Molecular dynamics-based simulation of trace amine ... - Springer Link

J Neural Transm (2011) 118:1119–1128 DOI 10.1007/s00702-010-0569-2

BASIC NEUROSCIENCES, GENETICS AND IMMUNOLOGY - ORIGINAL ARTICLE

Molecular dynamics-based simulation of trace amine membrane permeability Mark D. Berry • Jarrod Nickel • Mithila R. Shitut Bruno Tomberli

•

Received: 4 October 2010 / Accepted: 17 December 2010 / Published online: 6 January 2011 Ó Springer-Verlag 2011

Abstract Trace amines are endogenous compounds, typified by 2-phenylethylamine (PE) and p-tyramine (TA), found in the vertebrate central nervous system. Although synthesized in pre-synaptic terminals, trace amines do not appear to act as neurotransmitters, but rather modulate responsivity to co-existing neurotransmitters. Trace amines are neither actively accumulated in synaptic vesicles, nor released in an activity-dependent manner. Further, Trace Amine-Associated Receptor 1 (TAAR1), which is selectively activated by PE and TA, is intracellular. As such, PE and TA need to cross cell membranes in order to exert their effects. This has been assumed to occur by simple diffusion, but has not previously been systematically examined. Experimental data were obtained using FluorosomeÒ ˚ /s technology. A permeability coefficient of 25.3 ± 3.8 A (n = 6) was obtained for TA which was not significantly different from that obtained for the monoamine neuro˚ /s, n = 8). PE was transmitter noradrenaline (20.3 ± 3.8 A unsuitable for use with this system. We have also used molecular dynamics computer simulation techniques to

M. D. Berry and B. Tomberli have contributed equally to this work. M. D. Berry (&) Department of Chemistry, Brandon University, 270 18th Street, Brandon, MB R7A 6A9, Canada e-mail: [email protected] M. D. Berry M. R. Shitut Toxicology Centre, University of Saskatchewan, Saskatoon, SK S7N 5B3, Canada J. Nickel B. Tomberli (&) Department of Physics & Astronomy, Brandon University, 270 18th Street, Brandon, MB R7A 6A9, Canada e-mail: [email protected]

determine the potential of mean force (PMF) associated with trace amine passage across lipid bilayers. A PMF peak barrier of 25 ± 6 kcal/mol (protonated) and 13 ± 1 kcal/ mol (deprotonated) was obtained for PE. Protonated TA peak energy barriers were even greater at 31 ± 1 kcal/mol. Application of a homogeneous solubility-diffusion model combining the measured permeability coefficients and simulated PMF allows fitting of the diffusion coefficient for trace amines in the hydrophobic region of the lipid bilayer. The diffusion coefficients in other regions of the membrane were found to make negligible contributions to the permeability coefficient for the calculated PMF. The fit obtained a value for the diffusion coefficient of (163 ± 25) 9 10-10 m2/s for TA? in the hydrophobic core region. The diffusion coefficient for TA? in the aqueous compartment was also calculated directly by simulation yielding a value of (0.62 ± 0.26) 9 10-10 m2/s. The adopted simulation methods failed to yield diffusion coefficients in the core region indicating that further work will be required to accurately predict permeability coefficients for trace amines passing through membranes. Keywords Molecular dynamics simulations Diffusion coefficient Potential of mean force Membrane permeability Trace amines 2-Phenylethylamine Tyramine Biogenic amines

Introduction The trace amines are a group of endogenous compounds that have been identified in all species so far studied (Berry 2004). In vertebrates, trace amine synthesis occurs in the pre-synaptic terminals of central nervous system neurons (Paterson et al. 1990). Unlike the well-established

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monoamine neurotransmitters dopamine, noradrenaline and 5-hydroxytryptamine (5-HT), trace amines do not appear to be actively accumulated in synaptic vesicles (Boulton et al. 1977; Juorio et al. 1988; Dyck 1989). Further, their release does not appear to be activity dependent (Dyck 1988, 1989; Henry et al. 1988). This suggests that trace amines do not function as traditional neurotransmitters (Berry 2004). Consistent with this, it was previously demonstrated that at physiologically relevant levels, the archetypal trace amines 2-phenylethylamine (PE) and p-tyramine (TA) do not mediate changes in neuronal activity (see Paterson et al. 1990; Berry 2004). Rather, at these concentrations, PE and TA both alter the responsivity of neurons to co-existing neurotransmitters, effects which occur in a neurotransmitter-selective manner (Jones and Boulton 1980; Paterson and Boulton 1988; Paterson 1993; Berry et al. 1994) and are mediated post-synaptically (Paterson 1988, 1993). This requires that the trace amines have a mechanism, presumably other than exocytosis, to exit pre-synaptic terminals. The most likely mechanism by which the effects of PE and TA are mediated is through one or more of the recently identified Trace Amine-Associated Receptors (TAAR). Both TAAR1 and TAAR4 have been shown to be selectively activated by PE and TA (Borowsky et al. 2001; Bunzow et al. 2001). Although G-protein coupled, these receptors appear to remain intracellular rather than being expressed on the outer membrane of cells (Bunzow et al. 2001; Lindemann and Hoener 2005; Xie et al. 2008). Such a situation again necessitates that for post-synaptic effects, a mechanism be present whereby trace amines can readily cross cell membranes. Previously, it has been assumed that trace amines can readily diffuse across lipid bilayers (Paterson et al. 1990; Berry 2004), largely because of their somewhat greater lipophilicity when compared to other biogenic neuronal monoamines (Oldendorf 1971; Blakeley and Nicol 1978; Mack and Bonisch 1979). Consistent with this, studies have shown that TA can cross biological membranes with the characteristics of simple diffusion (Blakeley and Nicol 1978; Tchercansky et al. 1994). Trace amine transport across lipid bilayers in the absence of membrane transport proteins has, however, not previously been directly assessed. Molecular dynamics (MD) is a long established (Alder and Wainwright 1962) simulation technique that applies Newtonian laws of physics to a system of virtual particles to make thermodynamic predictions based on the laws of statistical mechanics (for a comprehensive introduction, see Allen and Tildesley 1989). For example, the average free energy as a function of the configuration between biomolecules can be predicted. The parameters defining the configurations act as reaction co-ordinates with the free energy defining a potential landscape. The slope at any

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point in this landscape is the effective force, and often in simulations, this landscape is determined by averaging the net force on the biomolecule and is thus called the potential of mean force (PMF). By determination of the PMF, it is possible to predict the free energy changes associated with different reaction co-ordinates in a defined system, also taking into account solvent effects as well as the interactions between the molecules of interest. This extra information comes with a price: the determination of the PMF involves considerable effort and computer time (Darve 2007). In a constrained MD system, the molecules of interest are held in defined positions by use of a harmonic potential. The constraint force (PMF) required to maintain these positions is determined by calculating the average position of the molecule of interest within this well over a time much longer than the time the system takes to reach equilibrium. This will give the constraining force required to hold the molecule in the chosen position. Since the molecule is at mechanical equilibrium, the net force upon it is zero and thus the force applied by the harmonic constraint is equal and opposite (on average) to the average force applied by the surrounding solvent. There is also a considerable body of work detailing sophisticated nonequilibrium methods of extracting the PMF from simulations (Sevick et al. 2008). In the current study, both equilibrium and non-equilibrium simulation techniques have been used. In equilibrium techniques, the molecule of interest is held at a distance z, above a phosphatidylcholine (POPC) membrane by a harmonic potential exerting a position-dependent force F(z, t) at each time step, t, of the simulation. This force also depends on the particular orientation of the PE with respect to the membrane and the local solvent configuration, however, by collecting data over many thousands of time steps, the local solvent variations and orientational dependence may be averaged to yield, hF(z)i, the mean force at height z, upon the PE from the surroundings. Once hF(z)i is known, the following expression can be used to determine the PMF PMFðzÞ ¼

Zz

hFðz0 Þidz0 ;

ð1Þ

1

where the PMF at large distances is chosen to be zero. From the value of the simulated force at large distances, increasing contributions from the simulation can be added as the membrane is approached to yield the PMF at height z, as compared to the reference state of a PE molecule in the bulk aqueous solvent far from the membrane. For this geometry, it has previously been shown (Vivcharuk et al. 2008) that the net free energy change, DF, in going from far distances to a height, z, above the membrane is related to a binding constant, K, as shown below (Eq. 2):

MD-based simulation of trace amine membrane permeability

DF ¼ kB T lnðK Þ;

1121

ð2Þ

where kB is Boltzmann’s constant and T is the temperature and q ð3Þ K ¼ B; qF where qB is the concentration of compound of interest associated with the membrane and qF is the bulk concentration of compound of interest. It has previously been shown (Vivcharuk et al. 2008) that K is also related to the PMF, according to Eq. 4. 1 K¼ l l0

Zl0

dz expðPMFðzÞ=ðkB T ÞÞ:

ð4Þ

l

This has considerable advantages over previous expressions as it does not rely on the use of arbitrary reference states, and the limits l and l0 are clearly defined. The exclusion volume defines l0 , and l is where PMF(z) & 0 and z [ l. A recently developed non-equilibrium method (Nateghol Eslam et al. 2011) has also been used. Here, the free energy change from an initial configuration A to a final configuration B is determined. In non-equilibrium methods, the system is pushed too rapidly toward the final configuration B to equilibrate. This has obvious advantages in that the molecule will achieve its final configuration more rapidly than in the system taking time to equilibrate. A problem arises, however, in the determination of the unknown amount of heat generated by the dissipative work required to overcome the friction caused by moving at finite velocity. The celebrated Jarzynski equality (Jarzynski 1997) allows the determination of the free energy by averaging the work, W, to go between A and B at finite velocity over many paths (each yielding different work because of variations in the system) from A to B and weighting them exponentially: ebDF ¼ ebW ; ð5Þ where the bracketed term denotes an average over many paths from A to B. This average is generated by pulling many initial solvent configurations all sharing the same initial configuration of the molecule of interest relative to the membrane to many final configurations again all sharing the same configuration of the molecule of interest relative to the membrane. By using the weighting in the average proven by Jarzynski to yield the correct free energy, the problem of the dissipative work (i.e., heat) disappears and thus the PMF may be determined in a system driven away from equilibrium by an applied force doing work, W.

Unfortunately, methods based on Eq. 5 have the disadvantage of converging more slowly than equilibrium methods carried out with the same computational effort. Therefore, many methods have been developed that accelerate convergence considerably (reviewed in Sevick et al. 2008). The PMF can be determined by the recently developed Oscillating Forward-Reverse (OFR) non-equilibrium method (Nateghol Eslam et al. 2011). In OFR, the molecule of interest is subjected to rapid oscillation of small amplitude (compared to the distance between A and B) while slowly drifting from configuration A to B. The work required to reach a step at height z in the forward change from A to B, WF(z), and the similar work to reach that step in the reverse direction, WR(z), are determined. It has been shown (Kosztin et al. 2006) that PMFðzÞ ¼

hWF ðzÞi hWR ðzÞi ; 2

ð6Þ

thus yielding the PMF. When pulls are executed from A to B and back, the method is called the FR method. Although this method converges much more quickly than methods based on Eq. 5, it is necessary to proceed from A to B as well as from B to A. This is not feasible in many systems, especially those containing complex biological molecules where it may be difficult to return back to configuration A. Imagine, for example, a folded protein (state A) that is pulled by a force applied at each terminus to an unfolded state B. The work hWFi could be determined by averaging over many trials but hWRi is also required to determine the PMF. It has been well established that this system is unlikely to return to the folded state in a time accessible on current hardware (Galera-Prat et al. 2010) and thus the FR method may not be applicable. OFR gets around this difficulty by making smaller reversible changes in the form of oscillations to compute hWFi and hWRi in a piecewise manner which can be used to reconstruct the PMF (Nateghol Eslam et al. 2011). Molecular dynamics can also be used to determine the position-dependent diffusion coefficient, D(z). The normal way to do this is to let the molecule of interest (in this case a trace amine) move freely from a given location parametrized by the height, z, and determine the mean square displacement (Marrink and Berendsen 1996). The x and y co-ordinates are not important because, on average, the membrane does not vary in those directions and hence neither should, D(z). OFR and FR methods can determine the dissipative work, Wdiss(z), using the following relation Wdiss ðzÞ ¼

hWF ðzÞi þ hWR ðzÞi ; 2

ð7Þ

which can be used to determine the position-dependent diffusion coefficient, D(z), as follows (Kosztin et al. 2006)

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oWdiss ðzÞ DðzÞ ¼ v oz

1 :

ð8Þ

Once PMF(z) and D(z) are known, they may be substituted into the inhomogeneous solubility-diffusion equation (Marrink and Berendsen 1996) to obtain the permeability coefficient, P: Zz2 1 expðPMFðzÞ=ðkB T ÞÞ ¼ dz; ð9Þ P DðzÞ z1

where z1 denotes a position on one side of the membrane and z2 a position on the other side. Thus, equilibrium- and non-equilibrium-based MD simulations can be used to predict the permeability coefficient of any compound of interest across a lipid bilayer. In the current study, we have applied these techniques to the transit of trace amines across sphingomyelin and POPC lipid bilayers. Further, we have sought to validate such simulations by using the commercially available FluorosomesÒ (GLSynthesis Inc., Worcester, MA) system. The FluorosomeÒ system consists of uniformly sized, egg phosphatidylcholine, lipid bilayer vesicles that have a water soluble fluorescent probe trapped within the vesicle. With this system, the membrane permeability of any compound of interest can be determined by following the quenching of fluorescence in real time. The only requirement is that compounds of interest quench the fluorescence of the probe, which is readily verified using a solution of free (non-vesicle trapped) probe.

Fig. 1 System consisting of one 2PE? molecule, thirty two 18:0 SSM molecules arranged in a bilayer. The system also included 1,600 TIP3P water molecules which have been omitted from the image for clarity

protonated (ionized) or non-protonated (unionized) forms (Fig. 2). The assembled membrane was equilibrated for 5 ns at 1 atmosphere pressure and a temperature of 299 K (25–26°C). The final area per lipid in the system ˚ 2 [SSM]; 64.1 ± 1.3 A ˚ 2 [POPC]) (Fig. 3) (49.5 ± 1.1 A was consistent with the literature values for SSM of ˚ 2 (Maulik et al. 1991) and 65.8 ± 0.9 A ˚ 2 (Zhao 45.0 A et al. 2007) for POPC. The orientation of the trace amine molecule was not restrained, but the molecule and the

NH2

Materials and methods

NH3

MD simulations Computer simulations utilized the narwhal and requin nodes of the SHARCNet (http://www.sharcnet.ca) parallel computing cluster and the Brandon University HPC node of the Westgrid (http://www.westgrid.ca) parallel computing cluster. Nanoscale molecular dynamics (NAMD) version 2.71b (PE) and version 2.72b (TA) software was used, with a 2-fs time step, the SHAKEH algorithm to monitor hydrogen positions and the PARAM27 force field. Previous work (Vivcharuk et al. 2008) has shown that the MD trajectories become uncorrelated after 10 ps and that statistical error due to system fluctuations can be reduced by averaging force data over at least 5 ns. The simulations consisted of a 32 molecule stearylsphingomyelin (18:0; SSM; 16 molecules per leaflet) or 64 molecule POPC (18:0; 32 molecules per leaflet) lipid bilayer membranes, 1600 TIP3P water molecules, and 1 molecule of either PE or TA (Fig. 1), in both the

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2-Phenylethylamine

2-Phenylethylamine (ionized)

NH2

HO

NH3

HO

p -Tyramine (ionized)

p -Tyramine

OH HO

NH2

HO

Noradrenaline

Fig. 2 Structures of ionized and unionized trace amines


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For the OFR run, a single 13.5 ns pull was executed with a drift speed of 0.37 m/s for a total displacement of ˚ from 1.2 to 50.8 A ˚ from the membrane centre. 49.6 A During this long pull, the TA executed 100 sinusoidal ˚ . The total cumulative work oscillations of amplitude 1.0 A required to move the TA in its oscillating trajectory was stored at each 2 fs time step. The PMF was then obtained ˚ span into bins of 0.1 A ˚ and anaby breaking the 49.6 A lyzing the average work of the approximately 100 bin crossings in the forward direction and reverse direction and using Eq. 6 to obtain the PMF.

Area /Angstrom

2

55

53

51

49

47

45 0

100 200 300 400

500 600 700 800 900 1000

time /ps

Fig. 3 Stabilization of the assembled 18:0 SSM membrane bilayer at 310 K as a function of time. The membrane stabilized to an average ˚ after 1–2 ns. All subsequent simulations allowed lipid area of 49.5 A a membrane equilibration time of 5 ns

membrane were restrained at defined reaction co-ordinates ˚ 2] applied to using a spherical harmonic [100(kcal/mol)/A the centre of mass of each. Twenty-one different starting systems were constructed with different values of the PE height, z, from the membrane centre for each one. The constrained systems were each allowed to equilibrate for 0.5 ns during which solvent forces, hF(z)isolvent, push the trace amine molecule to its equilibrium position such that the mean total force, hF(z)i, is described by Eq. 10. hF ðzÞi ¼ hF ðzÞisolvent þ hF ðzÞiconstraint ¼ 0:

ð10Þ

It has previously been shown that measuring the constraint force gives the same result as measuring the solvent force, but converges faster (Vivcharuk et al. 2008). During simulations, the total external force on the trace amine molecule was determined at 1 ps intervals and averaged over 5–10 ns at each reaction coordinate. Each of the twenty-one different starting reaction co-ordinates ˚ intervals for each trace amine, were simulated at 2 A spanning distances from the centre of the membrane to ˚ above the membrane. Where the trace amine mol20 A ecule was placed within the membrane, a second molecule was placed symmetrically in the opposite leaflet in order to minimize leaflet disparity. The work was then integrated using a trapezoid quadrature (Eq. 1) to give the PMF over the range where forces differ significantly from zero. Initial studies verified the equilibrium calculation by substituting the trace amine molecule with Na? and the membrane with Cl-. Here, the Cl- ion was fixed and the ˚ 2 constraint applied to the Na? stretch of a 100(kcal/mol)/A ion monitored at 0.1 ps intervals to determine the average work. This was integrated as described above to obtain the PMF, which was then compared to literature values.

FluorosomeÒ studies Studies were conducted using either a SpectraMax M5 or SpectraMax M2 plate reader (Molecular Devices, Sunnyvale, CA) operating in kinetic mode and using standard opaque 96-well multi-well plates. Probe fluorescence was measured using an excitation wavelength of 494 nm and an emission wavelength of 523 nm as per the manufacturer’s instructions. All studies were conducted at a chamber temperature of 24 ± 2°C. Initial studies determined the suitability of PE and TA for use, by incubation with free probe solution. Here, fluorescence of the free probe was monitored at 1 s intervals for 25 s at which point either PE, TA, or noradrenaline (dissolved in 18 MX distilled water, 85 mM final concentration) was added and fluorescence followed for a further 25 s. Only compounds showing an immediate quenching of fluorescence greater than 10% of the average baseline value were used in subsequent studies. FluorosomeÒ assays consisted of 150 ll of the manufacturers supplied buffer (pH adjusted to 7.4) and 10 ll of FluorosomeÒ solution. Baseline fluorescence was determined at 1 s intervals for 50 s, at which point 15 ll of the compound of interest (85 mM final concentration) was added and fluorescence monitored at 2 s intervals for up to a further 350 s. Each day of experiment, a separate assay was conducted with the manufacturers supplied positive control, to verify that the assay was performing according to specifications. In each case, the permeability coefficient for the positive control was within 10% of the manufacturers supplied value. For all assays, data were exported and the post addition data fit to a one-phase exponential decay function using GraphPad Prism 4.0 software (La Jolla, CA). Equation parameters were then entered into the manufacturers supplied software in order to obtain a permeability coefficient and diffusion half-life. Data represents the mean ± SEM of 6–8 independent observations, with no more than one observation obtained per day. Differences between groups were determined by unpaired t test using GraphPad Instat 3.10 software (La Jolla, CA) and statistical significance taken at a level of P \ 0.05.

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Initial studies with a variable simulation box size and constant pressure verified that an equilibration time of 5 ns was sufficient to allow membrane stabilization (Fig. 3). Once the correct area per lipid was achieved in this manner and shown to be stable, the box size (and hence area per lipid) was fixed. The accuracy of the equilibrium method was confirmed by first determining the PMF for Na? (Fig. 4), which was in good agreement with the accepted literature value (Timko et al. 2010). The position-dependent PMF for unionized and protonated PE is shown in Fig. 5. For all trace amine data presented, the PMF was generated from large distances to the center and then, using the assumption that since the environment above and below the membrane was identical (indeed because of the periodic boundary conditions required in the simulation they are really both the same volume), a mirror image of the data was generated for the second leaflet of the membrane. An energy barrier of 13.6 ± 1.0 kcal/mol was observed for unionized PE and 25.0 ± 6.0 kcal/mol for the ionized form. A weak attractive well of -1.3 ± 0.7 kcal/mol was ˚ from the membrane observed for the protonated PE at 24 A center which is just above the phosphate headgroups as located by electron diffraction (Maulik et al. 1991). PMF curves for the ionized form of TA are shown in Fig. 6. An energy barrier of 31 ± 1 kcal/mol was observed for ionized TA. A weak attractive potential well of ˚ from the mem-4.5 ± 1.2 kcal/mol can be seen at 33 A brane centre, while the expected approximate location of the phosphate headgroups (i.e., the phosphate to phosphate distance or membrane thickness) is similar to that for sphingomyelin (Zhao et al. 2007).

20 15

2PE+ in SSM bilayer 2PE in SSM bilayer

10

e-/nm^3/20

5 0 -5 -50

-40

-30

-20

-10

0

10

20

30

40

50

distance from membrane centre /Ang

Fig. 5 PMF as a function of the distance from the center of an 18:0 SSM bilayer membrane for 2PE and 2PE? in TIP3P water at 310 K. The electron density (black curve) was constructed from the data in Maulik et al. (1991) and is shown to indicate the location of the ˚ from the membrane phosphate headgroups (the two peaks at *22 A centre in each direction). The PMF was determined through one leaflet of the membrane only, with the mirror image added for the second leaflet for illustrative purposes 35

PMF (KCal/mol)

30 25 20

Tyramine+ in POPC

15 10 5 0 -5 -10 -50

-40

-30

-20

-10

0

10

20

30

40

50

Distance from membrane centre (Angstrom)

Fig. 6 PMF as a function of the distance from the center of an 18:0 POPC bilayer membrane for TA? in TIP3P water at 310 K. The PMF was determined for one leaflet of the membrane only, with the mirror image added for the second leaflet for illustrative purposes

4 3

PMF (Kcal/mol)

PMF /KCal/mol

Results

PMF(r ) - this work

2

Literature (Timko 2010)

1 0 -1 -2 -3 2

3

4

5

6

7

8

r (Angstrom)

Fig. 4 PMF from simulation as a function of the separation between Na? and Cl- ions in water. The functionality of the simulation system was verified by determining the variation of PMF associated with a Na? ion approaching a Cl- ion and comparison to the accepted literature values for this system (Timko et al. 2010) which have been superimposed on the experimental data for illustrative purposes

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Control studies revealed that PE was unable to quench the fluorescence of the free probe (Fig. 7) and was therefore unsuitable for use with the current assay system. In contrast, TA was suitable for use. A rapid quenching of fluorescence was seen when TA was added to the FluorosomeÒ vesicle system (Fig. 8). A permeability coefficient ˚ /s and diffusion half-life of 9.7 ± 1.7 s of 25.3 ± 3.8 A (n = 6) were obtained. The permeability of the related monoamine neurotransmitter noradrenaline was also determined for comparative purposes. Although a trend for a slower membrane passage may have been present ˚ /s; diffusion half(permeability coefficient = 20.3 ± 3.8 A life = 14.7 ± 3.4 s; n = 8), this was not statistically significant (P [ 0.05).


Relative Fluorescence Units

PE added

1750 1500 1250 1000 750 500 250 0 0

10

20

30

40

50

Time (secs) Fig. 7 The effect of PE addition to the free fluorescence probe used in the manufacture of FluorosomesÒ. Fluorescence of the free probe solution was determined at 1 s intervals for 25 s at which point the compound of interest was added and fluorescence monitored at 1 s intervals for a further 25 s. Only compounds showing a greater than 10% reduction in fluorescence were used in subsequent assays

Relative Fluorescence Units

1600 1200 800 400 0 100

Eq. 8 assumes a constant velocity, whereas in the OFR method the velocity varies sinusoidally. Future work will correct for this discrepancy. Had useable values for D(z) been obtained for all parts of the membrane, they could have been used in Eq. 9 to obtain a predicted permeability coefficient (P) for comparison to our experimental values for TA diffusing across POPC bilayers. The high values of the PMF near the barrier at the center of the membrane result in the D(z) value near the membrane centre dominating the contributions to P in Eq. 9. The use of a constant D(z) in Eq. 9 effectively renders the equation a homogenous solubility-diffusion equation. Therefore, the value of D(z) that best approximates the measured permeability coefficient (i.e., FluorosomeÒ results) is a measure of the average diffusion coefficient in the hydrophobic core region. The value of D(z) was manually fit to reproduce the measured P and its error using Eq. 9. The resulting value from the fit was (163 ± 25) 9 10-10 m2/s.

Discussion

TA added

0

1125

200

300

400

Time (secs) Fig. 8 Time course for tyramine diffusion into phosphatidylcholine bilayer FluorosomeÒ vesicles. Fluorescence of FluorosomesÒ was monitored at 1 s intervals for 50 s at which point the compound of interest was added. Post addition, fluorescence was monitored at 2 s intervals for a further 350 s. Post addition data were fit to a one-phase exponential decay function using GraphPad Prism 4.0 software

Application of Eqs. 7 and 8 yielded the positiondependent diffusion coefficient D(z). This plot varied little outside the membrane region and was very noisy inside the membrane. Hence, it was decided to use a constant value for D(z) in each of three regions defined as follows: (1) ˚ , (2) interfacial region, bulk solvent region, z [ 41.7 A ˚ [ z [ 21 A ˚ , and (3) hydrophobic core region, 41.7 A ˚ [ z. The corresponding values were (1) (0.62 ± 21 A 0.26) 9 10-10 m2/s, (2) (0.5 ± 7.6) 9 10–10 m2/s, and (3) (2.3 ± 30) 9 10–10 m2/s. The values in regions (2) and (3) are clearly not significant and therefore a plot of D(z) is not shown. The reason for the poor results for D(z) is that

The discovery of a family of G-protein coupled receptors, at least a sub-set of which show high selectivity for trace amines (Borowsky et al. 2001; Bunzow et al. 2001), has led to a resurgence of interest in the physiological role(s) of these compounds. Although trace amines have close structural similarity to the monoamine neurotransmitters and are synthesized in neurons by comparable pathways, there is increasing evidence that they do not function as traditional neurotransmitters, at least in vertebrates (Berry 2004). At physiological concentrations, neither PE nor TA directly affects neuronal activity, although the effects of co-existing neurotransmitters are modified (reviewed in Paterson et al. 1990; Berry 2004). Further, available evidence suggests that trace amines are not actively stored in synaptic vesicles (Boulton et al. 1977; Juorio et al. 1988; Dyck 1989), nor released in an activity-dependent manner (Dyck 1988, 1989; Henry et al. 1988). Finally, unlike other G-protein coupled receptors, TAAR do not appear to be expressed on the outer surface of cells, rather remaining intracellular (Bunzow et al. 2001; Lindemann and Hoener 2005; Xie et al. 2008). Since the modulatory effects of PE and TA have been shown to be post-synaptically mediated (Paterson 1988, 1993), this requires that the trace amines readily cross cell membranes. This has previously been assumed to occur by simple diffusion (Paterson et al. 1990; Berry 2004), but has not been systematically examined in the absence of membrane transporters that can complicate data interpretation. Molecular dynamics-based simulations are being increasingly used to predict interactions with biological molecules, including the ability of various chemical

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species to cross lipid bilayers in the absence of protein transporters. While techniques have been established for the accurate prediction of the interactions of atom-sized ions (Timko et al. 2010), very few studies have been conducted with more typical drug-sized molecules (molecular weight range 100–500 Da). Boggara and Krishnamoorti (2010) described MD simulations for the passage of non-steroidal anti-inflammatory drugs across a dipalmitoylphosphatidylcholine bilayer membrane, but the simulated data was not compared with direct measurement of membrane passage. Since trace amines fall within the molecular weight range of typical drug-sized molecules, and non-exocytotic membrane passage appears to be inherent to their physiological activity, we have investigated the ability of MD simulations to accurately predict membrane diffusion of PE and TA. We chose to use both SSM (18:0) and POPC (18:0) molecules to construct the lipid bilayers since trace amines are synthesized in neurons and sphingomyelin is particularly enriched in neural membranes, while our validation system uses POPC vesicles. Initial studies validated the functioning of the system by comparing the PMF curves obtained for Na? to those in the literature. A good agreement was found between our system (Fig. 4) and the accepted literature values (Timko et al. 2010). Both PE and TA are primary amines with pKa values of 9.8 (Hall 1957; Tuckerman et al. 1959) and 9.2 (Tuckerman et al. 1959), respectively. Hence, at typical physiological pH both will be in excess of 90% ionized. We therefore simulated the membrane permeability of the ionized form of both. For comparative purposes, the non-ionized form of 2PE was also simulated. As expected, the ionized forms were predicted to have a considerably higher energy barrier for membrane passage (Figs. 5, 6). Further, an initial favorable, attractive force was observed for the ionized forms ˚ of the phosphate head groups. when they were within 2 A This likely represents electrostatic interactions between the positively charged trace amine and negatively charged phospholipid head groups. Such interactions will be governed by Coulomb’s Law (Eq. 11) Ecoulomb ¼

kq1 q2 ; Dr

ð11Þ

where k is a proportionality constant (322 for energies expressed in kcal/mol), q1 and q2 are the charges on the interacting molecules, D is the dielectric constant of the medium (80 for water, 2 in the hydrophobic core and lying in between those values in intermediate regions), and r is the distance between the interacting molecules. Using Fig. 5, a distance between opposing elementary charges ˚ was estimated. Equation 11 predicts an energy of of 2.0 A -2 kcal/mol for either trace amine interacting with ˚ in an phospholipid head groups at a distance of 2 A

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aqueous medium. This is in good agreement with the observed -1.3 kcal/mol for PE and -4.5 kcal/mol attractive forces observed for PE and TA, respectively (Figs. 5, 6). Better agreement would likely be obtained if the actual value of the local dielectric constant were determined. Application of the homogeneous solubility-diffusion equation to determine the diffusion coefficient within the hydrophobic core for TA? yielded a diffusion coefficient of (163 ± 25) 9 10-10 m2/s. This is about 10 times higher than the diffusion coefficients typical for uncharged amino acids in aqueous media (Pras et al. 1989; Umecky et al. 2006). The simulation qualitatively (i.e., with error larger than the predicted value) predicts higher D(z) in the hydrophobic core than in water, but not to the extent suggested by the calculated coefficient of (0.63 ± 0.26) 9 10-10 m2/s in water above the membrane and the fit coefficient of (163 ± 25) 9 10-10 m2/s in the hydrophobic core. It is possible that the hydrated ion diffuses more slowly than the uncharged amino acid in water where the hydration shell could slow diffusion due to frictional constraints. As there are no results available for TA and the data of Umecky et al. (2006) show factor of two variations between amino acids, this must be regarded as an open question for now. With more data available, it would be possible to make more meaningful comparisons. Certainly, the algorithm needs to be improved as it does not account for the changing velocity used in OFR and only uses an average velocity. However, it is unlikely that this will produce errors of a factor greater than order unity. The value for the charged TA is lower than that for uncharged amino acids which is consistent with commonly held qualitative belief, but no charged amino acid diffusion coefficient data was found to determine if the value for D(z) of TA? in water found by OFR is accurate. If it is, then there is quite an astounding increase in diffusion coefficient for TA? in the hydrophobic core. This seems unlikely and it seems more likely that the MD results will, once obtained independently (i.e., without fitting to experimental data as was done here) for the hydrophobic core, yield permeability coefficients that are low compared to experiment. This will indicate that the force model used is inaccurate for these substances and that either the model must be improved or be limited to qualitative (relative) conclusions only. FluorosomesÒ represent a convenient method to validate the simulation studies. The FluorosomeÒ system consists of uniformly sized phosphatidylcholine bilayer vesicles, with a fluorescent probe trapped within the vesicles. Membrane diffusion can then be followed in real time by monitoring the quenching of fluorescence. PE was not suitable for use, as significant quenching of untrapped fluorescence was not observed (Fig. 7). TA resulted in a very rapid quenching of vesicle-trapped fluorescence (Fig. 8), with a permeability


˚ /s and diffusion half-life of coefficient of 25.3 ± 3.8 A 9.7 ± 1.7 s. These data agree with previous studies using isolated biological membranes, where a very rapid, temperature independent transport of TA was observed (Blakeley and Nicol 1978). Further the data here indicate that the differences in trace amine and monoamine neurotransmitter transport previously observed (Blakeley and Nicol 1978) represents the presence of specific transporters for monoamine neurotransmitters that counteract their ability to readily diffuse across lipid bilayers, rather than differences in membrane diffusion which we have shown here to be negligible. Transporters with a high affinity/ selectivity for trace amines have not been identified. Although at high concentrations trace amines can interact with neurotransmitter transporters (Baker et al. 1976; Raiteri et al. 1977; Parker and Cubeddu 1988), it is unlikely that they reach such levels under physiological conditions (Berry 2004). Thus, direct measurement of TA permeability indicates that although the MD system was validated using Na?, it does not accurately predict the membrane permeability of larger, more typically drug-sized molecules. FluorosomesÒ are constructed using chicken egg phosphatidylcholine. Although this contains a mixture of fatty acids, it is primarily palmitate (16:0) and oleate (18:1) (Kuksis and Marai 1967). The physicochemical differences between this and the pure 18:0 SSM and 18:0 POPC membranes employed in the simulations is unlikely to explain the large difference in diffusion rates obtained. Since biological membrane thickness is typically reported to be in the ˚ range, while the in vivo neuronal effects of trace 30–50 A amines are seen within a few seconds of administration (Paterson et al. 1991; Berry et al. 1994), our FluorosomeÒ data indicate that the physiological effects of trace amines can occur following ‘‘release’’ by simple diffusion and do not necessitate the involvement of specific membrane transporter systems. In summary, we have provided the first direct measurement of trace amine diffusion across lipid bilayer membranes in the absence of transporter systems. The experimental data indicate that previously observed physiological effects of trace amines can occur following simple diffusion across lipid bilayers, consistent with previous suggestions (Paterson et al. 1990; Berry 2004). Further, the data indicate that monoamine neurotransmitters also readily cross lipid bilayers. Physiologically, this is likely counteracted by the presence of specific high-affinity reuptake transport systems. Such systems have not been identified for trace amines, which are thus free to exert effects following diffusion across membranes. The hypothesized physiological role of trace amines (Berry 2004) is consistent with such a situation, as trace amines only exert effects if neurotransmitters are co-existing. Such

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co-existence will, under normal conditions, only occur following exocytotic, activity-dependent release of neurotransmitter. Further, the data indicate that MD simulations established for atom-sized ions may not accurately predict the membrane diffusion of typical drug-sized molecules and may require additional refinement once an accurate method for determining D(z) in the hydrophobic core is applied. The MD data clearly indicate that the high potential barrier in the hydrophobic core is the main obstacle to permeability. This localized high barrier also causes the diffusion coefficients outside the barrier region to carry very little weight, hence it is important to determine D(z) in the hydrophobic barrier region accurately for quantitative permeability coefficient predictions. Only a high-diffusion coefficient in the core will reconcile the experimental and simulated data. The data further emphasize the need to validate MD simulations by direct measurement of the interactions using compounds with physicochemical characteristics as close as possible to those used in the simulations. Future work will be directed to these problems. Acknowledgments Financial support was provided by National Science and Engineering Research Council (MDB and BT), Canadian Foundation for Innovation (MDB), Manitoba Research Infrastructure Fund (MDB), and Brandon University (MDB and BT). During the course of these studies, JN was in receipt of a NSERC Undergraduate Student Research Award and MRS a University of Saskatchewan graduate student scholarship. The authors gratefully acknowledge Dr. Deborah Anderson (Saskatoon Cancer Centre) for providing SpectraMax M5 plate-reader access, Dr. Chris Gray, and Dr. Frances Sharom (University of Guelph) for useful discussions and Bryan Holland (University of Guelph) for providing OFR trajectory analysis software.

References Alder BJ, Wainwright TE (1962) Phase transition in elastic disks. Phys Rev 127:359–361 Allen MP, Tildesley DJ (1989) The computer simulation of liquids. Clarendon Press, Oxford Baker GB, Raiteri M, Bertollini A, del Carmine R, Keane PE et al (1976) Interaction of b-phenylethylamine with dopamine and noradrenaline in the central nervous system of the rat. J Pharm Pharmacol 28:456–457 Berry MD (2004) Mammalian central nervous system trace amines. Pharmacologic amphetamines, physiologic neuromodulators. J Neurochem 90:257–271 Berry MD, Scarr E, Zhu M-Y, Paterson IA, Juorio AV (1994) The effects of administration of monoamine oxidase-B inhibitors on rat striatal neurone responses to dopamine. Br J Pharmacol 113:1159–1166 Blakeley AGH, Nicol CJM (1978) Accumulation of amines by rabbit erythrocytes in vitro. J Physiol 277:77–90 Boggara MB, Krishnamoorti R (2010) Partitioning of nonsteroidal antiinflammatory drugs in lipid membranes: a molecular dynamics simulation study. Biophys J 98:586–595 Borowsky B, Adham N, Jones KA, Raddatz R, Artymyshyn R et al (2001) Trace amines: identification of a family of mammalian G

123

1128 protein-coupled receptors. Proc Natl Acad Sci USA 98:8966– 8971 Boulton AA, Juorio AV, Philips SR, Wu PH (1977) The effects of reserpine and 6-hydroxydopamine on the concentrations of some arylalkylamines in rat brain. Br J Pharmacol 59:209– 214 Bunzow JR, Sonders MS, Arttamangkul S, Harrison LM, Zhang G et al (2001) Amphetamine, 3,4-methylenedioxymethamphetamine, lysergic acid diethylamide, and metabolites of the catecholamine neurotransmitters are agonists of a rat trace amine receptor. Mol Pharmacol 60:1181–1188 Darve E (2007) Thermodynamic integration using constrained and unconstrained dynamics. In: Chipot C, Pohorille A (eds) Free energy calculations: theory and applications in chemistry and biology. Springer, Berlin, pp 119–170 Dyck LE (1988) Release of some endogenous trace amines from rat striatal slices in the presence and absence of a monoamine oxidase inhibitor. In: Boulton AA, Juorio AV, Downer RGH (eds) Trace amines: comparative and clinical neurobiology. Humana Press, Totowa, NJ, pp 223–237 Dyck LE (1989) Release of some endogenous trace amines from rat striatal slices in the presence and absence of a monoamine oxidase inhibitor. Life Sci 44:1149–1156 Galera-Prat A, Gomez-Sicilia A, Oberhauser AF, Cieplak M, CarrionVazquez M (2010) Understanding biology by stretching proteins: recent progress. Curr Opin Struct Biol 20:1–7 Hall HK Jr (1957) Correlation of base strengths of amines. J Am Chem Soc 79:5441–5444 Henry DP, Russell WL, Clemens JA, Plebus LA (1988) Phenylethylamine and p-tyramine in the extracellular space of the rat brain: quantification using a new radioenzymatic assay and in situ microdialysis. In: Boulton AA, Juorio AV, Downer RGH (eds) Trace amines: comparative and clinical neurobiology. Humana Press, Totowa, NJ, pp 239–250 Jarzynski C (1997) Nonequilibrium equality for free energy differences. Phys Rev Lett 78:2690–2693 Jones RSG, Boulton AA (1980) Interactions of p-tyramine, mtyramine, or b–phenylethylamine and dopamine on single neurons in the cortex and caudate nucleus of the rat. Can J Physiol Pharmacol 58:222–227 Juorio AV, Greenshaw AJ, Wishart TB (1988) Reciprocal changes in dopamine and b-phenylethylamine induced by reserpine in the presence of monoamine oxidase inhibitors. Naunyn Schmiedebergs Arch Pharmacol 338:644–648 Kosztin I, Barz B, Janosi L (2006) Calculating potentials of mean force and diffusion coefficients from nonequilibrium processes without Jarzynski’s equality. J Chem Phys 124:064106 Kuksis A, Marai L (1967) Determination of the complete structure of natural lecithins. Lipids 2:217–224 Lindemann L, Hoener MC (2005) A renaissance in trace amines inspired by a novel GPCR family. Trends Pharmacol Sci 26:274–281 Mack F, Bonisch H (1979) Dissociation constants and lipophilicity of catecholamines and related compounds. Naunyn Schmiedebergs Arch Pharmacol 310:1–9 Marrink SJ, Berendsen HJC (1996) Permeation process of small molecules across lipid membranes studied by molecular dynamics simulations. J Phys Chem 100:16729–16738 Maulik PR, Sripada PK, Shipley GG (1991) Structure and thermotropic properties of hydrated N-stearoyl sphingomyelin bilayer membranes. Biochim Biophys Acta 1062:211–219

123

M. D. Berry et al. Nateghol Eslam M, Holland BW, Gray CG, Tomberli B (2011) Driftoscillatory steering with the forward-reverse method for calculating the Potential of Mean Force. Phys Rev E (in press) Oldendorf WH (1971) Brain uptake of radiolabelled amino acids, amines, and hexoses after arterial injection. Am J Physiol 221:1629–1639 Parker EM, Cubeddu LX (1988) Comparative effects of amphetamine, phenylethylamine and related drugs on dopamine efflux, dopamine uptake and mazindol binding. J Pharmacol Exp Ther 245:199–210 Paterson IA (1988) The potentiation of cortical neurone responses to noradrenaline by b-phenylethylamine: effects of lesions of the locus coeruleus. Neurosci Lett 87:139–144 Paterson IA (1993) The potentiation of cortical neurone responses to noradrenaline by 2-phenylethylamine is independent of endogenous noradrenaline. Neurochem Res 18:1329–1336 Paterson IA, Boulton AA (1988) b-Phenylethylamine enhances single cortical neurone responses to noradrenaline in the rat. Brain Res Bull 20:173–177 Paterson IA, Juorio AV, Boulton AA (1990) 2-Phenylethylamine: a modulator of catecholamine transmission in the mammalian central nervous system? J Neurochem 55:1827–1837 Paterson IA, Juorio AV, Berry MD, Zhu M-Y (1991) Inhibition of monoamine oxidase-B by (-)-deprenyl potentiates neuronal responses to dopamine agonists but does not inhibit dopamine catabolism in the rat striatum. J Pharmacol Exp Ther 258:1019–1026 Pras N, Hesselink PGM, ten Tusscher J, Malingre TM (1989) Kinetic aspects of the bioconversion of L-tyrosine into L-dopa by cells of Mucuna pruriens L. entrapped in different matrices. Biotechnol Bioeng 34:214–222 Raiteri M, del Carmine R, Bertollini A, Levy G (1977) Effect of sympathomimetic amines on the synaptosomal transport of noradrenaline, dopamine and 5-hydroxytryptamine. Eur J Pharmacol 41:133–143 Sevick EM, Prabhakar R, Williams SR, Searles DJ (2008) Fluctuation theorems. Annu Rev Phys Chem 59:603–633 Tchercansky DM, Acevedo C, Rubio MC (1994) Studies of tyramine transfer and metabolism using an in vitro intestinal preparation. J Pharm Sci 83:549–552 Timko J, Bucher D, Kuyucak S (2010) Dissociation of NaCl in water from ab initio molecular dynamics simulations. J Chem Phys 132:114510 Tuckerman MM, Mayer JR, Nachod FC (1959) Anamolous pKa values of some substituted phenylethylamines. J Am Chem Soc 81:92–94 Umecky T, Kuga T, Funazukuri T (2006) Infinite dilution binary diffusion coefficients of several a-amino acids in water over a temperature range from (293.2 to 333.2) K with the Taylor dispersion technique. J Chem Eng Data 51:1705–1710 Vivcharuk V, Tomberli B, Tolokh IS, Gray CG (2008) Prediction of binding free energy for adsorption of antimicrobial peptide lactoferricin B on a POPC membrane. Phys Rev E 77:031913 Xie Z, Vallender EJ, Yu N, Kirstein SL, Yang H et al (2008) Cloning, expression and functional analysis of rhesus monkey trace amine-associated receptor 6: evidence for lack of monoaminergic association. J Neurosci Res 86:3435–3446 Zhao W, Rog T, Gurtovenko AA, Vattulainen I, Karttunen M (2007) Atomic-scale structure and electrostatics of anionic palmitoyloleoylphosphatidylglycerol lipid bilayers with Na? counterions. Biophys J 92:1114–1124