first term yields a first-order approximation j0(xb, t) to the flux that coincides with equation (12b),
Asymptotic exactness at low loading rates
Our escape rate k(F) and rupture force distribution p(F) both reduce to the results of DHS (equations 3 and 4 in ref. 14 for ν=1/2), in the limit →0. The flux j*(xb, F) in equation (12b) is a sum of the Gaussian flux and the diffusive flux . Due to their asymptotic behaviour,
with Fc=2/xb and F(t) defined according to equation (53) for each limit, respectively, the diffusive flux dominates over the Gaussian flux at low loading rates. Using the expressions found in Table 1, we can determine the escape rate under the assumption that S(F)≈1 for →0,
where k0 denotes the Kramers rate (equation 18). For χ=1 (that is, an external field or a soft spring, ) the rate above coincides with equation 3 in ref. 14 for ν=1/2. For an external spring we have and obtain equation (3-S) of the Supplementary Note 2. Similarly, for it can be shown that p(F) reduces to equation 4 in ref. 14 for ν=1/2 in the case of an external field (F(t)= t) and to equation (4-S) for springs (y(t)= t), respectively.
Mean rupture force
To compute the mean rupture force ‹F› shown in Fig. 2, we have eliminated the spurious zero crossings of p(F) at intermediate loading rates by setting
and computed from p*(F) the mean rupture force via
Alternatively, we can (for constant and μ=1) provide a rough analytical estimate that is exact in the limits of small and large loading rates, respectively,
For large loading rates the mean rupture force evaluates to
where In(z) is the modified Bessel function of the first kind. This result coincides with the deterministic mean rupture force originally derived in ref. 19.
For small loading rates F≪Fc, we arrive at a result previously obtained from the Bell–Evans model by Gergely et al.39,
Here, q=exp(β [1−χ]), X=χ1/2k0/β xb and E1(z) denotes the exponential integral,
Inserting equation (38a) and (38b) into equation (37), we thus end up with
It should be noted that we provide ‹F› only for the sake of completeness. In fact, it is wasteful to discard experimentally measured force fluctuations instead of directly fitting the full histograms p(F) and we thus advise against the use of equation (40) (as much as any other available predictions for ‹F›) for analysing the experimental data.
To generate rupture force histograms across a large range of external loading rates, we have used a stochastic Euler scheme to directly integrate the equivalent Langevin equation for the Fokker–Planck equation (3a),
where ξ(t) denotes Gaussian, white noise,
and γ the bond friction coefficient, γ=kBT/D. External force is applied either through an external field V(x,t)= −x t (corresponding to a deterministic force) or through a moving external spring centred at y(t)= t. Initial particle positions are drawn from a Boltzmann distribution; once the particle position x(t) crosses xb, we consider the bond broken and record the corresponding rupture force. Although one might argue that prior knowledge of the barrier position xb allowed us an unrealistic advantage over actual experiments, we note that even beyond the critical pulling force, strong variations in the intramolecular binding potential U around xb manifest themselves in experimentally detectable force signatures, see Supplementary Note 3 and the accompanying Supplementary Fig. 4.
Maximum-likelihood method
Following ref. 25, the likelihood P of a given set of parameters , xb, D is computed as follows,
where {F} denotes the totality of rupture forces taken into consideration and
the rupture force distribution p given by equation (16), evaluated at the measured rupture forces F=Fj, with model parameters ( , xb, D) and = i. The logarithm of the right-hand side is then maximized using the 'NMaximize' method provided by Wolfram Mathematica. Since the maximum-likelihood method is somewhat more involved than conventional fitting procedures, we provide a ready-made Mathematica notebook that allows the user to analyse her data through a simple graphical interface (Supplementary Data 1).
Nonconstant loading rates and arbitrary initial conditions
In deriving equation (17), we have started from a localized initial condition W(x,t=0)=δ(x−x0), calculated the corresponding distribution of first passage times and in the end averaged over all possible starting points x0<xb using an equilibrium Boltzmann distribution. This choice of initial condition should be appropriate to most real-world scenarios, but since our theory readily extends to nonequilibrium initial conditions (corresponding, for example, to a particle held fixed by an auxiliary trapping potential that is turned off at t=0), Table 1 provides a generic rupture force distribution for arbitrary choices of W(x, t=0)≡W0(x). Importantly, for a thermally stable, smoothly varying binding potential U the initial distribution is generally Gaussian around the energy minimum at x=0,
but its width may deviate from the value obtained from our cusp-shaped model potential. To better account for other types of binding potentials (such as the often used linear-cubic potential), we can thus treat
as an additional fit parameter, in analogy to the parameter ν used by Dudko, Hummer & Szabo14 (although in contrast to ν, our fit parameter μ is relevant only at high loading rates since at low loading rates the memory of the initial condition fades away long before rupture occurs).
In Table 1, we also provide a generic expression for arbitrary force protocols F(t) that do not necessarily scale linearly in time.
Stiff force transducers
For stiff transducers, that is, external spring constants , the relation between rupture time and rupture force depends to a certain degree on the experimental time resolution. Instead of a deterministic time-dependent pulling force F(t), one measures then a force within the transducer that fluctuates with the bond coordinate x(t). These fast fluctuations are typically smoothed out using a time-moving average, which in a conventional low-speed experiment corresponds to an equilibrium average, with respect to the time-dependent combined potential U(x)+V(x, t) (molecular bond+transducer), yielding thus as the measured rupture force
As long as the effective free energy barrier is still large compared with kBT (which can safely be assumed in the limit of low loading rates ), the actual distribution of bound particles is essentially a Gaussian centred within the bound state. Hence, the anharmonicity of the molecular binding potential beyond xb can be neglected and the equilibrium position ‹x› of bound particles follows from a simple force-balance argument17 (see Fig. 4a),
Figure 4: Measuring rupture forces with a stiff transducer.
(a) As long as the bond remains intact, the combined bond-transducer system can be seen as two harmonic springs connected in series. At low pulling speeds, positional fluctuations within the bound state translate into force fluctuations that can be smoothed out via a time-moving average (see inset). (b) As long as the effective free energy barrier is still large compared with kBT, the probability distribution W(x, t) closely approximates a Gaussian centred within the bound state and ‹x›slow(t) virtually coincides with ‹x›G(t). (c) At high pulling forces, the static force-balance argument a fails, as it yields an equilibrium position ‹x›slow(t) beyond xb. The improved approximation ‹x›G(t) instead is always bounded above by xb.
where for the cusp potential. Setting , this simplifies to
Large external forces, on the other hand, may shift ‹x›slow(t) beyond xb, rendering the static force-balance argument obviously inadequate. We obtain a reasonable generalization of equation (48b) by instead truncating the time-dependent approximate probability distribution WG(x, t|x0) at x=xb and using that to compute ‹x›(t),
with mean , variance and the autocorrelation function C(t) defined as usual (note that the particle position x0 at t=0 is irrelevant in the low-force limit and is eliminated in the high-force limit by averaging over the initial distribution of particle positions W(x0, t=0)),
In the limit of low pulling forces, equation (50) reduces to the established result equation (48b), . In the high-force limit, however, an equilibrium average is no longer warranted as a force spectroscopy setup with sufficient time resolution should instead measure the transducer force at the very moment of rupture,
This equation coincides with the operational definition of 'rupture force' used by Hummer & Szabo19. Since in the limit of high loading rates, xb is generally negligible compared with the transducer position y(t) at the moment of rupture and since ‹x›G(t) is bound above by xb, we can use κ[y(t)−‹x›G(t)] as a global approximation to the rupture force; the disadvantage of this approach is that F(t) becomes difficult to solve for t. At intermediate pulling speeds, it may be reasonable to perform the functional inversion numerically; in practice, however, we propose to simply replace F(t) by its respective asymptotic limits,
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We acknowledge financial support from the European Union and the Free State of Saxony, the Deutsche Forschungsgemeinschaft (DFG) through FOR 877 and the Leipzig School of Natural Sciences—Building with Molecules and Nano-objects (BuildMoNa).
Universität Leipzig, Institut für theoretische Physik, Leipzig, 04103, Germany
Jakob T. Bullerjahn, Sebastian Sturm & Klaus Kroy
Jakob T. Bullerjahn
Sebastian Sturm
Klaus Kroy
J.T.B. and S.S. developed the theory and analysed the simulation data. S.S. and K.K. wrote the paper. J.T.B. and S.S. contributed equally to the study. All authors discussed the results and commented on the manuscript.
Correspondence to Klaus Kroy.
The authors declare no competing financial interests.
Supplementary Figures and Notes
Supplementary Figures 1-4 and Supplementary Notes 1-3 (PDF 549 kb)
Supplementary Data 1
Mathematica Notebook for data analysis and User's Guide accompanying Mathematica Notebook (ZIP 386 kb)
This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
Bullerjahn, J., Sturm, S. & Kroy, K. Theory of rapid force spectroscopy. Nat Commun 5, 4463 (2014). https://doi.org/10.1038/ncomms5463
Received: 22 January 2014
DOI: https://doi.org/10.1038/ncomms5463
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Well, I've lost another pound! This morning I weighed 184, down from 185. I weigh myself the same time every morning to keep myself in check, and it feels good to no longer see 215 pounds on the scale. I had a sugar free Instant Breakfast for breakfast, another for brunch, then for lunch ate a yummy bacon cheeseburger with fries and a king size chocolate malt at the Health Camp here in Waco!! But, now I will just have another Instant Breakfast for dinner and it will knock out the hunger like it always does. I don't kill myself with working out, and actually HATE jogging for extended distances, though I used to be a pretty good long distance runner in High School. Instead, I speed walk and then sprint for about 200 yards, speed walk and then sprint again. I repeat this pattern for about a mile and a half around the neighborhood. I actually think I get a better workout this way instead of continually jogging. It seems to get my heart rate up more and work my muscles WAY more than doing the jogging thing alone. Comments welcome!
Unfortunately, playing the piano doesn't burn many calories or get your heart rate above 120, so I had to figure out something to lose some weight. In October of 2011 I weighed 215 pounds, the heaviest of my life. I tried low carb diets, exercise, and some other things but nothing worked for me. In the picture above which I took today, I weigh 185 pounds and am still losing. Here's how I did it, and how I will keep doing it until I've lost a total of 45 pounds and tip the scales at a healthy 170.
i HAD seriously tho't about doing this too, to lose weight. I have a Hiatal Hernia and the Dr. told me to eat smaller meals more often! But I do get hungry too in between,and that's when I want the snacks.., chips, popcorn, cheese, pop... etc.
I want to be able to eat more fruits and veggies too. I have started eating oats, every morning, like my Mom said she did all her life, growing up. And that's good for you too. She also took a Vit. C every day 81mg. aspirin and zinc.. & I never saw her sick with the flu or colds EVER. But i have shrunk my stomach, also from some days not eating at all and I know that isn't good...so trying to adjust to eating more often. It doesn't take much to fill me up anymore because of that. But I know I need to adjust better things to eat and when. Got any ideas on that? I have you in my mail, so I cna see what songs you're doing next. I have enjoyed most of the songs you do and some have helped me. I took lessons at age 8, then got stopeed from school and moving, and took them again at age 14, for awhile! But eventually became a Bass guitar player/singer. Took voice in school for 3 yrs. Have been in many bands, in Cali and now Ks. But I want to be able to play solos...(take a lead solo), in songs and that's what's hard for me, unless I have practiced that lead solo for that song, I haven't been able to just pick it act, if asked to take a lead? DOn't know how to accomplish this one? HELP me on that if you can! Thanks...a fan! C.S.
Way to go!!! Remember that as you develop muscle you will not loose as much weight, that is to say that fat% is what matters. Most gyms will have a device to measure fat %. I like aerobics classes...more fun and motivating than running.
Just joined ... love your "site" Hope to bring some better chops to band practice.
You don't look fat, at least not for an American!
First Thank You. Regarding your health quest. Please get the book; "Wheat Belly" by William Davis. It changed my life for the better. Starting at 218 and ending up at 192 in approx: 9 weeks and still losing. Other than the gift of the atonement, I can't think of a better gift to give you.
Thanks again for the lessons.
I took a nutrition class in university so I can help.
Eat 1-2 healthy snacks if you're not on a diet. (Or, just eat them if you exercise that day.) An apple. Peanuts. Kettle popcorn. The list is endless.
Vitamin A, D, E, K are fat soluble, so they don't need to be consumed often. A nutritious meal has different colours and has at least three food groups.
Losing weight follows a simple equation. Energy spent is greater than energy consumed.
That means exercise! And exercise doesn't have to be boring. There are four sections to fitness: flexibility (prevents injuries! but is considered a stretch not! exercise), core conditioning (helps find balance!), strength training, and cardiovascular (expends the most energy). Exercise can be a lot of fun and an ever rewarding experience. We all know everyone dislikes running, but many of us love swimming, rugby, martial arts, grappling, skipping, biking, badminton, and so many other activities and sports created by us being.
An hour and a half of exercise is adequate exercise. Varies on the amount of effort put into it.
So be serious and have a lot of fun!
And one more thing, losing 0.5-2 pounds a week is good diet. Anything more than 2 pounds would result in extraneous loss of water, muscles, and other important things. hehe It would also likely result in regaining weight because the hormones in the stomach would soon drive you to consume more because fat cells have been shrinking and devoid of nurture.
I just want to address a comment above on hunger pain. It's natural-especially for anyone on a diet. Why? To simplify things, it's because the body has been trained to eat lots. So must practice. Relearning is always harder than learning for the first time. But the end reward is not having to do too much exercise a day, close to no health problem, and eating right for a lifetime.
And one more thing, knowing how to cook will help tremendously. Youtube has everything else I can say on this.
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text:
The Underlying Problem of The Courtier's Reply
June 5, 2014 6:13 pm \ 3 Comments \ by Intellectual Lusts
You're probably already familiar with the Hans Christian Andersen story of The Emperor's New Clothes, in which the eponymous emperor is fooled into purchasing a set of clothes so fine that only the most intelligent and sophisticated people can see them. In fact, the clothes don't exist, but the emperor, all his courtiers, and much of the population all pretend to be able to see them for fear of appearing foolish and unsophisticated.
I have often wondered why the emperor didn't raise the objection that he didn't want unsophisticated people looking at his balls.
This tale also lends a name to an argumentative tactic known as the Courtier's Reply, echoing what one of the emperor's courtiers might say when quizzed on the emperor's junk-baring status: "you're not sophisticated enough to see the clothes". The prototypical example is the theist who turns to the atheist and says "if you'd read all of Augustine and Anslem and Thomas Aquinas, you'd see that, actually, our arguments for the existence of God are very well-substantiated, and until you read and understand this material, you're not in a position to criticise it."
The Courtier's Reply is regarded in some quarters (particularly atheist areas of the internet) as an out-and-out fallacy. I have some sympathy for this position. As a rhetorical device, "you don't know enough about this topic, and if you did you would agree with me" is frustrating, unproductive and just plain rude. That said, I don't think we can legitimately call it fallacious in its own right. Moreover, its existence points to a genuine underlying problem for which I don't have a good answer.
We should probably first look at the problems with issuing Courtier's Replies from a practical standpoint.
So, burden of proof is a messy and awkward concept that lots of people get wrong, but at its heart, in the context of argumentative discourse, it boils down to the notion that if you make an assertion, you have to provide support for it. There are a few practical reasons behind this, one of the most salient being that without it, Interlocutor-B can force Interlocutor-A to carry out an arbitrary amount of work before conceding the point. Unless Interlocutor-B holds responsibility for substantiating their own assertions, they can keep manufacturing claims for Interlocutor A to evaluate for relevance, at Interlocutor-A's expense.
Issuing a Courtier's Reply has a very similar problem. Interlocutor-B can generate an arbitrary amount of work for Interlocutor A for as long as they can name areas Interlocutor-A is not familiar with. This might sound like a rules-lawyery, infinite-oregano concern, but I suspect most people who have tried to carry out productive discussion on the internet will concede that other people have minimal regard for your time or effort.
It's worth mentioning that, much like the relevance problem which burden-of-proof tries to circumvent, this isn't an infraction of logic, but of courtesy. You can't use either to substantiate factual claims. Provided you're not doing this, you're not making a fallacious argument. You are, however, being kind of a dick, and if you persistently generate work for your interlocutor, they would be quite justified in not engaging with you.
There is another very important reason why a Courtier's Reply is not intrinsically fallacious: sometimes it's quite correct. If you believe the moon is made of green cheese, there are some books you can read, and once you've read and understood them, they will quite probably change your mind.
The green-cheese-moon example, though exotic, is a surprisingly apposite one. Someone who has come to the belief of the moon being made of green cheese has a very wrong conceptual model of a lot of astronomical phenomena, and rather than figure out how this bad model is put together, the least amount of collective work probably involves pointing them in the direction of appropriate educational materials. There are a lot of similarly exotic memeplexes out there which people buy into through ignorance. I have no idea what diseased ideas lead people to believe in the Redemption Movement, or the Phantom Time Hypothesis, but the materials necessary to disabuse them of these notions are fairly identifiable, and it's doesn't feel like it's worth your time or mine to hold their hand while they work through it1.
As you may have established from other posts on this blog, I have a modest economics background. This is an area of public discourse where ignorance reigns like a mighty tyrant god-emperor. A significant number of pressing public issues are economics issues, and it should come as no surprise that the discipline has input into them. Nonetheless, certain subsets of the public imagination have cast economics as the bastard offspring of Mr. Spock and Margaret Thatcher, and many people, from a position of complete ignorance, have decided the subject is end-to-end nonsense unworthy of their time. When these people make pronouncements about Robin Hood Taxes and the inevitable collapse of global capitalism, the Courtier's Reply looks deliciously tempting.
We now come to what I see as the underlying problem of the Courtier's Reply: how do I know I'm not the ignorant one?
It's not like I've never thought along the same lines as my economically-illiterate nemeses. I'm pretty sure that if I were presented with a post-structuralist Marxist critical post-colonial analysis of Russia's current actions in Ukraine, I'd probably assume it was of extremely limited value, and this is largely based on my own preconceptions. But how do I know these preconceptions are serving me well? How do I know I'm not labouring under some exotic combination of falsehoods that would be torn apart if I just read the original Jacques Derrida?
The "PoMo cluster" radiates very strong repulsion forces to those of a technical bent. I shall ostensively define the PoMo cluster with the following examples: postmodernism; post-structuralism; post-*; critical anything; continental philosophy. The output from these areas all look like the same sort of loopy word-salad to the median STEM-background observer.
At time of writing, I'm fairly sure I could provide an explanation for what is meant by "postmodernism" that would satisfy a plurality of proponents, and I'm deferring final judgement on the broader cluster until I've explored it further, but I still mistrust the cluster. Part (though by no means all) of the reason for this mistrust is that various bits of it feel like machines for manufacturing irrelevant claims and Courtier's Replies.
That said, I imagine this is what economics might look like to my economically-illiterate nemeses.
As I said at the beginning, I don't really have a satisfactory answer for this. It falls into the general problem of "where is the good stuff that I should be reading?" The very term "Courtier's Reply" implies that the replier is defending a naked emperor. Naked emperors certainly do exist (figuratively); there are ideologies and disciplines and sets of belief which must be wrong, and yet their proponents will, in good faith, say they are right, and provide you with a litany of corroborative material beyond your resources to study. There are also ideologies and disciplines and sets of belief that look exotic from our perspective, but turn out to be extremely useful. In some cases they can demonstrate that usefulness immediately, but in others, there's little to distinguish them from a naked emperor.
How do you distinguish a naked emperor from an emperor who merely looks like his balls are showing?
Less charitably, we might suppose that people who have manoeuvred themselves into seemingly-untenable positions have done so for motives other than pure rational inquiry, in which case we're probably wasting everyone's time even further. ↩
Posted in: Uncategorized \ Tagged: atheism, bad arguments
3 Thoughts on "The Underlying Problem of The Courtier's Reply"
stephenrbenson on June 6, 2014 at 8:23 am said:
"if you'd read all of Augustine and Anslem and Thomas Aquinas, you'd see that, actually, our arguments for the existence of God are very well-substantiated, and until you read and understand this material, you're not in a position to criticise it."
No, but you've read even a bit of the Fathers of the Church, maybe some school of Alexandria, a bit of Abelard, Bernardus Silvestris, John of Salisbury, and moved up to touch on de Chardin), you would realise the positions taken by both sides of this 'debate' are reductive to the point of absurdity and farce.
Corkscrew on June 6, 2014 at 6:59 pm said:
Well, the important thing is that you've found a way to feel superior to both sides...
(Awesome reading list, though. That is genuinely impressive.)
satt on June 9, 2014 at 3:33 am said:
My current heuristic is to take criticism & disagreement seriously in proportion to how specific they are.
If someone tells me, "if you'd read anything on this subject you'd realize how woefully uninformed you really are", I give that basically zero weight. If someone waves me off by telling me to read an author or an unnamed textbook, I give that a bit more weight. If someone names a specific book or article or whatever to read, I give that more weight still. But I take someone most seriously if they extract rebuttals from their source and summarize them for me, as that indicates they're not sending me off on a wild goose chase.
If someone has enough information to know that a writer has brilliant thoughts about a topic, then presumably they can show me some of those brilliant thoughts. If they instead wave their hands and go, "no, really, no, there are many obscure dollops of insight secreted in there, they're just, like, really hard to find and impossible to summarize or even adumbrate", I find that a very bad sign.
When I'm the one who's tempted to use the Courtier's Reply, I try not to resort to it. If someone says something truly thick, I try to summarize or hint at why it was thick, even if just with a sarcastic reductio ad absurdum, rather than pointing vaguely at some authority.

redpajama_set_name: RedPajamaCommonCrawl


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Follow Dereham Road/A1074 towards Norwich. At the roundabout take the 3rd exit onto Wendene. Drive past shopping centre on left, then turn left after mini roundabout onto Bowthorpe Hall Road. Continue to end of road and turn right into Bowthorpe Hall driveway.
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text:
Publication - Factsheet
Cross-border placements of children and young people in residential care in Scotland: regulation of Deprivation of Liberty (DOL) orders
Children and Families Directorate
Children and families, Law and order
This policy relates to when a High Court in a part of the UK other than Scotland has exercised its inherent jurisdiction to authorise deprivation of liberty of a child in a residential care setting in Scotland.
Choose section
All responses and enquiries in relation to this policy should be sent to Looked_After_Children@gov.scot
Introduction: regulation of cross-border DOL placements
On 6 January 2022, we published a policy position paper on the cross-border placements of children and young people into residential care in Scotland.
The policy related to placing children and young people into Scottish residential care when the High Court in another part of the UK has granted a Deprivation of Liberty order. These DOL orders are made under the High Court's so-called "inherent jurisdiction" because there is no statutory provision to authorise deprivation of liberty in residential accommodation.
We sought views, by 28 January 2022, on proposals for regulations that would recognise DOL orders in Scotland as if they were Compulsory Supervision Orders (CSOs). CSOs are made under the Children's Hearings (Scotland) Act 2011 ('the 2011 Act'). We set out our intention to lay draft regulations in Parliament in Spring 2022 to achieve this, under section 190 of the 2011 Act.
A variety of feedback was received from around 30 stakeholders. That included responses from regulatory and oversight organisations, health and social care providers, third sector organisations, and legal stakeholders.
The engagement was focused, inviting views by email - in lieu of a formal 12-week consultation. That means most responses were submitted without the expectation that we would publish them.
We have since contacted all those who provided feedback, to seek permission to cite their views in this summary document.
Where stakeholders have published their responses on their own websites, we have included links in Annex A.
Current situation and proposal: overall response
The Independent Care Review completed its work in 2020. Its conclusions, written in 'The Promise', set out the transformational change required by 2030. The Promise was clear that the practice of selling care placements to local authorities across borders must end.
We set out our concerns that such placements result in children and young people being separated and distanced from their families, peers, community support networks and services. This impacts on the ability to plan for the child and on their ability to maintain meaningful relationships.
Most respondents shared our concerns about the current situation, for example, citing an inadequacy in current legal and care structures to support children effectively. Respondents were clear that current policy and practice provisions around cross-border DOL placements should be improved. On that basis, many expressed support, in principle, for the intention to better regulate the placement process.
Respondents agreed that cross-border placements should only occur in exceptional circumstances where the placement is in the best interests of an individual child. Many focused on the importance of Keeping The Promise, which involves reducing all cross-border placements to a minimum. One response highlighted that this could not be done abruptly, as this could make things worse for some children.
Respondents emphasised that it would be important to consider a wider strategic plan to address all types of cross-border placements (including, but not limited to, DOL placements). However, there was no shared consensus about how to approach and sequence this work. Some acknowledged the need for interim action, whereas others felt we should re-focus efforts on longer-term thinking instead. Many agreed that the proposed Children's Care and Justice (Scotland) Bill could provide a vehicle for a longer-term solution.
Many responses emphasised that children's needs and rights must be central to any work in this area.
Proposed regulations: taking key feedback into account
Responding to the specifics of the proposed regulations, there were some key details that respondents agreed upon. For example, many agreed with the proposal for the non-Scottish placing authority to be the implementation authority. This would mean they would retain full responsibility for the implementation, oversight, review and financial costs of the placement.
Respondents also agreed that converting the DOL order 'as if it were a CSO' would be more appropriate than fully converting into a CSO. For example, some stated that they would have been concerned that a full conversion would not necessarily be right for the child. It would place burdens on Scottish authorities, displacing responsibility from non-Scottish authorities. Many agreed that it is vital to address the root cause of lack of adequate provision in England in particular. Some asked whether the scope of the regulations could be extended to encompass possible cross-border DOL placements from Northern Ireland.
Respondents were also supportive of improving information-sharing processes, for example, by setting out that the placing authority should notify key Scottish stakeholders before a DOL placement occurs. They felt it would be important to create a better structure for this, helping to clarify roles and responsibilities.
However, respondents also raised a number of key concerns about some aspects of the proposal. Often respondents were supportive of the underlying policy intention, but were concerned that the proposal would not achieve the intention in practice. We have briefly summarised and responded below to the key points raised.
Policy principles
some respondents disagreed with the policy principle of legislating to recognise deprivation of liberty from another jurisdiction
At present, without Scotland accepting these placements, there would be nowhere else for these children in vulnerable situations to go. These regulations are a first step towards better regulating cross-border DOL placements, ahead of longer-term measures in primary legislation to reduce them. We recognise the complexities of this concern and continue to press the UK Government to address the issues of provision, particularly in England.
some expressed concern that the regulations could lead to an increase in cross-border DOL placements, which would run counter to the commitment to reduce them. Some emphasised the need to consider all types of cross-border placements, to avoid unintended consequences of focusing on a small subset (i.e. DOL placements)
We recognise this concern and will closely monitor the impact of the regulations. The draft regulations will include key conditions for legal recognition, which are designed to better regulate the placement process. These are more detailed than current information-sharing arrangements, so we do not anticipate that the placement process will be made 'easier' by the regulations. We will also progress shortly with the consultation on the Care and Justice Bill, seeking input on how to reduce cross-border placements to a minimum through primary legislation.
Children's rights and needs
a number of respondents raised concerns that the proposal seemed to focus on addressing the pressures that the current system places on the courts in Scotland. They emphasised that children's rights and needs should be paramount
Whilst there is a legal imperative to address a current statutory gap, the draft regulations are an opportunity to better regulate these placements and improve the status quo. It will ensure that the conditions for recognition of a DOL order in Scotland are set by Ministers, with the approval of the Parliament.
There is currently no clarity on roles and responsibilities of placing and receiving authorities. Regulations and associated administrative arrangements will clarify this, making clear that the placing authority is responsible for implementation of the DOL order and for ensuring the child's welfare. It will also provide a robust mechanism for information-sharing, which will streamline and better regulate the process.
We have also developed a proposal for an offer of advocacy to children and young people on DOL order placements, outlined in further detail below.
Children's Hearing System
many respondents supported the principle behind proposing a role for the Children's Hearing System (CHS). However, most were concerned about the lack of power available to the CHS, meaning the proposal would not lead to parity of treatment between Scottish and non-Scottish children. They highlighted that it could be confusing for the child to be involved in another legal jurisdiction when they are already involved in the non-Scottish court process
Responding to this key area of consistent concern, we are no longer proposing through these regulations a role for the CHS. Whilst the intention was to provide for parity of treatment, we recognise the lack of dispositive power available to the hearing. We also acknowledge concerns that it could increase confusion and trauma for the child, needing to interact with two different legal systems.
Operational clarity
some welcomed the intention to supplement the draft regulations with administrative agreements to support a better-regulated placement process. However, they raised concerns that these agreements would be non-statutory. They highlighted the risk that non-Scottish placing authorities would not be legally accountable for following the agreements
We acknowledge this concern, and intend that the regulations to ensure that entering into a placement agreement is also a condition for recognition of the order. We also intend to provide for Scottish Ministers to be able to apply to the sheriff court for an order to enforce the implementation authority's duty in relation to the child, if the authority is in breach of that duty.
some respondents wanted further information on some topics. For example, they asked how oversight and scrutiny of these placements could be improved. They also wanted to ensure that the roles and responsibilities of non-Scottish and Scottish authorities are clearly delineated
The regulations provide an opportunity to clearly set out the responsibilities of the non-Scottish authority as the implementation authority. We will continue to work with all key stakeholders – particularly through consultation on the Care and Justice Bill – on developing policy to further improve oversight and scrutiny of these placements.
Draft regulations: updated proposal summary
Our continued intention is to lay the proposed regulations as a short-term interim step, ahead of primary legislation. The regulations and administrative agreements provide an opportunity to ensure cross-border DOL placements are better regulated. It is necessary for us to address the current gap in legislation, and for Scottish Parliament to scrutinise the draft regulations.
In summary, we propose the following key features in the draft regulations:
provide for recognition of DOL orders granted or extended by the High Court in exercise of its inherent jurisdiction in another part of the UK, to have effect as if they were a CSO in certain circumstances. This recognition would be for a period of up to three months at a time
require the non-Scottish placing authority to notify a number key Scottish authorities in writing of key information about the DOL order as a condition of the recognition
require the non-Scottish placing authority to enter into a placement agreement as a further condition of the recognition, with the agreement containing appropriate undertakings including: to provide or secure the provision of all services required to support the child and bear all the costs arising from – or in consequence of – the placement
set out the provisions of the 2011 Act which apply and to designate the non-Scottish placing authority as the implementation authority
provide for Scottish Ministers to apply to the relevant sheriff court for an order to enforce the implementation authority's duty in relation to the child, if the authority is in breach of that duty
We also intend to put in place an offer of advocacy to children and young people on cross-border DOL placements. This would operate as an extension to the existing national children's hearings advocacy scheme in the relevant Scottish local authorities. This offer of advocacy will be intended to support affected children to understand and realise their rights, and to provide their views to the residential provider - as to how their in-placement experience aligns with their child's plan and how their welfare is being protected, in line with the welfare analysis submitted to the High Court when the placing authority first applied for the DOL order.
We welcome the feedback on the policy proposal we published in January. We are grateful to respondents for indicating which aspects they support and where they have concerns. We recognise that this is a complex policy landscape and that continued collaboration will be required to reduce all cross-border placements to a minimum.
Looked_After_Children@gov.scot


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Most spine-tingling moment of the week
July 25, 2011 by thundie
You know what's a most magical moment for me in a kdrama? When an unexpected scene comes along and stuns me with its sheer power or poignancy. I'm blown away by the intensity of emotions, both on the screen and felt by me. I feel my hair standing (in a good way).
Two nights ago I experienced such a spine-tingling moment. It was Episode 3 of You've Fallen For Me. After the opening scene (which I replayed ad nauseam; watch it and you'll know why), I could barely keep my eyes open. The episode felt plodding, shrill in parts and snail-paced in others. The jerky camerawork which had plagued Episode 1 was again making my head spin. Two female characters (both long-haired and self-absorbed) I wanted to slap silly. No, it didn't bode well.
He came. He sang. Oh, how he sang.
I first wrote about Lee Hyun-jin a year and the half ago in a brief character study that I did for Assorted Gems. That drama, incidentally, was also my first look at him. My second Lee Hyun-jin drama was Family Honor. Alas, both dramas did not leave me with a positive impression of him, the first because his character was barely more than a cameo (the writer remembered him only occasionally) and the second because he played a clingy and lovelorn student.
All those less-than-flattering impressions have been wiped clean, thanks to this scene:
This scene ranks up there with a certain scene in Can You Hear My Heart where a son, who had never acknowledged the slow-witted father who raised him, yelled for the first time in his life: "APPA!!" The chills. The goose pimples. The tears. Mine, mine, mine.
Why do I love this scene so much? It's not simply the way Lee Hyun-jin sings, the emotions so raw and searing. It's also because he sings THIS SONG from the Last Empress OST: "If I Leave."
In 2003 I bought a CD compilation of kdrama OSTs. Among the dozens of tracks in that compilation, the one I loved the most was this same song (sung by Jo Sumi).
(warning: second half of MV is spoilery]
The empress in the drama (which aired 2001) is Empress Myeongseong. I wrote about this historical figure in my Jejoongwon (Part 1: The History) post.
I don't know if I'll ever get the chance to watch the Last Empress (aka Empress Myeongseong aka The Lost Empire). But I know I'll be replaying Lee Hyun-jin's spellbinding version of "If I Leave" many times over.
K-actors K-dramas	Lee Hyun JinYou've Fallen for Me 35 Comments
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35 thoughts on "Most spine-tingling moment of the week"
soluna413 says:
I couldn't have put it better myself, my dear. I couldn't take my eyes off Lee Hyun Jin during this scene, and it's entirely possible that I'm still plodding through Heartstrings just for more glimpses of him as Ki Young, who is hands down my favorite character (even over Song Chang Eui's Seok Hyun!). Thank you much for the YT link because I will now proceed to rip it and watch it until the sun comes up. ❤
That scene was sheer magic. What I love the most was the surprise; never expected him to sing a theme song from a sageuk!
Also, I just love Kyu-won's reaction. She was so calm about it. Watching her I suddenly remembered Kim Jung-eun in Lovers in Paris when Park Shin-yang was serenading her and she responded with her OTT expressions and gestures. OMG, completely ruined the scene!
Hahanzyy says:
Same here. I find dat though Lee Hyun Jin only has a small part so far, each time he appears, he steals the whole show. I like the show on the whole but I'm always hoping for more Ki Young's appearance.
He once shared (100 point out of 100 point) that he was offered a role in Boys over Flowers (as one of the F4s) but was advised by his manager not to take it, and had since then regretted the decision after seeing what a hit the show was. I wonder wat BOF would hv been like with him in it. Hope he'll become more popular, I think he deserves it
Soluna tells me he has like five minutes per episode. Noooo!!
I have only seen him in ep 3 so far. Tried to watch ep 4 and didn't last long, alas. Going to keep watching, though. I still like the drama; there's something about it that I find strangely sweet and touching. Certain scenes take my breath away or keep me glued (Shin singing at the beginning of ep 3, Ki-young's song in the middle, and drummerboy's song toward the end); certain scenes bore me to tears.
I watched Boys Over Flowers last week. Oh boy, that was some experience! Can't imagine Lee Hyun-jin in it. Who was he supposed to be?
He didn't reveal which character he was supposed to be and the MC (park myung su) didn't push. But MC told him dat given how popular the 4 guys become, he shd sack his manager for the bad advice. Haha….
Sometimes, certain moments in the show reminds me of the movie Twilight…. When it was slow moving & playing some slow-tempo background music. Did any of you feel so?
mihinikki says:
I just saw this episode the other day too and was sooo disappointed that I spoiled myself by reading the recap of ep.3 beforehand. Still, the moment was AMAZING. Now, that YFFM is in live- shooting the writers need to put more in Ki Young NOW.
I knew from Softy's blog that LHJ was going to be in ep 3, but that was all. Had no idea what he was going to do or how he was going to steal the show. So glad I stayed away from spoilers! 😀
I have the mp3 of him singing this song I got it before I even started watching the drama LOL I heard it and I was captivated! So beautiful. Also – Wow Last Empress seems a little dark 🙂
I was really impressed by the production values. Looks like Hu Joon-ho, one of my favorite actors, is a key character here. The last two times I watched him was a very long time ago, in Jumong and All In.
QuaTrang says:
That's is one sad, emotional song and LHJ conveyed it sooooo well! But unlike you, I did like him with his role in Family Honor, especially towards the end but PSH stealt that show, so I have not enough love for anyone else 🙂 So, I am very very very happy that he came back in YFFM and will possibly steal this show (YJH as LS has not impressed me with his actiong so far and SCE's role does not leave me wanted to explore more of the back story)
I thought LHJ's acting was much better in FH than in AG; at least he had a chance to act instead of just sitting around studying! 😀 Must confess I skipped many of his scenes in FH because I just couldn't stand him being so annoying and possessive! He did change and become very sweet… once he realized he was no match for Park Shi-hoo, LOL!
Oh yes, I didnot watch AG! But I watched till episode 7 of YFFM and he had a scene or two only each episode! I hope they will pay more attention to his role! But maybe they are afraid that he could</strikethrough) will steal the show, that's why they deliberately limit his airtime (just my conspiracy theory :D)
blue says:
I love this song! I haven't watched Last Empress, but whenever I listen to this song, it makes me cry as I imagine the lyrics to be Empress Myeongseong's own words. But even if not heard in relations to Empress Myeongseong, the lyrics make me think about life in general and force me to contemplate whether I'm living my life meaningfully. I don't think anyone can beat the original, but Lee Hyun Jin really did justice to it… something that even many seasoned singers failed to do.
That said, on the most recent episode of "I Am a Singer," singer Park Jung Hyun did an amazing rendition of this song! Do check it out! And thanks for this post, Thundie! I'm so glad that you're posting regularly these days! They're like food to my soul.
Thank you for the clip, blue! I was trying to find an English-subbed version of the MV on YouTube but nothing. I actually own a DVD collection which has the Last Empress MV with English subs but I don't know how to rip it.
Was looking around minutes ago for Jo Sumi performing the song live. Couldn't find it but found this gem instead! Little girl's voice is amazing!
Just Oh My God!!!
Oops, forgot to say thank you for being so sweet and supportive, blue! Muahh! I'm trying to post more often. Shorter but more frequent posts. Not sure if I'll succeed but will keep trying! 😀
Laica says:
Wow, beautiful! It gave me chills. This song is so majestic and sorrowful. I wish I knew what the lyrics meant, although I can take a guess after watching the Last Empress mv.
mansae says:
like your banner and the quote
guess, it is from City Hunter, right?
not watching it, maybe I should..uh
Ripping lessons can be had on demand. 😎 That is one seriously great rendition. I pretty much watch the show for the music.
Sere says:
He's such a scene stealer!
NGL if it wasn't for Song Chang-ui, I wouldn't have started watching Heartstrings, but I'll keep watching it for him and Lee Hyun-jin.
I pretty much gave up on the directing. Every single time I watch an ep, I get a migraine. I also used to get angry at the PD, but at this point I'm just resigned. No point in ranting about something that'll never get better. Le sigh.
Kristal says:
I am embarassed to admit because it is so not my usual type of music but the You've Fallen For Me theme is my favorite song to listen to in the morning. Such a good pick me up! Besides the music I really am on the fence about this show. I usually watch while cleaning or folding laundry because really not much is happening that holds my attenion. I am just holding out hope that there will be some good Shin/Kyu Won scenes now that they are living in close proximity and he has given up on his useless crush on the teacher because the slave contract was completely pointless. Please don't let me down dear writer!
Lettle says:
I had no interest at all in watching Heartstrings/You've Fallen for Me(couldn't get thru the second epi of YB) But just watching that scene has me rethinking my position. Plus I've loved Lee Hyun Jin since I saw him in the movie short Boy Meets boy with Kim Hye Sung. He just stole my heart as the "bully" who really liked the other boy. Mucho chemistry between those two!!
Ooh, yes – that was definitely the high point of episode 3. Such a beautiful song, and the original is even better. That Last Empress mv is absolutely gorgeous.
I'm actually really enjoying YFFM, and I realize it's out of proportion to how good it actually is – but it touches my heart in ways that a lot of better dramas have failed to do. And I LOVE the music, which helps 🙂 I just have to look away during the performance scenes or my head starts spinning. Someone needs to tell the director that we really don't need the camera to dance along with the music, we can appreciate it on its own. Argh.
Episodes 6 and 7 were really good, IMO, and show some story development, so don't give up on YFFM! And I'm hoping for more Ki-young now that the centennial show is getting more prominent in the plot.
Omona! Beauteous song. And I watched that Empress Myeongsong clip. I think I HAVE to watch that as my next sageuk. No, I lie, I'll just watch the part when they're still kids (since the adult cast look nowhere near as compelling), it just looks so heartachingly beautiful. 2011's sageuks need to watch and learn from the production values of the days of yore.
Oh yes, I didnot watch AG! But I watched till episode 7 of YFFM and he had a scene or two only each episode! I hope they will pay more attention to his role! But maybe they are afraid that he could will steal the show, that's why they deliberately limit his airtime (just my conspiracy theory :D)
Ooops, sorry thundie, somehow I doubleposted!
Haha I agree with your conspiracy theory!
Dat's wat I thot too. He really steals the show with however little screen time he has. So I was thot script-writer is afraid dat the male lead's fans will get upset with him stealing the limelight.
Linda165 ♥ Minho says:
Now, why don't we see more of this guy per episode?
got curious on this guy and found out that he had worked with park shin hye in a cf way back..the free hugs cf of shinhye with the hot joo ji hoon (of goong) , he is the guy with the banner in that cf….i was hoping that he will complete the love triangle with shinhye and YH in this drama but seeing that until ep 7 and there is no interaction yet with him and KW, i dont think it will happen anymore…
CherKell says:
Wow. Just WOW. Hard to believe that Lee Hyun Jin progressed from the Min Guk character of "Happiness in the Wind" to this amazing performance. At least his love interest is closer to his own age this time… 🙂
Pleinair says:
wow where is like or love buttons for the posts:D i wacthed the 8 episodes and ki young's scenes are the most anticipated than the leads!! and this particular one is really a precious one!
sorry, my comment here was kinda late… but, GAH! this was the highlight so far of all episodes of YFFM… and I mean episodes 1-9! Tho, unlike most… I love this drama, Shin and Kyu-won have such chemistry and Seok-hyun is really good. And I almost left out Joon-hee. 🙂
Marsh says:
I have been wondering when they will give Ki Young more screen time in this drama. The guy could have been the better second lead. I thought that he will be one side of the triangle or square in the Gyu Won- Shin's love story. I was disappointed from ep 2-6 then come 7 and boom 8 Shin in love with Kyu WOn… so soon for me but what the heck I love Yong Hwa and Shi Hye's chemistry.. They are so beautiful together. Love yong Hwa's facial expressions and the smile I died and went ot heaven. I am still hoping that Ki Young will be part of that triangle/rectangle. I am in for the long haul now. Thanks
I love him in Family Honor anyd esp. toward the end…those kisses with the sister. But somehow he looks different now that back in the days of Family Honor..seen like a different face shape….I almost couldn't tell he was the same guy until he flash his killer smile. Anyone else gets that impression too or is it just me???