Dear Charles, we have tried to describe the advantages and pitfalls of ThermoFluor (thermal shift assay) in our chapter that I have attached here.

My guess would be that your ligand binds weaker than 100 uM Kd. Your ligand needs to be at least about 10 uM strong to exhibit definite shift at your described conditions. Please let me know if you have more questions.

Try to change scan velocity

Dear Charles, If you see a good melting transition without your compound, it is possible that the binding stabilizes your protein too much that the Tm is now beyond the detection limit. Reducing compound concentration may solve the problem.

Possibly your protein does not bind the ligand at high temperatures. How did you measure the protein unfolding in your pilot studies? Longtime stability at lower temperatures and the Tm do not necessarily correllate. Although often there is a relationship.

If the protein is thermo stable, unfolding of the protein may be due to charge variations aroused in the protein due to ligand binding. Here the solvation conditions are also to be considered during the study.

Screen for different buffer conditions.

The Tm in thermofluor assay can change by more than 10°c given the composition of buffer. Maybe in your present buffer, your thermal stability is already optimal, and you can't see a shift when binding the ligand. If you perform the experiment in a buffer that gives you a lower thermal stability, maybe you will be able to see a shift with the ligand.

Is your ligand soluble in the same buffer as your protein? Do you have residual DMSO? Are you are measuring a simple two-state unfolding equilibrium. Is the thermal denaturation reversible? Or are you just measuring aggregation?

If protein and ligand are available at these concentrations why not CD or DSC

Why not use another methods? For example CD melting curve can help, if buffer allows

"However when I add the ligand (100 microM ligand to 1microM protein) I can not detect a shift in Tm" -- what do you mean, you don't observe unfolding at all after adding the ligand, so no Tm? Did I get you right? First of all, isn't the ligand concentration too large? Second, what kind of ligand you have, low molecular, high molecular? Third, what is your control parameter? Temperature, I guess... So are you increasing it, or decreasing? How does the ligand bind? H-bonding, like urea and water, or covalent bonds? If h-bonding, it may well happen that you have shifted your system to the interval of temperatures, where system is stable. As an example, take a look at this: Phys. Rev. E 83, 051903 (2011). Or if you have large ligands and they act as osmolytes (like PEG, not bonding), you may look here: Phys. Rev. Lett. 109, 068101 (2012).

I am not sure the ligand can affect the melting temperature (Tm) of your protein. One may assume that ligand binding can stabilize the native state of the protein below the "melting temperature" of the binding between the ligand and your protein. However, this Tm of binding could be much lower than Tm of your protein. So you may only be able to see difference on the native baseline of the melting curve.

I agree with the others that you may need to screen for different buffer conditions such as ionic strength as it can strongly affect the ligand binding.

To check the potential aggregation during the protein melting measurement, you also want to check the reversibility or concentration dependence on the melting curve.

For direct measurement of protein melting, CD or DSC is better since DSF (good for rapid screening) relys on hydrophonic attachment of a fluoresence dye to your protein. Maybe the added ligand interfered or competed for the attachement at the given condition.

Some disadvantages or factors affecting DSF measurement are listed in the link below:

http://thermofluor.org/resources/Niesen-fingerprinting_Oxford.pdf

􀂾 Interactions between compounds and unfolding-monitoring

dye may mask stabilization or give rise to artifacts.

􀂾 Coloured compounds may interfere with optical detection of

fluorescence.

􀂾 Ambiguous results for stabilization of multi-domain proteins

that show non-two state unfolding by compounds.

􀂾 Not applicable to conditions comprising hydrophobic additives

I agree with Sebastian, Xiaowen and Stephen. Try using CD or intrinsic fluorescence if you have enough protein. And you might try using Urea and/or Guanidinium instead of temperature to measure the folding transition and stability of the protein with vs without ligand.

Charles, you did not mention the initial Tm of your protein, but in case it is really high prio to ligand binding, as Guillermo said, you may miss your curve because of the method limitation around 90ºC. Taking a variation of Kambiz's idea, you can also add some urea to your protein:ligand complex, trying to destabilize your protein, and in that way confirming if there is a melting curve to be seen, now at a lower Tm. If that is the case, just perform your both experiments (with and without the ligand) always in the presence of urea - this will give you a hint on the stabilizing effect of your compound.

As kambiz suggested try doing melting curves of your protein + ligand usingTryptophan intrinsic fluorescence by exciting at 295 nm as a function of both Temperature as well as Guanidinium-HCl (0-6 M). This requires very little of your protein. Remember far-UV CD will only determine the stability of secondary structure and not tertiary structure whereas DSC is very good method but requires ~ 0.5 mg/ml protein. However, first you have to be sure your ligand does bind your protein. For this isothermal titration calorimetry is best method if you have access to one.

Before carrying out any binding experiment you must understand the behavior of your protein with temperature. This can be done with the tryptophan fluorescence (few tryptophans is better), also following the emission maximum. The dichroic activity in the far UV is very useful to follow the global behavior of the protein with the temperature. The binding should be carryed out in a temperature range in which the protein is still acceptably stable. In determining the stability, the instrumental observables should describe a sigmoidal curve rather steep. If the slope is low and insists on a very broad base, then you can suspect that you're not following a two-step transition or the protein is aggregating irreversibly. The sigmoidal curve should be reversible by decreasing the temperature. Only if these checks have been done, you can start the binding studies.

You will see an increased Tm if the ligand either stabilzes the native state or destabilizes the unfolded state.

But are you sure that ligand is binding. Many times you see molecules in crystal structures, like eg Ca2+ or PEG but you not be able to determine a binding constant because the binding is very weak.

I would make first determine the affinity by ITC or other methods and then continue with your Tm demtermination. CD or DSC are much better then fluorescence based methods as the fluorescence itself is strongyl dependent on the temperature.

Sebastian. Fluorescence per se is independent of temperature in the physiologically relevant range, because you need much larger temperature changes to affect electron energy levels. If fluorescence of a protein depends on temperature, it means that your protein undergoes structural or dynamic changes and that is what causes changes to fluorescence.

Dear Charles, we have tried to describe the advantages and pitfalls of ThermoFluor (thermal shift assay) in our chapter that I have attached here.

My guess would be that your ligand binds weaker than 100 uM Kd. Your ligand needs to be at least about 10 uM strong to exhibit definite shift at your described conditions. Please let me know if you have more questions.

Marina, sorry for my no very scientific phrasing. What i meant is the following:

If you follow temperature induced unfolding of proteins by fluorescence, then you ll see the the baselines in the native and unfolded region has a negative slope (due to thermal quenching). For the analysis it is better if the baselines in the folded and unfolded region dont have a slope. Thats why CD is a much better technique.

I would second Khawar's suggestion to use isothermal titration calorimetry if you possibly can. This is the gold standard for protein-ligand interactions. I guess that your institute has access to this equipment.

My guess is that you really want to use DSF as it allows a lot of data to be collected rapidly. In your case, it appears that the change in melting temperature on binding of the ligand is zero by DSF. That is unfortunate, but if the data tells you that, then that is the case. You will have to use another method. As the other methods are potentially as time consuming as ITC, but don't give the same data quality, I would go for ITC if you can.

The trouble with CD (etc.) is that you will need to do at least eight data points, in triplicate, to be able to properly fit a binding curve. ITC gives you enough data to determine kD, dH, dS and dG in a single experiment that takes less than two hours (although of course you must do it in triplicate). I'd go for that.

Erdtman H, Frank A, Lindstedt G. Constituents of Pine Heartwood XXVII. The content of Pinosylvin Phenols in Swedish Pines. Svensk Papperstidn. 1951;54(8):1–5.

Carlsson B, Erdtman H, Frank A, Harvey WH. The Chemistry of the Natural Order Cupressales. VIII. Heartwood Constitutents of Chamaecyparis nootkatensis – Carvacrol, Nootkatin, and Chamic Acid. Acta Chim Scand. 1952;6:690–696.

Frank A. A modification of the McCord and Zemp method for the determination of lead in urine.

Am Ind Hyg Ass J. 1962;23:424–430.

Bonnichsen R, Maehly AC, Frank A. Barbiturate analysis: Method and statistical Survey. J Forensic Sci 1961;6:411–443.

Frank A, Gerhardsson G. Några 3,4 benspyrenundersökningar i Stockholm.

Investigations of3,4 Benzpyrene content in the air of Stockholm.

Nord Hyg Tidskr 1962; 43:42–45.

Andersson E, Engqvist A, Frank A. Tungmetaller i livsmedelsförpackningar Svensk Vet tidn. 1977;29:833–836. (Lead and cadmium contents in some plastic packing materials mainly used in food industry, in Swedish with Summary in English.)

Frank A. Automated wet ashing and multi-metal determination in biological materials by atomic absorption spectrometry. Fresenius Z. Anal. Chem. 1976;279:101 - 102.

Arora RG, Andersson L, Bucht RS, Frank A, Kronevi T. Chronic copper toxicosis in sheep.

Nord Vet Med 1977;29:181-187.

Frank A, Borg K. Heavy metals in tissues of the mute swan (Cygnus olor). Acta vet Scand

1979;20:447-465.

Frank A, Borg K. Cadmium in the mute swan, Cygnus olor. In: The use of ecological variables

in environmental monitoring. OIKOS. The National Swedish Environment Protection Board, Report PM 1151. 1979. pp. 275-279.

Frank A, Lindgren O, Petersson L. Closed glass cage for metabolism studies in birds using

labelled compounds. Laboratory Animals. 1979;13:107-110.

Frank A, Petersson LR, Mörner T. Bly Kadmium i älg, rådjur och hare.Sv Vet tidn 1981;33:151–

156 (Lead and cadmium in tissues from elk (Alces alces), roe deer, (Capreolus capreolus) and

hares (Lepus europeus, Lepus timidus) in Swedish with English Summary.)

Mattson P, Albanus R, Frank A. Kadmium och vissa andra metaller i lever och njure från älg.

Vår föda 1981;32:335–345. (Cadmium and some other elements in liver and kidney from moose (Alces alces). In Swedish with English Summary.)

Frank A, Larsson B, Fabiansson S. Autoradiography in mice of tritiated 2-(2-furyl)benzimidazole

and melanin-binding in vitro. Toxicol. Lett. 1983;17:267-273.

Frank A, Petersson LR, Mörner T. The moose (Alces alces) as an indicator of the bioavailability

of cadmium in the Swedish environment. In: Das freilebende Tier als Indikator für den

funktionszustand der Umwelt. Proceedings. Symposium. Wien, 1984. pp. 83-94.

Hussein KSM, Frank A, Jones B-E V, Edqvist L. Effects of 2-mercaptoethanol on the solubility

of copper and zinc containing proteins in liver samples from normal and chronic copper poisoned

sheep. Acta vet scand. 1984;25:10-20.

Hussein KSM, Frank A, Jones B-E V, Edqvist L. Solubility of copper and zinc containing

proteins before and after 2-mercaptoethanol treatment of liver samples from normal and from

chronically copper poisoned sheep. Acta Pharmacol Toxicol 1984;55:247-251.

Hussein KSM, Jones B-E V, Frank A. Selenium copper interaction in goats. Zbl. Vet. Med. A,

1985;32:321-330.

Hussein KSM, Frank A, Jones B-E V. Influence of intramuscular selenium injections on copper

metabolism in copper-loaded sheep. Zbl. Vet. Med. A,1985;32:729-738.

Frank A, Petersson LR. Direct current plasma-atomic emission spectrometer as a simultaneous

multi-element tool for analysis of biological materials. Kemia-Kemi 1985;12:426-430.

Frank A, Pehrson B, Petersson LR. Concentration of some important elements in the

liver of young cattle supplemented with selenite enriched feed. J Vet Med A, 1986;33:422-425.

Blomqvist S, Frank A, Petersson LR. Metals in liver and kidney tissues of autumn-

migrating dunlin Calidris alpina and curlew sandpiper Calidris ferruginea staging at the

Baltic sea. Mar. Ecol . Prog. Ser. 1987;35:1-13.

Schwan O, Jacobsson S-O, Frank A, Rudby-Martin L., Petersson LR. Cobalt and copper deficiency in Swedish landrace pelt sheep J Vet Med A 1987;34:709-718.

Frank A. Semi-micro accessory to an automated wet digestion system for ashing small

sample amounts. In: Brätter P, Schramel P, editors. Trace element analytical chemistry in

medicine and biology, vol. 5. Berlin, New York: Walter de Gruyter, 1988:78-83.

Galgan V, Frank A. Automated system for determination of selenium in biological materials.

In: P. Brätter P, Schramel P, editors. Trace element analytical chemistry in medicine and

biology, vol. 5. Berlin, New York: Walter de Gruyter, 1988:84-89.

Forsberg Å, Söderlund S, Frank A, Petersson LR, Pedersén M. Studies on metal

content in the brown seaweed, Fucus vesiculosus, from the archipelago of Stockholm.

Environmental Pollution 1988;49:245-263.

Frank A, Hellström L-E, Hoppe A. Xantinstenar, nu även hos hund i Sverige. Svensk Veterinärtidn 1988;40:547-549. [Xanthine urolith, detected in dog also in Sweden] (In Swedish with English summary)

Stéen M, Frank A, Bergsten M, Rehbinder C. En ny sjukdomsbild hos älg. [A new pathological picture of moose disease. In Swedish.] Svensk Veterinärtidn 1989;41:73-77.

Frank A, Petersson LR. Kemisk diagnostik vid förgiftningar hos husdjur. [Chemical diagnosis of poisonings in domestic animals.] Svensk Veterinärtidn 1989;41. Supplement 19. 47-55.

(in Swedish with English summary).

Frank A, Widmark K, Hoppe A. Sulfabehandling som orsak till urinsten hos hund. (Treatment with sulfadiazine, the cause of urolith in the dog] (In Swedish with English summary) Svensk Veterinärtidn 1989;41:585-587.

Eriksson O, Frank A, Nordkvist M, Petersson LR. Heavy metals in reindeer and their

forage plants. Rangifer, 1990. Special Issue No. 3, 315-331.

Frank A, Kristiansson L, Petersson LR Vanadinförgiftning hos nötkreatur - första kända

fallet i Sverige. Vanadium poisoning in cattle - the first recognised case in Sweden. Svensk

Veterinärtidn.1990;42:447-451. (in Swedish with English summary).

Frank A, Feinstein RE. Hepatic lipidosis associated with severe vitamin B12 deficiency recognized by liver cobalt status in three cats. Feline Pract. 1991;19:16-20.

Luthman J, Jacobsson SO, Frank A. Endotoxin-induced changes in plasma mineral and vitamin levels in calves. Acta vet scand. 1991;32:403-404.

Petersson LR, Frank A. Warning to DCP users! The Influence of a damaged entrance slit on the

optical and analytical performance in direct-current plasma-atomic emission spectrometry.

Applied Spectroscopy. 1991;45:498-500.

Frank A, Wennerholm M. The Equilibrium Extractor and its use in the study of rancidity.

In Focus. 1991;14:4-5.

The Swedish National Atlas, Environment; Cadmium in moose kidney cortex. Bernes C., Grundsten C. Eds. Bokförlaget Bra Böcker. Höganäs, Sweden, 1991; p. 42.

Jacobsson SO, Larsson B, Luthman J, Frank A, Alenius S. Trace elements, minerals retinol and alfa-tocoferol in calves persistently infected with bovine virus diarrhoea virus. Acta vet scand. 1992;33:185-187.

Frank A, Galgan V, Roos, A, Olsson M, Petersson LR, Bignert A. Metal concentrations in seals

from Swedish waters. Ambio 1992;21:529-538.

Frank A, Wiberg M, Petersson LR, Åström P. Fältmässig behandling av blyförgiftning hos

nötkreatur.Treatment of cattle after acute lead poisoning. Svensk Veterinärtidn. 1992;44:3-8

(in Swedish with English summary).

Petersson LR, Frank A, Hoppe A. Simultaneous multi-element determination of selected elements

in dog urine by direct current plasma-atomic emission spectrometry. J Trace Elem Electrolytes

Health Dis. 1993;7:177-183.

Hoppe A, Denneberg T, Frank A, Kågedal B, Petersson LR. Urinary excretion of metals during treatment with D-penicillamine and mercaptopropionylglycine in normal and cystinuric dogs. J vet Pharmacol Therap. 1993;16:93-102.

Galgan V, Frank A. Notes and comments on the determination of selenium in biological

materials. Norwegian J Agric Sci. 1993:Suppl.11:57-74. ISSN 0802-1600.

Frank A, Egenvall A. Sulphanilamide toxicity and crystalluria in a dog after suspected ingestion of a wound treatment ointment. J Small Animal Pract. 1994;33:531-534.

Frank A. Spårelementbrist hos älg, en bieffekt av kalkning? (Trace element deficiency in the moose,

a side effect of liming?) In: Proceedings of "Konsekvenser av kalkning i skog og vatn" Bö i Telemark 14. - 15. november 1995. Seminarrapport. Högskolen i Telemark. Norsk Limnologförening.

ISBN 82-90814-03-8

Galgan V, Frank A. Survey of bioavailable selenium in Sweden with the moose (Alces alces

L.) as monitoring animal. Sci Total Environ 1995;172:37-45.

Frank A, Galgan V. Vanadium concentrations in bovine liver, toxicological aspects - normal values. In: Anke et al. (eds). Proceedings of "Mengen - und Spurenelemente", 15th Workshop, 8-9 December 1995, Jena, Germany pp. 552-560. (ISBN 3-929526 34-4)

Frank A, Madej A, Galgan V, Petersson LR. Vanadium poisoning of cattle with basic slag.

Concentrations in tissues from poisoned animals and from a reference slaughter-house material.

Sci Total Environ. 1996;181:73-92.

Selinus O, Frank A, Galgan V. Biogeochemistry and metal biology. – An integrated Swedish approach for metal related health effects In:Appleton JD, Fuge R, McCall G.J.H. (eds), Environmental Geochemistry and Health in Developing Countries. Geological Society of London. Special Publication No. 113, pp. 81-89. 1996.

Frank A, Galgan V. The moose (Alces alces L.), a fast and sensitive monitor of environmental

changes. In: Subramanian, K.S., Iyengar, G.V. (eds.). Environmental biomonitoring,

ACS Symposium Series, No. 654. 1997;57-64.

Frank, A. Too Much and Too Little, Both Equally Harmful. In: Environmental Biochemistry of

heavy metals. (Szilágyi, M. Editor) Proceedings of Workshop. Nyiregyháza, Hungary

January 15-17, 1997. pp. 7-23.

Danielsson R, Petersson LR, Frank A. Multivariate data analysis as a tool for evaluating emission intensity, background equivalent concentration (BEC) and detection limit (DL) obtained for different plasma positions in direct current plasma-atomic emission spectrometry.

ANALYTICA CHIMICA ACTA 1997;354 (1-3): 211-224.

Iskandar, Petersson L, Frank A. Determination of lead and multi metal in tissue samples using

methyl isobutyl keton extraction and atomic absorption spectrophotometry.

Indon J Trop Agric 1998;3:14–19.

Frank A. Spårelementbrist hos älg, en bieffekt av kalkning? (Trace element deficiency in the moose,

a side effect of liming?) In: Proceedings of "Konsekvenser av kalkning i skog og vatn" Bö i Telemark 14. - 15. november 1995. Seminarrapport. Högskolen i Telemark. Norsk Limnologförening.

ISBN 82-90814-03-8

Galgan V, Frank A. Survey of bioavailable selenium in Sweden with the moose (Alces alces

L.) as monitoring animal. Sci Total Environ 1995;172:37-45.

Frank A, Galgan V. Vanadium concentrations in bovine liver, toxicological aspects - normal values. In: Anke et al. (eds). Proceedings of "Mengen - und Spurenelemente", 15th Workshop, 8-9 December 1995, Jena, Germany pp. 552-560. (ISBN 3-929526 34-4)

Frank A, Madej A, Galgan V, Petersson LR. Vanadium poisoning of cattle with basic slag.

Concentrations in tissues from poisoned animals and from a reference slaughter-house material.

Sci Total Environ. 1996;181:73-92.

Selinus O, Frank A, Galgan V. Biogeochemistry and metal biology. – An integrated Swedish approach for metal related health effects In:Appleton JD, Fuge R, McCall G.J.H. (eds), Environmental Geochemistry and Health in Developing Countries. Geological Society of London. Special Publication No. 113, pp. 81-89. 1996.

Frank A, Galgan V. The moose (Alces alces L.), a fast and sensitive monitor of environmental

changes. In: Subramanian, K.S., Iyengar, G.V. (eds.). Environmental biomonitoring,

ACS Symposium Series, No. 654. 1997;57-64.

Frank, A. Too Much and Too Little, Both Equally Harmful. In: Environmental Biochemistry of

heavy metals. (Szilágyi, M. Editor) Proceedings of Workshop. Nyiregyháza, Hungary

January 15-17, 1997. pp. 7-23.

Danielsson R, Petersson LR, Frank A. Multivariate data analysis as a tool for evaluating emission intensity, background equivalent concentration (BEC) and detection limit (DL) obtained for different plasma positions in direct current plasma-atomic emission spectrometry.

ANALYTICA CHIMICA ACTA 1997;354 (1-3): 211-224.

Iskandar, Petersson L, Frank A. Determination of lead and multi metal in tissue samples using

methyl isobutyl keton extraction and atomic absorption spectrophotometry. Indon J Trop Agric

1998;3:14–19.

Selinus O, Frank A. Medical geology. In Möller L. (ed.) Environmental medicine. Joint Industrial Safety council Product No. 333, pp. 164-183. 2000. Stockholm. Sweden. ISBN 91-7522-634-0

Aupperle H, Schoon H-A, Frank A. Experimental copper and chromium deficiency and additional

molybdenum supplementation in goats – Pathological findings.

Acta Vet. Scand 2001;43 (3):311-322

Frank A, Wibom R, Danielsson R. Myocardial cytochrome c oxidase activity in Swedish moose

(Alces alces L.) affected by molybdenosis. Sci Total Environ 2002; 290:121-129.

Frank A. Vitamin B12 deficiency in moose [debate]. Rondel 2004; 18. March 15, 2004

URL: http://www.rondellen.net.

Frank A. A Review of the “Mysterious” Wasting Disease in Swedish Moose (Alces alces L.) Related to Molybdenosis and Disturbances in Copper Metabolism. Biol Trace Elem Res 2004;102/ 1-3: 143-160.

Frank A. Dr, Stasiak Aranka emlékére 1896 – 1945. Egészségtudomány.2010, LIV. (2). 78-84.

Frank Adorján/ Adrian Frank In the memory of Dr. Aranka Stasiak MD.)

Frank A. A Frank-féle bakteriumtenyésztö lombik.Egy magyar találmány, anno 1885.

Frank´s flask for culturing bacteria. A Hungarian invention, anno 1885.

Egészségtudomány. 2012, LVI. (1). 108-112. Frank Adorján/ Adrian Frank,

Some addition to the list of papers from Adrian Frank

Please, How to calculate the Kd value at physiological temperature from ThermoFluor data?

Best regards.

Many times it is possible to detect a shift in Tm by the addtion of a ligand. To detemine the Kd using thermal denaturation studies one assumes that the ligand increases the Tm by stabilizing the native conformation. But one has to be careful, because in principle the higher Tm can also be due to the destabilisation of the unfolded state through the ligand.

Questions 1: How did you get the ligand in your cystal. Did you co-crystallize or soak with very high concentration. Ofen you can see sulfates, phosphates or PEG molecules bound to the protein in the crystal structure. However, I never could detect binding of sulfate or phosphate by ITC. So it is a matter of concentration.

Question 2: DId you incubate the protein and the ligand for sufficient time so that you are sure to reach the steady state. If the k(on) is slow and you just mix protein and ligand and start the thermal denaturation then the complex might not have been formed.

I would directly consider to use another techniqe like ITC, Microscale thermophoresis, ... to get some quantiative information.

In reply to David's question - I am afraid that it is not possible to extrapolate from the Kd determined by DSF/Thermofluor to the Kd at physiological temperature.

The reason for this is that Kd is linked mathematically to the dG for the reaction. dG is itself defined as:

dG = dH - TdS

There are several good studies from ITC at different temperatures showing that both dH and dS change as a function of temperature. They do so in a non-linear manner, and the nature of this non-linear manner is different for each interaction.

Consequently, the only way to really know what the Kd is at physiological temperature is to measure it at the physiological temperature. This is clearly impossible for DSF, unless you have the good fortune to have an interaction where the Tm at Kd is physiological (rare).

However, this is also true for all other methods too. The vast majority of Kd data are measured at room temperature, and so have exactly the same temperature dependence issues at DSF data. Moreover, they are almost always also measured in conditions where the interacting partners are essentially purified of all other cellular components, where there is no macromolecular crowding effect, and where membranes, surfaces, active transport etc. are not accounted for. One has to accept all these caveats. For protein-protein interactions, it is possible to measure the Kd in the cell using methods like BRET, but even then there are probably artefacts of overexpression and tagging.

In summary, the Kd's that we measure are a very good guide for comparing interactions to rank as to which is the most significant. They should not be taken as gospel for the physiological Kd!

Thank you for your answer,

Best regards.

To Nicolas J. Harmer:

You wrote: "There are several good studies from ITC at different temperatures showing that both dH and dS change as a function of temperature. They do so in a non-linear manner, and the nature of this non-linear manner is different for each interaction."

May I ask you for particular citations on the results you have mentioned? I was not aware of such systematic studies, yet what you have mentioned seems entirely reasonable. Need those to read and cite in my papers and will be thankful if you can give refs of those papers. Thanks!

Artem Badasyan. Changes of dH and dS with temperature are reflected in a set of basic thermodynamic equations:

dH(T) = dH(ref) + dCp*(T-Tref), where T is temperature

dS(T) = dS(ref) + dCp*ln(T/Tref), where T is in Kelvin

This dependence is linear, when you assume that dCp is constant at all temperatures. Although it's a good first approximation, the dCp can change with temperature, thus introducing non-linearity in dH and dS behavior.

Dear Marina Kasimova, thanks for your comment. I know those relations, and know the limits of applicability of them. What is missing in the picture, formed in my head, the experimental study, showing the deviation of linear behavior together with the explanation why it happens. The model with Cp=const is very very rough and is at least for me very surprising that it worked in many situations.

Thank you!

Artem

Hi Artem. I thought so (that you knew those relations). Your questions was not clear though, that's why I posted that comment.

It is not surprising for me that dCp = const approximation is good enough in that tiny temperature window, where physiological processes are taking place. Assuming no structural alterations of the two reacting components, why would dCp be different between 15 or 45 C? For example, take a look at water - not much is changing between 0 and 100 C, with the deviation from the constant value being ~1%. Why would you expect anything different?

T, C Cp

0 4.2176

10 4.1921

20 4.1818

25 4.1814

30 4.1784

40 4.1785

50 4.1806

60 4.1843

70 4.1895

80 4.1963

90 4.205

100 4.2159

Hi Marina!

What about water in the region between -10 C to +10 C :-)

The experimental observation of existence of cold denaturation in proteins tells me that the assumption of linear dependence of enthalpy and entropy on temperature is probably only true in the transition interval, and in general, it is at least quadratic outside. One can approximate any function by linear on short scales :-)

Working on a paper on these topics, actually...

Hi Artem. In my previous post, I specifically noted the absence of structural alterations, meaning the absence of transitions of any kind. Since water has a phase transition between -10 and 10C, the heat capacity is bound to change. The heat capacity is about bonds and degrees of freedom, you know...

Hi Marina!

Agree with what you said. There are several transitions in water in the range mentioned. Similarily, in the temperature range, that includes both cold denaturation and protein folding, and in between these two phase transitions, enthalpy/entropy cannot be linear functions of temperature. Only within the transition intervals of cold denaturation and regular folding one can approximate these dependencies as roughly linear. But it is not true in between these two transitions.

Hi Marina,

Could you give a reference for the equations that you gave earlier? It would be very good to have this to quote back to complaining reviewers! I agree with the effect on dH; however, experimental determination of dS by isothermal calorimetry shows that sometimes the effects on dS are more complex (e.g. doi:10.1074/jbc.M112.366120).

I suspect that this is because proteins don't really have a single heat capacity, especially if they have multiple domains. Of course, it is very difficult to get enough data out to start to model these multiple effects....

Hi Nicholas,

It is difficult to give a reference for those equations, as they stem from works of Gibbs, Joule and Thomson. It's basic thermodynamics, really. But, I know what you mean by "complaining reviewers". That drives me crazy sometimes that no one knows the basics any longer and soon we will be asked to give a reference if we use Newton's equation for the gravity law. If you must, you can reference one of the pioneering works of Peter Privalov. As for me, I always use these equations without referencing anyone (e.g. doi:10.1006/jmbi.1997.1613)

Now to the derivations.

The first one (dH(T) = dHref + dCp*(T-Tref)) is easy. It is directly derived from the definition of the heat capacity at constant pressure.

By definition, the heat capacity of a substance is equal to heat (Q) absorbed or released by this substance upon the change of temperature from T1 to T2, that is C = Q/dT. Or in terms of derivatives, in order to get the heat capacity at a certain temperature, C(T) = dQ/dT.

Furthermore, the enthalpy is: dH = dQ + VdP, where V is volume and P is pressure. When the pressure is constant, dP = 0 and then dH = dQ. This is why one can use a constant pressure calorimeter to directly access the enthalpy function.

Substituting one into the other you get the heat capacity at a constant pressure:

Cp = dH/dT and therefore, assuming Cp = const you can calculate the enthalpy at any other temperature from a linear dependence, where the slope is Cp.

Unfortunately, there is no device that can measure the entropy directly. But you can calculate its dependence on temperature from the same set of equations as above.

Sorry for the long answer. If you need more info, you can contact me directly.

Thank you,

Marina

PS. BTW, you have a very good point about multiple heat capacities of multi-domain proteins. Could be fun to investigate.

Dear Marina,

Thank you for your detailed and well reasoned post. I found this really helpful to think through and improve my own understanding. This does highlight the importance of doing very good experiments to access these thermodynamic parameters as accurately as possible.

I would have voted it up more than once if I could!

Thank you Nicholas. It's very nice to know that you could use my explanations.

I cannot agree with the approach, used by Marina -- if you do not know the derivation of the formula, and therefore, the limits of applicability of it, you cannot blindly apply it. Even the gravity law is written differently, depending on which distances you consider the phenomenon, and the ratio of masses of interacting objects. Blind application of formulas, without giving accord to the origin is a road to nowhere.

Sorry, this is the science, not arts.

Hi Artem. Sorry, I do not understand, why you call my derivations "arts"? What exactly you disagree with?

Hi Marina!

My comment refers not to your derivations, but to this paragraph:

"It is difficult to give a reference for those equations, as they stem from works of Gibbs, Joule and Thomson. It's basic thermodynamics, really. But, I know what you mean by "complaining reviewers". That drives me crazy sometimes that no one knows the basics any longer and soon we will be asked to give a reference if we use Newton's equation for the gravity law. If you must, you can reference one of the pioneering works of Peter Privalov. As for me, I always use these equations without referencing anyone (e.g. doi:10.1006/jmbi.1997.1613)"

I understood these sentences as if you say that there is no need to derive the formulas used. If so it sounds like arts.

Regarding the derivation you have suggested. Leaving aside the issues with full and partial derivatives (which are just hard to type), the assumption of having constant heat capacity is not a simple one. While it works for ideal gas and some other models (crystalline soldis, for instance) at high enough temperature, as a consequence of equipartition theorem, it is tricky to determine if the temperature is high enough in every particular system. Even more, it usually works when the temperature is so high that the quantum effects can be neglected, on one hand, and should be lower than the temperature at which the structural transformations started. (see, e.g. International Journal of Quantum Chemistry, Vol 109, 3482–3499 (2009)).

Other than that, I do not see the reason to accept the constant heat capacity and, as a consequence, linear thermodynamic potentials describing dilute solutions of biopolymers in all points of phase diagram.

Landau and Lifshits volume 5 of Theoretical Physics Course, paragraph 43 is entitled: "Ideal gases with constant specific heat". It nicely describes the consequences of assuming constant heat capacity for ideal gas, including the linearity over temperature for heat function (enthalpy, W in Landau's definitions).

Artem, I am aware of the fact that the heat capacity of proteins is a function of temperature. There are numerous articles discussing this subject from both theoretical and experimental point of view. My point was that you can make a rough estimation of the enthalpy, if dT is more or less within physiological range. We are not talking about super high temperatures, as these are irrelevant for protein function.

As for referencing the right people... Even though the Gibbs free energy was introduced by Gibbs, I have never seen a reference to his original work. Unfortunately. That is because more often than not, people tend to quote irrelevant articles to satisfy the reviewers, who are not necessarily experts in the fields they are reviewing.

In fact I have a question related to DSC. Any body knows of an example where the Nucleic acid-free protein has higher Tm than nucleic acid bound-protein?

Secondly, any example where the Tm of a protein is higher in the 1st scan than the 2nd identical thermal scan, although the delta H of both scans are similar?

Thanks a lot.

I have a situation where a known inhibitor doesn't give melt curve in Thermal Shift Assay, whereas my ligands were giving proper Tm shift. What might be the reasons ?

Dear Vinothkannan, I suppose there is a chance that "a known inhibitor" is not really an inhibitor. However, I would caution, that you have to be very careful and check by MS whether you have the right chemicals. In addition, I would suggest to not limit your study to thermal shift. It would be great to test it by a direct assay of inhibition of enzymatic activity of your protein.

Daumantas Matulis Thank you so much sir. I will do as you suggested sir.