Editing Feed forward (control) (section)

===Gene regulation and feed-forward===
Feed-forward loops (FFLs), a three-node graph of the form A affects B and C and B affects C, are frequently observed in transcription networks in several organisms including [[Escherichia coli|''E. coli'']] and [[Saccharomyces cerevisiae|''S. cerevisiae'']], suggesting that they perform functions that are important for the functioning of these organisms. In ''E. coli'' and ''S. cerevisiae'' transcription networks have been extensively studied, FFLs occur approximately three times more frequently than expected based on random ([[Erdős–Rényi model|Erdös-Rényi]]) networks.<ref>{{Cite journal |last1=Lee |first1=Tong Ihn |last2=Rinaldi |first2=Nicola J. |last3=Robert |first3=François |last4=Odom |first4=Duncan T. |last5=Bar-Joseph |first5=Ziv |last6=Gerber |first6=Georg K. |last7=Hannett |first7=Nancy M. |last8=Harbison |first8=Christopher T. |last9=Thompson |first9=Craig M. |last10=Simon |first10=Itamar |last11=Zeitlinger |first11=Julia |last12=Jennings |first12=Ezra G. |last13=Murray |first13=Heather L. |last14=Gordon |first14=D. Benjamin |last15=Ren |first15=Bing |date=2002-10-25 |title=Transcriptional Regulatory Networks in Saccharomyces cerevisiae |url=https://www.science.org/doi/10.1126/science.1075090 |journal=Science |language=en |volume=298 |issue=5594 |pages=799–804 |doi=10.1126/science.1075090 |pmid=12399584 |bibcode=2002Sci...298..799L |s2cid=4841222 |issn=0036-8075|url-access=subscription }}</ref><ref>{{Cite journal |last1=Milo |first1=R. |last2=Shen-Orr |first2=S. |last3=Itzkovitz |first3=S. |last4=Kashtan |first4=N. |last5=Chklovskii |first5=D. |last6=Alon |first6=U. |date=2002-10-25 |title=Network Motifs: Simple Building Blocks of Complex Networks |url=https://www.science.org/doi/10.1126/science.298.5594.824 |journal=Science |language=en |volume=298 |issue=5594 |pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590 |bibcode=2002Sci...298..824M |s2cid=9884096 |issn=0036-8075|url-access=subscription }}</ref>

Edges in [[Gene regulatory network|transcription networks]] are directed and signed, as they represent activation (+) or repression (-). The sign of a path in a transcription network can be obtained by multiplying the signs of the edges in the path, so a path with an odd number of negative signs is negative. There are eight possible three-node FFLs as each of the three arrows can be either repression or activation, which can be classified into coherent or incoherent FFLs. Coherent FFLs have the same sign for both the paths from A to C, and incoherent FFLs have different signs for the two paths.<ref name=":0">{{Cite journal |last1=Mangan |first1=S. |last2=Alon |first2=U. |date=2003-10-14 |title=Structure and function of the feed-forward loop network motif |journal=Proceedings of the National Academy of Sciences |language=en |volume=100 |issue=21 |pages=11980–11985 |doi=10.1073/pnas.2133841100 |issn=0027-8424 |pmc=218699 |pmid=14530388|bibcode=2003PNAS..10011980M |doi-access=free }}</ref>

The temporal dynamics of FFLs show that coherent FFLs can be sign-sensitive delays that filter input into the circuit. We consider the [[differential equation]]s for a Type-I coherent FFL, where all the arrows are positive:

<math>\frac{\delta B}{\delta t} = \beta_B (A) - \gamma_{B}B</math>

<math>\frac{\delta C}{\delta t} = \beta_C (A, B) - \gamma_{C}C</math>

Where <math>\beta_y</math> and <math>\beta_z</math> are increasing functions in <math>A</math> and <math>B</math> representing production, and <math>\gamma_Y</math> and <math>\gamma_z</math> are rate constants representing degradation or dilution of <math>B</math> and <math>C</math> respectively. <math>\beta_C (A,B)</math> can represent an [[AND gate]] where <math>\beta_C (A,B)=0</math> if either <math>A = 0</math> or <math>B = 0</math>, for instance if <math> \beta_C (A,B)=\beta_C \theta_A (A>k_{AC} ) \theta_A (B>k_{ABC} )</math> where <math>\theta_A</math> and <math>\theta_B</math> are [[step function]]s. In this case the FFL creates a time-delay between a sustained on-signal, i.e. increase in <math>A</math> and the output increase in <math>C</math>. This is because production of <math>A</math> must first induce production of <math>B</math>, which is then needed to induce production of <math>C</math>. However, there is no time-delay in for an off-signal because a reduction of <math>A</math> immediately results in a decrease in the production term <math>\beta_C (A,B)</math>. This system therefore filters out fluctuations in the on-signal and detects persistent signals. This is particularly relevant in settings with stochastically fluctuating signals. In bacteria these circuits create time delays ranging from a few minutes to a few hours.<ref name=":0" /><ref>{{Cite book |last=Alon |first=Uri |url=https://books.google.com/books?id=tcxCkIxzCO4C |title=An Introduction to Systems Biology: Design Principles of Biological Circuits |date=2006-07-07 |publisher=CRC Press |isbn=978-1-58488-642-6 |language=en}}</ref>

Similarly, an [[Inclusive OR gate|inclusive-OR gate]] in which <math>C</math> is activated by either <math>A</math> or <math>B</math> is a sign-sensitive delay with no delay after the ON step but with a delay after the OFF step. This is because an ON pulse immediately activates B and C, but an OFF step does not immediately result in deactivation of C because B can still be active. This can protect the system from fluctuations that result in the transient loss of the ON signal and can also provide a form of memory. Kalir, Mangan, and Alon, 2005 show that the regulatory system for flagella in ''E. coli'' is regulated with a Type 1 coherent feedforward loop.<ref>{{Cite journal |last1=Kalir |first1=Shiraz |last2=Mangan |first2=Shmoolik |last3=Alon |first3=Uri |date=2005-03-29 |title=A coherent feed-forward loop with a SUM input function prolongs flagella expression in Escherichia coli |journal=Molecular Systems Biology |volume=1 |pages=2005.0006 |doi=10.1038/msb4100010 |issn=1744-4292 |pmc=1681456 |pmid=16729041}}</ref>

For instance, the regulation of the shift from one carbon source to another in [[diauxic growth]] in ''E. coli'' can be controlled via a type-1 coherent FFL. In diauxic growth cells growth using two carbon sources by first rapidly consuming the preferred carbon source, and then slowing growth in a lag phase before consuming the second less preferred carbon source. In E. coli, glucose is preferred over both [[arabinose]] and [[lactose]]. The absence of glucose is represented via a small molecule cAMP. Diauxic growth in glucose and lactose is regulated by a simple regulatory system involving cAMP and the [[lac operon]]. However, growth in arabinose is regulated by a feedforward loop with an AND gate which confers an approximately 20 minute time delay between the ON-step in which cAMP concentration increases when glucose is consumed and when arabinose transporters are expressed. There is no time delay with the OFF signal which occurs when glucose is present. This prevents the cell from shifting to growth on arabinose based on short term fluctuations in glucose availability.<ref>{{Cite journal |last1=Mangan |first1=S. |last2=Zaslaver |first2=A. |last3=Alon |first3=U. |date=2003-11-21 |title=The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks |url=https://pubmed.ncbi.nlm.nih.gov/14607112/ |journal=Journal of Molecular Biology |volume=334 |issue=2 |pages=197–204 |doi=10.1016/j.jmb.2003.09.049 |issn=0022-2836 |pmid=14607112}}</ref>

Additionally, feedforward loops can facilitate cellular memory. Doncic and Skotheim (2003) show this effect in the regulation in the mating of yeast, where extracellular mating pheromone induces mating behavior, including preventing cells from entering the cell cycle.<ref>{{Cite journal |last1=Doncic |first1=Andreas |last2=Skotheim |first2=Jan M. |date=2013-06-27 |title=Feedforward Regulation Ensures Stability and Rapid Reversibility of a Cellular State |journal=Molecular Cell |language=English |volume=50 |issue=6 |pages=856–868 |doi=10.1016/j.molcel.2013.04.014 |issn=1097-2765 |pmid=23685071|pmc=3696412 }}</ref> The mating pheromone activates the MAPK pathway, which then activates the cell-cycle inhibitor Far1 and the transcription factor Ste12, which in turn increases the synthesis of inactive Far1. In this system, the concentration of active Far1 depends on the time [[integral]] of a function of the external mating pheromone concentration. This dependence on past levels of mating pheromone is a form of cellular memory. This system simultaneously allows for the stability and reversibility.

Incoherent feedforward loops, in which the two paths from the input to the output node have different signs result in short pulses in response to an ON signal. In this system, input A simultaneous directly increases and indirectly decreases synthesis of output node C. If the indirect path to C (via B) is slower than the direct path a pulse of output is produced in the time period before levels of B are high enough to inhibit synthesis of C. Response to [[epidermal growth factor|epidermal growth factor (EGF)]] in dividing mammalian cells is an example of a Type-1 incoherent FFL.<ref>{{Cite journal |last1=Amit |first1=Ido |last2=Citri |first2=Ami |last3=Shay |first3=Tal |last4=Lu |first4=Yiling |last5=Katz |first5=Menachem |last6=Zhang |first6=Fan |last7=Tarcic |first7=Gabi |last8=Siwak |first8=Doris |last9=Lahad |first9=John |last10=Jacob-Hirsch |first10=Jasmine |last11=Amariglio |first11=Ninette |last12=Vaisman |first12=Nora |last13=Segal |first13=Eran |last14=Rechavi |first14=Gideon |last15=Alon |first15=Uri |date=April 2007 |title=A module of negative feedback regulators defines growth factor signaling |url=https://pubmed.ncbi.nlm.nih.gov/17322878/ |journal=Nature Genetics |volume=39 |issue=4 |pages=503–512 |doi=10.1038/ng1987 |issn=1061-4036 |pmid=17322878|s2cid=16706055 }}</ref>

The frequent observation of feed-forward loops in various biological contexts across multiple scales suggests that they have structural properties that are highly adaptive in many contexts. Several theoretical and experimental studies including those discussed here show that FFLs create a mechanism for biological systems to process and store information, which is important for predictive behavior and survival in complex dynamically changing environments.