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+---
+layout: post
+title: "Relative Free Energy Calculation Setup: About mapping atoms with Kartograf"
+categories: Setup Kartograf RBFEs RelativeFreeEnergies
+---
+
+
+Relative Free Energy Calculation Setup: About mapping atoms with Kartograf
+==================================================================================================================
+
+In drug design or material sciences, thermodynamic properties of molecules are
+important guidelines in the design. One example of such a property is free
+energy, giving the likelihood of a given state to occur. More explicitly, we are
+interested in relative free energies, comparing two states and the likelihoods
+of those. In drug design, such a free energy difference between two different
+drug candidate molecules might be measured experimentally in labs as the IC50 or
+the kD, which describe the strength of the interaction between the molecule and
+some target biomolecule (usualy a protein). For example, these quantities can be
+used to estimate the potency of a small molecule to inhibit an enzyme, a
+fundamental mechanism in many drug design projects. In silico approaches like,
+for example, relative alchemical free energy calculations, can be used to reduce
+the required experiments, boosting the drug discovery process and reducing the
+required resources. In such approaches, small molecules binding to an enzyme are
+compared in computer simulations utilizing special molecular dynamics
+simulations. These simulations yield relative binding free energies (RBFE),
+directly giving insights into the molecules’ structure-function relationship.
+
+A lot of research has been conducted on such methods, showing great potential
+for many different use cases. We at OpenFE want to make the methods accessible
+to the public in an open source fashion, allowing easy setup, simulation
+execution and analysis of the free energy calculation methods. In this blog
+post, we will focus on RBFE calculation setup and give insights into one of the
+fundamental steps in the simulation process. Keep in mind that there are many
+different approaches out there, which we would like to cover in later posts.
+Atom mappings and their use for RBFEs
+
+Recently we published an article in [JCTC about Kartograf ](https://pubs.acs.org/doi/10.1021/acs.jctc.3c01206), a new atom mapping
+algorithm, based on an old idea. This is a very nice chemoinformatics problem,
+but you might want to ask, what does it have to do with RBFEs?
+
+![AlchemTransf.png](../assets/images/posts/kartograf/AlchemTransf.png)
+
+## RBFE Simulations and how to represent the alchemical molecule change
+In RBFE simulations, two small molecules of interest are simultaneously
+simulated in a given environment (the protein or the water box). The
+contributions of the different molecules in the simulation are slowly turned
+from one molecule to the other (in steps like molA 100% / molB 0%; molA 90% / 
+molB 10%; molA 80% / molB 20%; … molA 0% / molB 100%)
+
+One question is, how should those molecules be represented in the simulation?
+There are many different approaches out there that answer this question slightly
+differently. The RBFE protocol, which was developed by the [Perses](https://github.com/choderalab/perses) team and 
+which
+is present in OpenFE, uses hybrid-topology approaches. In those representations,
+the two molecules always should be able to share a common core (some chemical
+structure that is the same). This common core is represented by the identical
+set of atoms and is usually represented by the maximum common substructure (
+MCS). Every atom outside of the common core is represented independently of each
+other. This approach is very efficient, by not adding to many independent atoms,
+but also not limiting the present atoms too much. But as we want to be able to
+build these hybrid topology representations automatically, we need an algorithm
+that can find the common core for us.
+
+![alchemist1.png](..%2Fassets%2Fimages%2Fposts%2Fkartograf%2Falchemist1.png)
+
+## Atom Mappers
+Existing solutions in this area (for example [Lomap](https://github.
+com/OpenFreeEnergy/Lomap/blob/main/lomap/mcs.py), [fesetup](https://github.com/CCPBioSim/fesetup/blob/master/cheapmap.py), and 
+[timemachine](https://github.com/proteneer/timemachine/blob/master/timemachine/fe/atom_mapping.py))
+all use subgraph-matching based approaches to finding the MCS between two
+molecules. A good explanation of how these algorithms work is given by Andrew
+Dalke [here](https://www.dalkescientific.com/writings/diary/archive/2012/05/12/mcs_background.html). In general they can be said to first work on the 2D structures (
+ignoring their positions) then later filter to include this information.
+
+### Short Peak on Kartograf Theory
+Kartograf departs from this approach and instead primarily focuses on the
+coordinates of the two molecules to find the MCS, an idea that was developed
+thanks to conversations with [old colleagues](https://www.nextmovesoftware).
+com). This alternative approach is
+possible thanks to the fact that, for hybrid-topology approaches used in RBFEs,
+the molecules are already spatially superimposed. First we can calculate the
+distance between all pairs of atoms in between the two small molecules, which,
+after we discard distances larger than a threshold, can be viewed as a weighted
+bipartite graph. At this point the problem can be solved as an [assignment
+problem](https://en.wikipedia.org/wiki/Assignment_problem), where the distance matrix between the two small molecules form a
+weighted bipartite graph, which we solve using the [linear sum assignment](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linear_sum_assignment.html)
+implementation in scipy. While linear sum assignments can theoretically scale
+poorly, the tight distance maximum cutoff produces a very sparse input graph to
+be solved. Once this initial solution is created, some filtering based on
+chemistry constraints is then applied.
+
+![Kartograf_Algorithmic_Approach.png](..%2Fassets%2Fimages%2Fposts%2Fkartograf%2FKartograf_Algorithmic_Approach.png)
+reproduced from [](https://pubs.acs.org/doi/10.1021/acs.jctc.3c01206)
+# How To Use Kartograf?
+
+Let’s have a look at how Kartograf works!
+First we want to generate two molecules, that shall be mapped onto each other.
+To generate two molecules we use RDKit and
+
+## How to install:
+First we need to install the package!
+
+You can install the package with [PyPi](https://pypi.org/project/kartograf/):
+```bash
+pip install kartograf
+```
+
+Or you can simply install ith with [conda](https://anaconda.org/conda-forge/kartograf):
+```bash
+conda install -c conda-forge kartograf openfe
+```
+
+The rest of this blogpost was written with kartograf v1.1 and openfe v1.0 in
+mind!
+
+## How to generate an Atom Mapping
+Let's Start the journey with generating some input molecules, we will use 
+for our atom mapping adventure.
+```python
+from rdkit import Chem
+
+## Preprocessing from Smiles - Here you can add your Input instead!
+smiles = ["c1ccccc1", "c1ccccc1(CO)"]
+rdmols = [Chem.MolFromSmiles(s) for s in smiles]
+rdmols = [Chem.AddHs(m, addCoords=True) for m in rdmols]
+[Chem.rdDistGeom.EmbedMolecule(m, useRandomCoords=False, randomSeed = 0) for m in rdmols]
+```
+
+After generating the molecules as rdkit mols, we convert them to gufe
+Components. These Components, can be read and used everywhere in the OpenFE
+environment, they are part of the universal OpenFE language and can be
+translated in many other languages.
+
+```python
+# Build Small Molecule Components
+molA, molB = [SmallMoleculeComponent.from_rdkit(m) for m in rdmols]
+```
+
+Now we have two molecules with 3D coordinates, that we can use further for
+finding the atom mapping of the MCS. As mentioned before Kartograf assumes, that
+the molecules are well aligned, in order to find an atom mapping of the MCS. In
+our case, we have generated two molecules with independent coordinate spaces.
+With the alignment helper functions of kartograf, we can now generate a high
+coordinate overlap for our molecules. Here we use a helper for shape alignments
+from [RDKit](https://www.rdkit.org/):
+
+```python
+## Align the mols first - this might not needed, depends on input.
+a_molB = align_mol_shape(molB, ref_mol=molA)
+```
+Now we can start the mapping, let’s first build a mapper object:
+
+```python
+# Build Kartograf Atom Mapper
+
+mapper = KartografAtomMapper(atom_max_distance: float = 0.95,
+atom_map_hydrogens: bool = True,
+map_hydrogens_on_hydrogens_only: bool = False,
+map_exact_ring_matches_only: bool = True,
+additional_mapping_filter_functions: Optional[Iterable[Callable[[
+Chem.Mol, Chem.Mol, dict[int, int]], dict[int, int]]]] = None,
+)
+```
+A variety of settings can be set here:
+* **atom_max_distance : float** - geometric criteria for two to be mapped atoms, how 
+far their distance can be maximal (in Angstrom). Default 0.95
+* **map_hydrogens_on_hydrogens_only : bool** - 
+            map hydrogens only on hydrogens.
+* **map_exact_ring_matches_only : bool** - if true, only rings 
+  with matching ringsize and same bond-orders will be mapped. Additionally no ring-breaking is permitted.
+* **additional_mapping_filter_functions : Iterable[Callable[[Chem.Mol,
+        Chem.Mol, Dict[int, int]], Dict[int, int]]]** - with this optional parameter you can further filter the distance
+            based mappings with your own custom filters, provided as iterables.
+            as default we suggest to avoid ring size/breaking changes and only
+            allow whole rings to be mapped. This option will be explained in more detail further down.
+
+
+Let’s map the molecules with:
+```python
+kartograf_mapping = next(mapper.suggest_mappings(molA, a_molB))
+```
+
+If you use this code in a jupyter notebook, you can checkout the atom mapping in
+2D by simply executing the following cell:
+```python
+kartograf_mapping
+```
+
+![mapping.png](..%2Fassets%2Fimages%2Fposts%2Fkartograf%2Fmapping.png)
+
+Note that the 2D mapping might give wrong impressions of the mapping.
+
+But you can also look at the mapping in 3D with:
+```python
+from kartograf.utils.mapping_visualization_widget import display_mappings_3d
+display_mappings_3d(mappings)
+```
+
+![mappping3D.png](..%2Fassets%2Fimages%2Fposts%2Fkartograf%2Fmappping3D.png)
+
+This visualization is important because you can see the coordinate influence on
+the atom mapping directly and most accurate.
+
+## How can we build atom mappings with additional rules?
+After now getting an intro into, how atom mappings can be build, let's have a look on how you can customize the mappings with additional rules.
+
+Here we start with a custom filter, that removes element changes from our final mapping:
+```python
+def filter_element_changes(
+molA: Chem.Mol, molB: Chem.Mol, mapping: dict[int, int]
+) -> dict[int, int]:
+    filtered_mapping = {}
+
+    for i, j in mapping.items():
+        if (
+            molA.GetAtomWithIdx(i).GetAtomicNum()
+            != molB.GetAtomWithIdx(j).GetAtomicNum()
+        ):
+            continue
+        filtered_mapping[i] = j
+
+    return filtered_mapping
+```
+
+After this, let’s use this new filter:
+```python
+from kartograf import KartografAtomMapper
+
+# Build Kartograf Atom Mapper
+
+mapper = KartografAtomMapper(additional_mapping_filter_functions=[filter_element_changes])
+```
+Let’s map the molecules from the prior example again:
+```python
+kartograf_mapping = next(mapper.suggest_mappings(molA, a_molB))
+kartograf_mapping
+```
+![mapping_filter.png](..%2Fassets%2Fimages%2Fposts%2Fkartograf%2Fmapping_filter.png)
+
+And here the 3D representation:
+![mapping_filter_3D.png](..%2Fassets%2Fimages%2Fposts%2Fkartograf%2Fmapping_filter_3D.png)
+
+Some of these Filters are already pre-implemented and can be found in
+[kartograf/filters](https://github.com/OpenFreeEnergy/kartograf/tree/main/src/kartograf/filters):
+
+```python
+from kargoraf.filters import (filter_atoms_h_only_h_mapped,
+filter_element_changes,
+filter_hybridization_changes,
+filter_ringsize_changes,
+filter_ringbreak_changes,
+filter_whole_rings_only,
+)
+```
+
+## Can I use Kartograf directly from OpenFE?
+The kartograf tool has been integrated into the openfe ecosystem and can be
+included into workflows when planning RBFE networks. From the command line, the
+[`openfe plan-rbfe-network`](https://docs.openfree.energy/en/latest/reference/cli/plan_rbfe_network.html) command can take a yaml file to customise the
+algorithms used.
+
+```yaml
+mapper:
+method: KartografAtomMapper
+settings:
+atom_max_distance: 1.0
+atom_map_hydrogens: false
+
+network:
+method: generate_minimal_spanning_network
+```
+
+This `settings.yaml` will select the `KartografAtomMapper`, with some customised
+parameters to be used in planning a minimal spanning network.
+For further information checkout our [documentation](https://docs.openfree.energy/en/latest/tutorials/rbfe_cli_tutorial.html#customize-you-campaign-setup).
+
+
+Concluding, in this blog post, we discussed Kartograf's theory and showed you, how you can use Kartograf, customize it to your needs, and even seamlessly integrate it into your openFE workflow.
+And before we forget, you are interested in Atom Mappings for multistate simulations? There is a [multistate prototype for Kartograf](https://github.com/OpenFreeEnergy/kartograf/pull/12) doing this! If you want to try it we would love to get your feedback!
+
+This work is licensed under [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/).
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