Okay, so we can start. Welcome everyone and welcome to also Piqueli for today's seminar.

And today he will be speaking about the nonlinear and major theoretic methods for biological

networks. Please Piqueli, we're looking forward to your talk.

Yeah, so thank you very much for your kind invitation and for the organization.

So at this point, you have a panel saying this meeting is being recorded. Let's hope that, you know, I'm unable to throw it away.

Okay, I will try to do this way. So thank you so much for this kind invitation. It's a pleasure to be here and the title of the talk is nonlinear major theoretic tools for modeling

bio networks. So the idea is that to show some tools that were developed recently to deal with the large bio networks. So first of all, the term network obviously refers most of the time to the mathematical concept of graph.

And to my knowledge is using many different ways. Sometimes the component of a network are proteins. Sometimes our genes, all the way to sometimes being agent or cells or even organisms.

So, for instance, so there are different ways of conceiving what is a biological networks and obviously many different tools, my specific interest here is looking more at networks in the realm of biochemical networks.

So networks in which every node represents for instance a compound or a gene, and we are trying to understand not only the connections that sometimes are explored by specific experiments but how the network dynamics behave as a whole.

Once we understand the structure of the network.

In particular, I want to address the question, I mean, is it true that only linear approaches have the one that are going to work for large networks because they are obviously scalable.

And the reason and enormous literature, obviously, on on different tools that will develop there are classical network flows like the Ford-Fulkerton theorem.

These are linear problems and you are looking for identifying flows that would realize a given equilibrium or optimizing a given flow.

Sometimes we can even use Markov chains as an alternative model for networks with a large set of components and obviously probabilistic point of view.

So flux balance analysis, I don't know if you are familiar with this term but it's essentially one of the most successful approach of systems biology developed by Palson group and then few other down the way, in which you take a network and you try to understand the

possible flux values that would render the network at equilibrium.

So this theory initially developed is again mostly linear, but was assuming successfully analyzing very large networks. In this picture I show a typical problem that you end up in this analysis, assuming you take a simple network like in a network flow problem you want to address the

existence of flows that render the network stable, the target equilibrium. So mathematically we can solve this linear problem but then the interest biologically is to have all points

positive flows because most of the time they are, they correspond to directed edges. And so to transformation the going up precise direction.

And because of this constraint of positivity this renders this, the problem nonlinear, and you sometimes send up analyzing costs like the one showed in this picture that are the intersection between viable kernels of matrices and positive

call may be extremely complicated from the point of view of describing it. This is a picture of a cone in R3. And you see we if we are looking for positive basis that is vector through which that generate the corn through only positive combination

the number of needed vector could be much higher than the dimension of the space where the core lies. That's a typical difficulty.

Let me go quickly through La Pgesa Dynamics and compartmental systems these are specific approaches that were developed by researchers more in the first biomedical areas and the other one in in control theory, and compartmental

that was used for bioreactors, batch reactors,

but they develop a lot of tools that are useful for,

I would say all networks.

So again, covering all the different tools

and approaches we've developed would be impossible,

but a theory developed specifically for chemical networks

called Zero Deficiency Theory,

also attract a lot of interest,

people use monotone systems,

network motives, the approach by Alon

and a few others is a constructivity approach

in which you try to understand the function of the network

by analyzing specific pieces called motives.

And finally modularity,

it's a new way of looking at networks

in which you compose different pieces,

but in such a way that you don't like

do like a legal structure,

which one piece interact with the other,

but there are backstepping and backward interaction

render things more complicated.

Now, brief example, reverse cholesterol transport.

This is a very small network

that is a part of a much larger one

of the human cholesterol metabolism.

And you see the typical networks