Why is network evolution interesting and challenging?
Our lab studies how biological networks evolve.
Most evolutionary models consider the evolution of a single gene, regardless of its network context. Genes, however, are always part of a network, where the products of one gene often affect the activity of others. As each gene can potentially constrain the evolution of others, this brings about many interesting theoretical questions. For example: How can new genes emerge and join an already existing network? To what extent do the gene products interfere with each other’s function? Is there a maximal size to which biological networks could evolve?
I have previously studied how networks evolve to be modular, and studied how limited interaction specificity and the existence of numerous molecular species set limits on the functionality and evolution of gene regulatory networks.
Today, the main focus of the lab is the evolution of self-incompatibility in plant fertilization, a system whose functionality relies on existence and absence of molecular recognition between pairs of specialized proteins.
Evolution of self-incompatibility in plant fertilization
Plants that have both male and female organs in the same flower, have high risk of self-fertilization, which would produce less fit offspring (known as “inbreeding depression”). Hence, more than half of flowering plant families have developed various mechanisms to avoid self-fertilization, called “self-incompatibility” (SI).
The principle of all mechanisms is that the species is sub-divided into multiple ‘mating types’. A female can be successfully fertilized only by pollen having a different type than her owns. Here we focus on a particular mechanism found in the Solanaceae, Rosaceae and Plantaginaceae families. Interestingly, in this mechanism, fertilization success depends on molecular recognition between the female and the male-type specifying proteins. Its proper functionality requires that each individual should carry both components: the female protein which toxifies pollen and the male protein which recognizes the specific female protein and detoxifies it only if from a different type. Failure to have both male and female elements together will result in either sterility or loss of this mechanism, correspondingly.
This immediately raises fundamental theoretical questions about the evolutionary emergence and maintenance of this mechanism: increase in number of types requires both male and female parts altogether - how did these two components co-evolve? An individual that loses this mechanism might have an advantage over others, because it has access to a larger number of potential mates. Why is this mechanism evolutionary stable? What factors determine the number of mating types?
This system is an excellent example for a medium-sized network of interacting proteins. Their direct involvement in reproduction ensures strong selection pressures. All these considerations make SI an excellent case study to research network evolution.
Evolution on rugged fitness landscapes
Fitness landscapes are a metaphor, commonly used to visualize evolutionary dynamics. It is assumed that every genotype (a point in the x-y plane of the figure) has a well-defined reproductive rate, or fitness (represented by the height of the landscape at that point). The distance between genotypes in this description is representative of the number of mutations needed to change one genotype into the other. The set of all genotypes, their similarity to each other and their fitness values are then called fitness landscape. Evolutionary dynamics is then described as trajectories on this mountainous topography. The analysis of evolutionary trajectories is complicated because genotypes are typically very high-dimensional, and the fitness landscape is often rugged and has multiple peaks (local maxima).
We have previously proposed a biophysically realistic fitness landscape to study the evolution of a gene regulatory network. We synthesized a biophysical model of TF-DNA binding with the evolutionary model. In this framework, the fitness is determined by the whole network (a desired gene expression pattern), rather than by a single gene.
T. Friedlander*, R. Prizak*, N. Barton and G. Tkacik, “Evolution of new regulatory functions on biophysically realistic fitness landscapes”, (* - equal contribution), arXiv: 1610:02864, Nature Communications, 8(216), 2017, doi:10.1038/s41467-017-00238-8.
Intrinsic limits to gene regulation by global crosstalk
Gene activity is mediated by the specificity of binding interactions between special proteins, called transcription factors, and short regulatory sequences on the DNA, where different protein species preferentially bind different DNA targets. Limited interaction specificity may lead to crosstalk: a regulatory state in which a gene is either incorrectly activated due to spurious interactions or remains erroneously inactive. Since each protein can potentially interact with numerous DNA targets, crosstalk is inherently a global problem, yet has previously not been studied as such. Here, we constructed a theoretical framework to analyze the effects of global crosstalk on gene regulation, using statistical mechanics. We found that crosstalk in regulatory interactions puts fundamental limits on the reliability of gene regulation that are not easily mitigated by tuning protein concentrations or by complex regulatory schemes proposed in the literature. Our results suggest that crosstalk imposes a previously unexplored global constraint on the functioning and evolution of regulatory networks, which is qualitatively distinct from the known constraints that act at the level of individual gene regulatory elements. While our analysis assumes thermodynamic equilibrium, we suggest that out-of-equilibrium regulatory schemes, if they exist, may reduce crosstalk beyond our result. This problem demonstrates how the microscopic biophysical details of interactions can have far-reaching implications and constrain the possible complexity of the whole system.
T. Friedlander, R. Prizak, C. Guet. N. Barton and G. Tkačik, “Intrinsic limits to gene regulation by global crosstalk”, Nature Communications, 7(12307), Aug. 2016, doi:10.1038/ncomms12307; (arXiv:1506.06925).
R. Grah, T. Friedlander, “Transcriptional crosstalk varies between regulatory strategies”, BioRxiv, https://www.biorxiv.org/content/early/2018/07/19/372672.
Evolution of a new regulatory function
In the previous project we studied crosstalk assuming a given fixed set of proteins and DNA targets. We found that a major determinant of crosstalk is the degree of similarity between competing DNA targets. These molecules however are not fixed, but rather dynamically evolve in a concerted manner where each of them affects the evolution of the others. Here we asked: how do they evolve when their function depends on the maintenance of interactions with few partner molecules and the simultaneous avoidance of deleterious “crosstalk” with the remaining non-partner ones so that distinct regulatory pathways can ensue? So far most theoretical studies have focused on the evolution of individual genes, neglecting the network context. We began with the elementary step in the evolution of gene regulatory networks: duplication of a transcription factor followed by selection for the TFs to specialize in their inputs as well as in their regulatory function. We have synthesized biophysical models of TF-DNA interactions with population genetics models of evolution to study co-evolution of TFs and DNA binding sites forming a small network. We have demonstrated that taking into consideration the biophysics of interactions provides a much richer picture than the simple discrete description commonly used in the evolutionary literature. We found that even in such a small network each of these molecules constrains the evolution of the others, leading to very long evolutionary times to specialization and allowing for other sub-optimal evolutionary outcomes as well. We proposed that promiscuity-promoting mutations rendering TFs less specific to their targets can shorten evolutionary times.
T. Friedlander*, R. Prizak*, N. Barton and G. Tkacik, “Evolution of new regulatory functions on biophysically realistic fitness landscapes”, (* - equal contribution), arXiv: 1610:02864, Nature Communications, 8(216), 2017.
The evolutionary origins of modularity and network structures in biological systems
Modularity is the degree to which a system can be separated into sub-systems that are relatively independent. Modularity is ubiquitous in biology and is found for example in proteins, gene regulatory networks, organs and ecosystems. Yet, it is unclear how it evolved and became so common in biology. Designs obtained in computer simulations yield mostly non-modular solutions. Previous attempts to resolve this puzzle required very specific conditions or were applicable only to a limited range of parameters. In this work we focused on a new mechanism, based on the biological nature of mutations. Biological mutations affecting the connection strength between components are well approximated by a product rule, yet were mostly described in other works as having additive effect. Thus a weak interaction between components is very unlikely to become stronger by mutation. We show that the cumulative effect of mutations drives the system to sparseness – the state of very few connections. The combined effect of this mutational mechanism and selection for a modular goal brings about modular solutions. The generality and simplicity of the mutational mechanism suggest that it is likely to be broad in its explanatory range.
T. Friedlander, A. E. Mayo, T. Tlusty and U. Alon, "Mutation-rules and the evolution of sparseness and modularity in biological systems", PLoS One 8(8): e70444 (2013)..0070444 (arXiv: 1302.4267).
T. Friedlander, A. E. Mayo, T. Tlusty and U. Alon, "Evolution of bow-tie architectures in biology", PLOS Computational Biology,11(3): e1004055 (2015), (arXiv: 1404.7715, 2014).
Signal processing in membrane proteins
Cells continuously sense their external environment and respond accordingly. This task largely depends on a variety of membrane proteins that serve as environmental sensors. Examples include bacterial chemotactic receptors, synaptic and hormonal receptors and ion channels. The common functional hallmark of these systems is that when exposed to a strong and persistent signal, they adapt by re-tuning their sensitivity. This behavior is referred to as “adaptive response” or “desensitization”. Mechanistically, this is explained by slow transitions of these proteins (receptors or channels) to a state which is non-responsive to the signal, triggered by their continued activation. Despite apparent functional similarities between various membrane proteins, traditionally, researchers have addressed them separately based on their relevance to a specific biological system. Here, we identified the universal features of these systems and constructed a coarse-grained mathematical model that ties together different biological systems, showing that they are all special cases of the same universal model. For the first time, we derived the system response to a general input signal, showing how the interplay between fast and slow time-scales implements a balance between responses to current and historical inputs. We demonstrated how an extended version of our model can also exhibit a broad dynamic range of response, as observed in some of these systems.
T. Friedlander and N. Brenner, "Adaptive Response by State-Dependent Inactivation", Proceedings of the National Academy of Sciences, 106(52):22558-22563, 2009.
T. Friedlander and N. Brenner, "Adaptive response and enlargement of dynamic range", Mathematical Biosciences and Engineering, 8(2): 515-528, April 2011; (arXiv:1003.2791).
Universality of protein abundance distributions in dividing cell populations
Variation in organismal traits that cannot be attributed to either genetic or environmental factors is a well-known phenomenon that raises many theoretical questions. An example is protein abundance in single cells. Experiments reveal that protein abundances in unicellular populations typically exhibit broad distributions, even if the cells are genetically identical and grow in the same environment. This raises fundamental questions about the sources and universality of these distributions. Most theoretical works in this field focus on the limit of low-abundance proteins, where stochasticity in gene expression is the major source of variability, where other sources are mostly overlooked. Here, we addressed the other extreme of abundant proteins, where stochasticity in gene expression is negligible. Instead, we focused on the contribution of variability in cell division time. we found the latter sufficient to produce broad protein distributions as measured in experiments, even if protein production is deterministic. While protein abundance distributions were measured only for few proteins, our results suggest that their shape may be more universal than previously thought, since they emanate from fundamental processes common to all proteins, rather than from details specific to any protein production circuit.
T. Friedlander and N. Brenner, "Cellular Properties and Population Asymptotics in the Population Balance Equation", Physical Review Letters 101, 018104 (2008).
Also selected for publication in "Virtual Journal of Biological Physics Research", vol. 16, issue 2, July 15, 2008.
R. Arbel-Goren, A. Tal, T. Friedlander, S. Meshner, N. Costantino, D. L. Court and J. Stavans, "Effects of regulation by a small RNA on phenotypic variability in E. coli", Nucleic Acids Research, 1-10, March 2013.