Branched Pathway in TikZ

 I couldn't resist, here are some simple branched pathways using tikz. Note you can change the vertical splay and horizontal distance for the nodes by changing the node distance in the argument to tikzpicture. I also added some colors wshich really don't match, someone with more artistic tallent could do better.

\documentclass[12pt]{article}

\usepackage{tikz}
\usetikzlibrary{positioning}
\usepackage{xcolor}

\begin{document}

\begin{tikzpicture}[node distance=0.4cm and 1cm]
\node (Xo) at (0,0) {};
\node[right=of Xo] (S1) {\small $S_1$};
\node[above right=of S1] (S2) {};
\node[below right=of S1] (S3) {};

\draw[-latex, thick, blue] (Xo) -- (S1) node[pos=0.5,above,gray] {$v_1$};

\draw[-latex, thick, orange] (S1) -- (S2) node[above=0.15, left,pos=0.5,gray] {$v_2$};
\draw[-latex, thick, green!45!black] (S1) -- (S3) node[below=0.15, left,pos=0.5,gray] {$v_3$};
\end{tikzpicture}

\vspace{1cm}

\begin{tikzpicture}[node distance=0.4cm and 1cm]
%\draw [help lines,step=.1] (0,-6) grid (6,6);
\node (Xo) at (0,0) {};
\node[right=of Xo,yellow!20!red] (S1) {\small $S_1$};
\node[above right=of S1,blue!80!red] (S2) {\small $S_2$};
\node[below right=of S1,green!80!red] (S3) {\small $S_3$};

\node[above right=of S3] (S4) {};
\node[below right=of S3] (S5) {};

\draw[-latex, thick, blue] (Xo) -- (S1) node[pos=0.5,above,purple] {$v_1$};
\draw[-latex, thick, blue] (S1) -- (S2) node[above=0.15, left,pos=0.5,purple] {$v_2$};
\draw[-latex, thick, blue] (S1) -- (S3) node[below=0.15, left,pos=0.5,purple] {$v_3$};

\draw[-latex, thick, blue] (S3) -- (S4) node[below=-0.12, left,pos=0.5,purple] {$v_4$};
\draw[-latex, thick, blue] (S3) -- (S5) node[below=0.05, left,pos=0.5,purple] {$v_5$};
\end{tikzpicture}

\end{document}

Experimenting with foreach loops in TikZ to draw biochemical pathways

Here is an example of a foreach loop in TikZ that can be used to draw an arbitrary long linear chain of reactions.

By setting the value of N in the following TikZ code, you can get any length linear chain. Obviously, you're limited by the width of the page. It uses the xifthen package to provide a conditional that is used to print out the last species, which is X1. There could be a better way of doing this, but this works. For example, use newcommand instead of def

 

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{calc}
\usepackage{xifthen}

\begin{document}


\begin{tikzpicture}[>=latex', node distance=2cm]     
\node (X0) {$X_o$};
\pgfmathsetmacro{\N}{4}
\foreach \x in {0,...,\N}
{
  \pgfmathtruncatemacro{\nextval}{\x+1}
  \ifthenelse{\x = \N}
        {\def\speciesName{$X_1$}}
        {\def\speciesName{\large $x_\nextval$}}
  
  \node [right of = X\x] (X\nextval) {\speciesName};   
  \draw [->,ultra thick,blue] (X\x) -- node[above, black] {$v_{\nextval}$} (X\nextval);
}
\end{tikzpicture}

\end{document}

Here are some examples for N = 0, N = 2 and N = 4

More utter metabolic nonsense

When will researchers stop writing utter nonsense about metabolism? I was reading this review:

Molecular Metabolism
12 November 2022, 101635
Nitin Patil Orla Howe, Paul Cahill and Hugh J.Byrne

Monitoring and modelling the dynamics of the cellular glycolysis pathway: A review and future perspectives and spotted this sentence in the text:

"Alternately, the activity of rate-limiting glycolytic enzymes can be determined by quantifying their catalytic products in vivo [115]. "

I thought, that can't be true, it's not possible to ascertain rate limitingness just from the products. So I checked out the citation they used:

Methods in Enzymology
Volume 542, 2014, Pages 91-114
Chapter Five - Techniques to Monitor Glycolysis
Tara TeSlaa and Michael A.Teitell

Well I was in for a treat, so many illogical statements in one paper. Here is one such sentence:

"While the activity of any single glycolytic enzyme is not a proxy for carbon flux through the entire pathway, specific enzymes limit the rate of glycolysis, and therefore, their activities control the maximum possible flux. Hexokinase, phosphofructokinase, and PK are the main rate-limiting enzymes in glycolysis."
v So authors are mixing up the Vmax for rate-limitation as if enzymes are even running at their Vmax. These enzymes, using the more classical definition of rate-limitingness, are not rate-limiting other than HK, but that depends on the organism and conditions. The reason they aren't rate-limiting is that they are regulated, which means any changes to their activity results in no change to the pathway flux. Not only that, it turns out that for the mentioned enzymes, particularly HK and PK, don't even have low Vmax's so even if they were running at Vmax they wouldn't be limiting the flux anyway. PFK is also not that low, since PDC and ENO have lower Vmaxs (this is in yeast). The point is there is no necessary correlation between rate-limitingness (however they define it) and an enzyme's Vmax. There are other reasons at play for determining a Vmax.

Here is another one:

"while determining the activity of rate-limiting glycolytic enzymes can provide insights into points of metabolic regulation."

There is no reason why rate-limiting steps are regulated, quite the opposite in fact. I'm not sure how much experimental data, theory, or computational research need to be done to convince them this isn't true. I never did find any reference to my orginal quesiton in the 2014 paper. Me thinks the orginal authors didn't read the 2014 review. There is simply no way to tell if a step is rate-limiting or not just from its products. The authors also have a modeling section where they state:

"Ordinary and partial differential equation can be used for both deterministic and stochastic modelling."

what were they thinking?

And another:

Mass action kinetics, rate law (Michaelis Menten models, Hill kinetics),

MM and Hill models don't follow clasical mass-action kinetics, they show fractional kinetic orders.

The authors never mention Metabolic Control Analysis at all, which is a primary language for talking objectively about metabolic control and regualation.

We've obviously gone very wrong somewhere in our education and training of systems biology researchers.

Experimenting with GeoGebra

This is an example of using GeoGebra to interactively simulate a two step pathway, S1 -> S2 -> S3 using simple mass-action kinetics in each reaction.

Plot of 1/x using pgfplots

I noticed I couldn't find pgfplots version of the $1/x$ plot that describes $e$. I needed one, so here is the LaTeX I used.

\documentclass[margin=3mm]{standalone}

\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usepgfplotslibrary{fillbetween}

\begin{document


\begin{tikzpicture}
\begin{axis}[
ytick = {1,2},
xtick = {0,1,2,3},
xlabel=$x$, ylabel=$y$,
ymax=2.5, xmin=0, ymin=0,
xlabel style = {anchor=north east},
ylabel style = {anchor=north east}
]
\addplot [color = blue, name path=A,domain=0:4, line width = 1.4pt, samples=200] {1/x};
\path [name path=B]
    (\pgfkeysvalueof{/pgfplots/xmin},0) --
    (\pgfkeysvalueof{/pgfplots/xmax},0);
\addplot [blue!20]
    fill between [of=A and B,
                  soft clip={(1,0) rectangle (2.71,25)},];
\node at (axis cs:1.5,1.2) {$y=1/x$};
\node at (axis cs:1.6,0.31) {Area = $1$};
\node at (axis cs:2.71, 0.82) {$e$};
\addplot[-latex] coordinates
           {(2.71,0.75) (2.71,0.45)};
\end{axis}
\end{tikzpicture}

\end{document} 

To paraphrase an old saying....

 You can lead a modeler to a technical solution, but you can't make them use it.

This rephrasing of an old saying was inspired by our reproducibility work. There exist technical solutions to publishing reproducible results, and yet most studies are still not reproducible because we choose not to use those solutions. 

MCA Rediscovered

It looks like someone has rediscovered metabolic control analysis (MCA).

A structural approach to understanding enzymatic regulation of chemical reaction networks Biochem J (2022) 479 (11): 1265–1283. Atsushi Mochizuki

The analysis is exactly the same as MCA but uses different symbols and they focus on the unscaled sensitivities instead. eg the r symbols are the unscaled elasticities. The core equation (4) can be found in equation (1) of the appendix of the following paper, and I am sure its been published elsewhere too:

Taking enzyme kinetics out of control; putting control into regulation. Jan-Hendrik S. HOFMEYR, Athel CORNISH-BOWDEN and Johann M. ROHWER, Eur. J. Biochem. 212, 833-837 (1993).

However, unlike the original MCA, the latest reincarnation doesn't include support for conserved moieties so as it stands it's somewhat limited. Note equation (1) in the above paper includes additional terms to take into account any conserved moieties. 

What is more concerning is that the reviewers of the paper never spotted this duplication of work. 

Some textbooks on MCA: 

Systems Biology: An Introduction to Metabolic Control Analysis (2018)

Understanding the Control of Metabolism (Frontiers in Metabolism Ser. ; No. 2)) 1st Edition (1996)

Fundamentals of Enzyme Kinetics 4th Edition (2012)

Lorenz Attractor

I wanted to test out Google's skia 2D library so I wrote a simple interactive Lorenz attractor app over the weekend. Source code and binaries at 

https://github.com/hsauro/Lorenz_fmx

Binaries are only for Windows at the moment but hope to have a Mac version in a couple of weeks.

I used Object Pascal to write it but it should be easily translatable to something like C# and WinForms which were modeled after Object Pascal and the VCL. Looks like skia does a better job at antialiasing lines and also it's quite fast.

I use a simple Euler integration scheme to solve the Lorenz ODEs, nothing fancy but it seems to work perfectly well. 

Analogmachine reborn

I decided to rebuild my blog on blogger. Originally I used my own WordPress site but discovered that maintaining it was quite time-consuming. The main problem was stopping the site from being hacked and corrupted.  This happened again recently and it prompted me to move to a more resilient and less demanding platform.

Theory of the Origin, Evolution, and Nature of Life by Andrulis

 Ars Technica has an interesting article that I can't avoid bringing up here. The title of the article is:

"How the craziest f#@!ing "theory of everything" got published and promoted"

The Ars Technica article describes a paper (Theory of the Origin, Evolution, and Nature of Life) published by an assistant professor from Case Western. The author of the paper describes a theory of everything which because of a press release from Case Western manages to get amplified out of all proportion even though the content is highly suspect. Just reading the first sentence is enough to raise a big red flag. That sentence is:

"How life abides by the second law of thermodynamics yet evolutionarily complexifies and maintains its intrinsic order is a fundamental mystery in physics, chemistry, and biology [1]."

There is no mystery here as the author suggests. If he had bothered to read up on Prigogine's and Nichols well-known work on non-equilibrium thermodynamics published decades ago he would have an explanation for this "mystery".

Testing Code Formating using hightlight.js

# Python Program to find the area of triangle

if x == True:
   pass
   
a = 5
b = 6
c = 7

# Uncomment below to take inputs from the user
# a = float(input('Enter first side: '))
# b = float(input('Enter second side: '))
# c = float(input('Enter third side: '))

# calculate the semi-perimeter
s = (a + b + c) / 2

# calculate the area
area = (s*(s-a)*(s-b)*(s-c)) ** 0.5
print('The area of the triangle is %0.2f' %area)