A series of biochemical switches control transitions between and within the various phases of the cell cycle. The cell cycle is a series of complex, ordered, sequential events that control how a single cell divides into two cells, and involves several different phases. The phases include the G1 and G2 phases, DNA replication or S phase, and the actual process of cell division, mitosis or M phase.Morgan D. (2006), The Cell Cycle: Principles of Control, OUP/New Science Press During the M phase, the chromosomes separate and cytokinesis occurs.
The switches maintain the orderly progression of the cell cycle and act as checkpoints to ensure that each phase has been properly completed before progression to the next phase. For example, Cdk, or cyclin dependent kinase, is a major control switch for the cell cycle and it allows the cell to move from G1 to S or G2 to M by adding phosphate to protein substrates. Such multi-component (involving multiple inter-linked proteins) switches have been shown to generate decisive, robust (and potentially irreversible) transitions and trigger stable oscillations. As a result, they are a subject of active research that tries to understand how such complex properties are wired into biological control systems.
Feedback loops
Many biological circuits produce complex outputs by exploiting one or more feedback loops. In a sequence of biochemical events, feedback would refer to a downstream element in the sequence (B in the adjacent image) affecting some upstream component (A in the adjacent image) to affect its own production or activation (output) in the future. If this element acts to enhance its own output, then it engages in positive feedback (blue arrow). A positive feedback loop is also known as a self-reinforcing loop, and it is possible that these loops can be part of a larger loop, as this is characteristic of regulatory circuits.
Conversely, if this element leads to its own inhibition through upstream elements, this is canonically negative feedback (red blunt arrow). A negative feedback loop is also known as a balancing loop, and it may be common to see oscillations in which a delayed negative feedback signal is used to maintain homeostatic balance in the system.
Feedback loops can be used for amplification (positive) or self-correction (negative). The right combination of positive and negative feedback loops can generate ultrasensitivity and bistability, which in turn can generate decisive transitions and oscillations.
Combination of positive and negative feedback loops Positive and negative feedback loops do not always operate distinctly. In the mechanism of biochemical switches, they work together to create a flexible system. For example, according to Pfeuty & Kaneko (2009), to overcome a drawback in biochemical systems, positive feedback regulation loops may interact with negative regulation loops to facilitate escape from stable states. The coexistence of two stable states is known as bistability, which is often the result of positive feedback regulations.
An example that reveals the interaction of the multiple negative and positive feedback loops is the activation of cyclin-dependent protein kinases, or Cdks14. Positive feedback loops play a role by switching cells from low to high Cdk-activity. The interaction between the two types of loops is evident in mitosis. While positive feedback initiates mitosis, a negative feedback loop promotes the inactivation of the cyclin-dependent kinases by the anaphase-promoting complex. This example clearly shows the combined effects that positive and negative feedback loops have on cell-cycle regulation.
Ultrasensitivity
An "all-or-none" response to a stimulus is termed ultrasensitivity. In other words, a very small change in stimulus causes a very large change in response, producing a sigmoidal dose-response curve. An ultrasensitive response is described by the general equation V = Sn/(Sn + Km), known as the Hill equation, when n, the Hill coefficient, is more than 1. The steepness of the sigmoidal curve depends on the value of n. A value of n = 1 produces a hyperbolic or Michaelian response. Ultrasensitivity is achieved in a variety of systems; a notable example is the cooperative binding of the enzyme hemoglobin to its substrate. Since an ultrasensitive response is almost ‘digital’, it can be used to amplify a response to a stimulus or cause a decisive sharp transition (between ‘off’ and ‘on’ states).
Ultrasensitivity plays a large role in cell-cycle regulation. For example, Cdk1 and Wee1 are mitotic regulators, and they are able to inactivate each other through inhibitory phosphorylation. This represents a double negative feedback loop in which both regulators inactivate each other. According to Kim et al. (2007), there must be an ultrasensitive element to generate a bistable response. It turns out that Wee1 has an ultrasensitive response to Cdk1, and this likely arises because of substrate competition among the various phosphorylation sites on Wee1.
Bistability
Bistability implies hysteresis, and hysteresis implies multistability. Multistability indicates the presence of two or more stable states for a given input. Therefore, bistability is the ability of a system to exist in two steady states.Strogatz S.H. (1994), Nonlinear Dynamics and Chaos, Perseus Books Publishing In other words, there is a range of stimulus values for which the response can have two steady-state values. Bistability is accompanied by hysteresis, which means that the system approaches one of the two steady states preferentially depending on its history. Bistability requires feedback as well as an ultrasensitive circuit element.
Under the proper circumstances, positive and negative feedback loops can provide the conditions for bistability; for example, by having positive feedback coupled to an ultrasensitive response element with the circuit. A hysteretic bistable system can act as a robust reversible switch because it is harder for the system to transition between ‘on’ and ‘off’ states (compared to the equivalent monostable ultrasensitive response). The system could also be poised such that one of the transitions is physically unattainable; for example, no amount of reduction in the stimulus will return the system to the ‘off’-state once it is already in the ‘on’ state. This would form a robust irreversible switch. How to design a simple biological switch is described in a conference paper.https://dr.ntu.edu.sg/handle/10356/83213
There is no one-to-one correspondence between network topology, since many networks have a similar input and output relationship. A network topology does not imply input or output, and similarly input or output does not imply network topology. It is for this reason that parameterization is very important for circuit function. If the dynamics of the input are comparable or faster than the response of the system, the response may appear hysteretic.
Three cell cycle switches are described below that achieve abrupt and/or irreversible transitions by exploiting some of the mechanisms described above.
The G1/S switch
The G1/S transition, more commonly known as the Start checkpoint in budding yeast (the restriction point in other organisms) regulates cell cycle commitment. At this checkpoint, cells either arrest before DNA replication (due to limiting nutrients or a pheromone signal), prolong G1 (size control), or begin replication and progress through the rest of the cell cycle. The G1/S regulatory network or regulon in budding yeast includes the G1 cyclins Cln1, Cln2 and Cln3, Cdc28 (Cdk1), the transcription factors SBF and MBF, and the transcriptional inhibitor Whi5. Cln3 interacts with Cdk1 to initiate the sequence of events by phosphorylating a large number of targets, including SBF, MBF and Whi5. Phosphorylation of Whi5 causes it to translocate out of the nucleus, preventing it from inhibiting SBF and MBF. Active SBF/MBF drive the G1/S transition by turning on the B-type cyclins and initiating DNA replication, bud formation and spindle body duplication. Moreover, SBF/MBF drives expression of Cln1 and Cln2, which can also interact with Cdk1 to promote phosphorylation of its targets.
This G1/S switch was initially thought to function as a linear sequence of events starting with Cln3 and ending in S phase. However, the observation that any one of the Clns was sufficient to activate the regulon indicated that Cln1 and Cln2 might be able to engage positive feedback to activate their own transcription. This would result in a continuously accelerating cycle that could act as an irreversible bistable trigger. Skotheim et al. used single-cell measurements in budding yeast to show that this positive feedback does indeed occur. A small amount of Cln3 induces Cln1/2 expression and then the feedback loop takes over, leading to rapid and abrupt exit of Whi5 from the nucleus and consequently coherent expression of G1/S regulon genes. In the absence of coherent gene expression, cells take longer to exit G1 and a significant fraction even arrest before S phase, highlighting the importance of positive feedback in sharpening the G1/S switch.
The G1/S cell cycle checkpoint controls the passage of eukaryotic cells from the first gap phase, G1, into the DNA synthesis phase, S. In this switch in mammalian cells, there are two cell cycle kinases that help to control the checkpoint: cell cycle kinases CDK4/6-cyclin D and CDK2-cyclin E. The transcription complex that includes Rb and E2F is important in controlling this checkpoint. In the first gap phase, the Rb-HDAC repressor complex binds to the E2F-DP1 transcription factors, therefore inhibiting the downstream transcription. The phosphorylation of Rb by CDK4/6 and CDK2 dissociates the Rb-repressor complex and serves as an on/off switch for the cell cycle. Once Rb is phosphorylated, the inhibition is released on the E2F transcriptional activity. This allows for the transcription of S phase genes encoding for proteins that amplify the G1 to S phase switch.
Many different stimuli apply checkpoint controls including TGFb, DNA damage, contact inhibition, replicative senescence, and growth factor withdrawal. The first four act by inducing members of the INK4 or Kip/Cip families of cell cycle kinase inhibitors. TGFb inhibits the transcription of Cdc25A, a phosphatase that activates the cell cycle kinases, and growth factor withdrawal activates GSK3b, which phosphorylates cyclin D. This leads to its rapid ubiquitination.
The G2/M switch G2 is commenced by E2F-mediated transcription of cyclin A, which forms the cyclin A-Cdk2 complex. In order to proceed into mitosis, the cyclin B-Cdk1 complex (first discovered as MPF or M-phase promoting factor; Cdk1 is also known as Cdc2 in fission yeast and Cdc28 in budding yeast) is activated by Cdc25, a protein phosphatase. As mitosis starts, the nuclear envelope disintegrates, chromosomes condense and become visible, and the cell prepares for division. Cyclin B-Cdk1 activation results in nuclear envelope breakdown, which is a characteristic of the initiation of mitosis.
The cyclin B-Cdk1 complex participates in a regulatory circuit in which Cdk1 can phosphorylate and activate its activator, Cdc25 (positive feedback), and phosphorylate and inactivate its inactivator, the kinase Wee1 (double-negative feedback). This circuit could act as a bistable trigger with one stable steady state in G2 (Cdk1 and Cdc25 off, Wee1 on) and a second stable steady state in M phase (Cdk1 and Cdc25 active, Wee1 off). However, Wee1 is itself regulated by other factors, such as Cdr2.