# General Experimental Workflow

Before starting a full analysis of your system by means of INPHARMA the investigators should take care of different experimental aspects which will be here discussed.

## Ligand perspective

Determination of ligand concentration and evaluating the stability and aggregation features of the ligands wanted for the INPHARMA experiments is a pivotal aspect for success in the analysis.

### Ligands Purity

Ligands should be pure at least at 95&%, using contaminated ligand batches leads to errors in the evaluation of the NOEs.

### Ligands Concentration

The ligands are usually provided as dry crystals. Their solubility is generally different for each ligand in the library. What we usually do is to desolve a final concentration of 50-100 mM ligand in D2O or DMSO (if your target can cope with it), and add few microliters of the stock solution to the sample buffer for every ligand.

The stock ligand concentration is then evaluated by NMR via 1D experiments with a common internal reference (TSP).

- The experiments should be run with really long relaxation times (>= 15 s) to account for the long relaxation times of small molecules in D2O
- To avoid differences in the concentration of the TSP among the samples, a unique buffer should be made and aliquoted trough all the samples.
- An internal reference might also be added for the INPHARMA experiments, the measurement of the ligand concentration can however be hindered by the presence of the target resonances, overlapping chemical shifts among the ligands and differential peak broadening due to the binding of the ligands to the target. Generally T2-filtered experiments should be used to ease the concentration measurements.

### Ligands Stability

The ligands should not form aggregates once dissolved in buffer. A way to check the presence of eventual aggregates is to run a 2D NOESY with a relative long mixing time (100-200 ms) and check the sign of the NOEs. In case of aggregation the NOEs will be of the same sign of the diagonal, whereas the NOEs for small molecules in solution are expected to be opposite to the diagonal.

### Degradation of the ligands

Seldom ligands degrade during time. Since INPHARMA experiments can easily last days it is important to store the stock solution at (at least) 4 °C for DMSO solutions and -20 for water solutions. This will slow down the degradation of the ligands stocks. If the degradation is a fast process (e.g. quick oxidation of the ligands) it is of pivotal importance to prepare fresh stocks every time.

## Target perspective

It is important to prepare pure batches of target, which should be stable through all the analysis. Aspects as protein concentration, activity and aggregation should be checked and monitored.

### Concentration of the target

(Protein) target concentration is usually determined by UV spectroscopy (at 280 nm) once in the sample buffer. It is preferable to do this analysis in denaturing environment, adding target to a solution of 6 M guanidinium chloride pH 10, to avoid tertiary/quaternary structural-dependent systematic effects in the measurement.

### Activity of the target

The target folding and activity should be controlled either by NMR or independent assays (e.g. UV assays, colorimetric assays) . This controls should be made for every purification batch, since there might be a dependence on the activity of the target (normally dependent on purification issues).

## Complex Perspective

INPHARMA approach is based on the competitive binding of two ligands on the same target. The drawback of this assumption is that the competition should be assessed experimentally. This control is made preparing an INPHARMA sample with a deuterated target. The presence of interligand NOEs (or ILOEs) arising from the direct NOE transfer from one ligand to the second is assessed by NOESY experiments with long (>100 ms) mixing times. Another approach, although less accurate, would use protonated target and shorter NOESY mixing times (40-80ms). If interligand NOEs are seen in these conditions there is an high probability that the two ligands do not bind competitively. The latter approach is however dependent on the TauC of the complex and on the binding kinetics see Orts, J.; Griesinger, C.; Carlomagno, T. J. Magn. Reson. 2009, 200, 64–73.

Finally, INPHARMA analysis require the tuning of few parameters, namely the complex and ligand correlation time and the kinetic constants.

### Evaluation of the complex correlation time

Complex correlation time can be measured by T2 jump-return NMR experiments. There

[math]T_2 = \frac{2(\Delta_A-\Delta_B)}{ln(I_A/I_B)}[/math]

and

[math]\tau_c[ns] = \frac{1}{(5T_2)}[/math]

Where $\Delta$ and I (A and B) are respectively the length of the delays and the integral of the peaks in the reference experiment (A) and in the T2 jump return experiment (B). Experiments at different $\Delta_B$ are recorded (e.g. 2ms, 4ms, 8ms) and for each experiment selected target resonances $I_B$ are compared to the reference spectrum according to the formula above. A theoretical estimation is also possible, when the target structure is known, using the software HydroNMR. The obtained estimation might however differ quite a lot from the real value depending on the viscosity and temperature of the sample.

### Evaluation of the ligands correlation time

Ligands correlation time can be estimated by T1 relaxation-recovery experiments or T2-CPMG experiments. The latter experiment is however trickier since artifacts might arise from the scalar coupling of the ligand moieties.

### Evaluation of the binding kinetics

INPHARMA NOEs as seen in section SpinpharmaR, are computed taking into account one of two kinetic models, namely Model 1 and 2. The second model assumes that the target is fully saturated with ligand, whereas the first model does not give this assumption. In the two cases kinetic parameters should be provided to the program in order to get an accurate value of the theoretical NOEs.

- Model 1: [math]TL_1 + L_2 \rightleftarrows L_1 + T + L_2 \rightleftarrows TL_2 + L_1[/math] Kinetic rate constants needed: [math]k_{1off}[/math], [math]k_{1on}[/math], [math]k_{2off}[/math] and [math]k_{2on}[/math]
- Model 2: [math]TL_1 + L_2 \rightleftarrows TL_2 + L_1[/math] Kinetic rate constants needed: [math]k_{L1}[/math] and [math]k_{L2}[/math]

Model 2 requirements are more easily obtainable since [math]k_{L1}[/math] and [math]k_{L2}[/math] are basically the inverse of the [math]K_D[/math] for the two ligands.

Ligands [math]K_D[/math] can be obtained either with NMR and non NMR methods. NMR methods encompass

Non NMR methods encompass:

The latter can provide direct measurements of the [math]K_{on}[/math] and [math]K_{off}[/math] rates for each ligand.

The NMR methods can provide, given a known ligand [math]k_D[/math], values of the inhibition constant for the second ligand. Since the precision of the methodologies relies strongly on assumptions of unique and competing binding sites, and to [math]K_D[/math] of similar range, non NMR methods might be preferable to get quality measurements on the binding kinetics.

### INPHARMA Acquisition

Inpharma experiments are simple NOESY experiments. However to average time dependent effects on the sample as degradation or precipitation of the sample, we would recommend the following:

- record a single NOESY experiment with variable mixing times in a fully interleaved scan-by-scan fashion
- use a relaxation delay in accordance to the relaxation of the ligands (for fragments of 200 Da generally in the order of 3 seconds).
- In this way the integrals of the NOEs on top of the diagonal will be identical to the ones in the bottom

- integrate all the inter-ligand NOEs. Sensible differences between the top-of-the diagonal and bottom-of-the diagonal should be investigated.