Hi Thomas, I have never worked in the determination of Tm. Nevertheless, I found this article

Interesting paper even though its a calculation on DNA structure. Seems the Tm calculation is about 11k away from experimental determination - I wonder what it would be for a much bigger biological system like a protein.

Thx for input

The problem should be formulated as a Global Optimisation Problem. There are two very well known algorithms 1. Simulated Annealing 2. Genetic Algorithm . Necessary and sufficient conditions for the convergence of the global optimum is vailable for both the algorithms. However , if the mathematical formulation is made available , I could definitely provide necessary guidelines.

Both SA and GA are known as Nonparametric Stochastic Algorithms for Global Optimisation.

I would not recommend that approach. Simulated annealing uses an effective temperature to set the average velocities of the atoms in the simulation. There is no correlation between this number and actual temperatures. The melting temperature of DNA can be estimated because there are only four kinds of residues and the H-bond is the primary interaction stabilizing the double helix.

Empirical potential energy calculations can sometimes give a rough estimate of the relative stabilities of proteins (e.g., mutant vs wt), But even then, the errors can be considerable.

My explanation has not been interpreted properly. What I am trying to explain is that both are in fact global optimisation algorithms and have been used widely in science and technology. For low dimensionality problems even Controlled random Search Algorithm will be sufficient.

Dear Pradosh,

I am afraid that you have not understood Greg's answer. The problem is not math. The problem is in a proper representation of a physical system by a math model. Tm is a complex physical entity that combines many features of a complicated (in math terms we use word complex) system. Complex systems are not easily amenable to any regular math treatments despite tremendous progress we made in understanding them. Additionally, what Greg was trying to explain is that known inadequacies of most of MD models make it almost impossible to do a precise correlation with know physical entities such as Tm. To understand it better you have to note that solvent plays a crucial role in measurements of Tm (for instance presence of osmolytes). We do not even have a rudimentary understanding how solvent couples with protein motions to produce the functionality we observe. We have only crude understanding how osmolytes work in stabilizing the protein structure thanks to more than two decades of work (see the latest paper by Bolen and Rose in PNAS). Therefore, I think that using MD to find Tm is a worthy task, I personally would not put any real faith in the result without a proper validation and this validation process kills the purpose of doing it anyway. It is really much simpler to go and measure it.

If it comes to the question posted by Thomas the answer is yes. There are several web servers that will estimate Tm. I have not validated them so I do not have any opinion which one is best. Thomas, try them and see what happens.

Thx all for the input. I do have a large dataset of experimental determined Tm values on proteins and with similar experimental setups eg pH and buffter. My hope is that a series of MD simulations could be used for neural network training on those calculated/predicted Tm from MD and of-course validate this with the experimental determined Tm values. My idea was to correlate the artificial MD temperature or another measure with the actual experimental Tm. Maybe loss of H-bonds (the fraction compared to initial native structure) will correlate with Tm. If any of the MD programs give the Tm directly then I dont have to estimate it from a series of 3D-structures at different temperatures.

I know the MD research area is a study in itself so im just trying to get some input on good MD programs and test the accuracy on machine learning using the MD Tm estimations. I can look for some of the web-servers (I do that) but also appreciate suggestions if you know a good one - Im not familiar with state-of-the-art in this area so a link (url adr) would be great help.

I have been completely misunderstood. What I had pointed out is a physicist - mathematician's standpoint on Simulated Annealing Algorithm. The Algo is well known Kirptrick [1983, Science, 220 , p.621-630] . What is more important is understanding the necessary and sufficinet conditions for the convergence of the algo. The objective function related to Molecular Dynamics is just antother function to be optimized , subject to constraints. Let me find out , if some researchers at NCL , India viz. Sudip Roy and his team is working on the problem using SA.

First some general comments. Simulated annealing can't be used to calculate thermodynamic properties like Tm. For that you need to sample the whole conformational space, not just local or global energy minima, with methods such as replica exchange or simulated tempering, or some of the generalized ensemble methods like Wang-Landau. This demands a lot both of the force fields used and computationally, and is way beyond the capability of all the presently available models and methods, for proteins of any reasonable size (say more than 40-50 residues). It's not unusual for MD simulations to give Tm-values that are off by several 100 K for small proteins/peptides.

What you might be able to do with reasonable precision is estimate the effect of one or a few mutations on the Tm of an already characterized protein. It might also be possible to get a ball-park estimate for Tm based on amino acid composition, see for example the work by Shakhnovich et al. on thermal adaption in bacteria (PLoS Comput Biol 3(1): e5).

Article Protein and DNA Sequence Determinants of Thermophilic Adaptation

I appreciate your comments. I do hear what you say Pradosh, I get your point. Also thanks to Simon for some good points about what can and cant be done with respect to Tm predictions based on SA. I just scanned the paper briefly that you linked to and I surely will take a closer look at it - thx. I know Tm prediction could be a very valuable feature to predict and that it will be quite difficult - I have tried several of the standard approaches i.e. correlating different structural features to Tm, incl the obvious amino acid frequency, but also alot of other structure derived features. It seems that there is still much work to be done and new 'out of the box' idea to emerge.

I think one can also do it using heating approaches. pls correct me if i am wrong.

1. estimate the bond distances in the molecule before heating

2. heat the molecule to a temperature of 3000K and then find at what temperature, the bond distances between pair of atoms deviates from the normal. This gives you an approximate melting temperature

You might start by comparing Thermophilus structures and sequences to other bacterial structure and sequences. Since thermophilus survives at high temperatures, it is likely that it incorporates many features in its sequence and structures to raise the Tm.

This paper would be a start

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC22336/

Also here

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2242557/

Using heating to estimate Tm, as Rathankar Rao suggested, has the same problem as using simulated annealing, both are non-equilibrium methods, and your result will depend on how fast you heat or anneal the system. Tm is an equilibrium property and can basically only be estimated through equilibrium sampling. In some cases it is possible to estimate equilibrium properties of a system using non-equilibrium methods (e.g. the Jarzinsky equality), but these are also relatively demanding.

Simulating the thermodynamic equilibrium requires that your force field describes all parts of conformational space accurately, and not only a local neighborhood around the native state. Predicting Tm reliably from simulations is therefore considerably more difficult than for example predicting the correct fold.