Laurent Gerbaud

Drissa Zié

Herve Diarra

Lauric Chazal

Garbuio

Obtaining the most exact Jacobian of the time modelling of power electronics structures for gradient-based optimisations

Keywords: Jacobian, Runge Kutta44, power electronics, SQP, time simulation, time sizing criteria

Purpose

The paper deals with the exact computation of the jacobian of a time criteria from a numerical simulation of power electronics structures, for the sizing by gradient-based optimization algorithm.

Design/methodology/approach -Runge Kutta 44 is used to solve the state equations. The generic approach combines numerical and symbolic approaches. The modelling of the static converter is based on ideal switches.

Finding -The paper extends the state equations to derivate any state variable according a sizing parameter. The integral expressions used for some sizing performances (e.g. average or rms values) mix symbolic and numerical approaches. Choices are made for the derivatives of the extrema of which the search is not a continuous process. The use of an object-oriented implementation allows to have generic formulation of some design performances.

Research limitations/implications -The paper aims to propose and to test formulations of sizing criteria and their gradients; so, the modelling of the study case is carried out manually. Due to generic modelling approach used for the power electronics, the model is not completely continuous. So, the derivatives according some parameters (e.g. switch controls) must be carried out by finite differences. However, as the global behavior is continuous, it is not critical.

Originality/value -The approach proposes formulations giving a numerical sizing dynamic model with a jacobian computed, if possible, by an exact derivation useful for optimization studies. The approach gives fast simulation and fast computation of the derivatives by combining numerical and analytical approaches.

Practical implications -The proposed formulations can be easily applied on simple static converter applications. For applications with large state equations, it should be possible to use the basic model of switches used in simulation tools of power electronics. The solving process and the sizing criteria formulation (with their derivatives) are generic and can be instantiate for any study.

I. Introduction

For the design of power electronics structures, symbolic approaches are limited to small structures with a priori on the operating mode (Bath et al. 1995). The use of time simulation tools (e.g. PSPice, Simplorer, Psim, Saber, Portunus, etc.) is a generic solution for the sizing by optimisation with stochastic algorithms [START_REF] Roboam | More Electricity in the Air: Toward Optimized Electrical Networks Embedded in More-Electrical Aircraft[END_REF]. However, this may be very time consuming and it is mainly adapted for applications with few constraints. Else, the use of gradient-based optimisation is better but this requires finite differences to compute the gradients [START_REF] Etayo | Optimization of parallelized power inverters using a direct modelling approach for More Electrical Aircraft[END_REF]. Even if finite differences on simulation tools is a simple way to obtain the derivatives of some sizing criteria (rms values, average values and extrema) according to the parameters of the circuit component; their quality may create optimisation convergence problems and they are time consuming.

Code derivation is possible [START_REF] Wojtusch | MBSlib-An Efficient Multibody Systems Library for Kinematics and Dynamics Simulation, Optimization and Sensitivity Analysis[END_REF]. It could be implemented for the dynamic simulation of power electronics. However, generally, if a mathematical alternative exists, it should be preferred.In this way, the paper proposes to use a numerical integration of the state equations and to use the mathematical properties of state equations to obtain the derivatives of any state variable or output variable (in the sense of state system representation) according to the sizing parameters of the studied application. From these variables, sizing criteria can be obtained. In the context of power electronics applications, the use of such an approach establishes some questions. Which model to use for the switches? Is the model entirely derivable? How to deduce performances from the state variables, and their gradients? How to deals with discontinuous formulations? ?

First, in the context of power electronics, the paper presents a way to obtain the exact gradients of the state variables with respect to the sizing parameters, by extending the state equations and their numerical solving.

Second, it presents the modelling choice for the static converters. Third, it details the computation of some sizing criteria and their gradients, trying to have an exact derivation way. Fourth, implementation aspects are presented.

Fifth, the approach is applied on a simple electrical drive in the context of sizing by optimisation (SQP), with only results dealing with the gradient computation performances.

II. Modelling to deal with state equation and their derivatives

In the paper, as the modelling level used for the power electronics deals with linear state equations, the paper focuses only on such state equations. However, the approach is applicable to non-linear state equations (the difference being only on the expressions of the derivatives).

II.1. State equation

The state equation of any application can be written as::

      ( ) ( ) , dX t A P X t B P u P t dt     (1)
where:

 t : the time,  X : the state vector,   , 1..

i P P P i n 
is the sizing parameter vector, u is the expression of the state inputs (e.g.: the sources of the electronic circuit).

A and B depend directly on   , 1..

i P P P i n .
Equation (1) can be extended to give the derivatives of the state system with respect to any sizing parameter 1..

P in P 

of the sizing model [START_REF] Fischer | From the electronic circuit to the simulation component : an automatic component building process[END_REF], [START_REF] Sengupta | Efficient gradient computation for dynamical models[END_REF]:

            , ( ) ( ) ( ) , ( )
i i i i i d dX
       (2)
A new state system can be obtained:

              1 1 1 ( ) 0 0 0 0 0 ( ) ( ) 0 0 0 0 ... ... ... 0 ( ) 0 0 0 ( ) 0 0 ( ) 0 0 ... 0 0 0 ( ) 0 ... ... ( ) 0 0 0 0 ( ) P P i i i n n X t
                                                                           1 1 , ( ) 0 0 0 0 0 , ( ) ( ) 0 0 0 0 ... ... 0 ( ) 0 0 0 ( ) , 0 0
                                                                                                 (3)
Due the block diagonal of the extended matrix made of A (equation (3)), the dynamic of the system stays the one given by A . So, the same simulation time step can be used for both equations (1) and (3).

II.2. Derivatives with respect to the outputs of the state equations

As X depends only on P and t , an output vector Y can be deduced from X and u , using:

      ( ) , ( ) , Y t C P X P t D P u P t     (4)
From, this, Y can be easily derivated according to , 1..

P i i n P  , as:         , ( ) (
        (5)
However, it is better. to compute only the variables necessary for the sizing. So, for each selected component of X and Y , a symbolic expression can be obtained, often very smaller for equations (1) and (3).

So, the gradients can be obtained with simpler equations that the general equations (3) and (5).

II.3. Numerical solving of the state equations

II.3.1. Runge Kutta 44

Here, Runge Kutta 44 is chosen with adaptive time step. This offers a good compromise between accuracy and simulation times, without the limit of symbolic solving that is limited to small equations. The use of adaptive time step allows to decrease the simulation time while keeping a good accuracy (see section II.3.2.).

To understand the implementation of the approach presented below, it is important to recall some implementation characteristics of this well known method [START_REF] Press | Numerical Recipes in C, The Art of Scientific Computing[END_REF]. This method uses a 4th-order formula that evaluates the time derivatives (equation ( 1)) four times (named minor steps) per time step (named major step), as shown in figure 1 . In numerous simulation software tools (FMI, 2021), such a method is implemented respecting a process similar to the one of figure 2 used in [START_REF] Simulink | Simulink Engine Interaction with C S-Functions[END_REF]. ) ). If an adaptive step is used, the new major step value is estimated ("timeStepManagement" in figure 2). After, Runge Kutta 44 is applied, using four calls to the time derivatives of the state vector ("computeTimeDerivatives" in figure 2).

n t  1 n n n t t t     n t ( ) n x t ( ) n n x t t   ( ) x t 2 n n t t  
n n Y t t    n t   dX dt  ( ) n n X t t   ( ) n n dX t t dt      n n dY t t dP       n n d dX t t dP dt     n n dX t t dP     d dX dP dt

II.3.2. Event management

Many discrete events exist in power electronics circuits. It is important to simulate correctly them to have a good compromise between computation time and accuracy. It is also interesting to stop the simulation on a design criterion (e.g.: at a reached steady state) and to use events for the computation of the sizing criteria during the simulation (see section III).

The best way for fast simulations, is to adapt the simulation step (major step) according to the events of the simulation and the dynamic of the state systems. Figure 3 shows an example of the solving differences between the fixed and adative time step for the simulation of a simple clock.

update Both fixed and adaptive time steps are implemented in our approach. The adaptive time step is managed using prediction of events [START_REF] Normand | Use of simulation in failure detection and diagnosis of an electromechanical system[END_REF], that combines zero-crossing approach [START_REF] Simulink | Simulink Engine Interaction with C S-Functions[END_REF] with event managements (like in figure 3b).

Event 1 t Event 2 t 1 1 1 1 2 2 2 2 ( ) 1 ( ) 0 if t t then reach t else out t t T endif if t t then reach t else out t t T endif               initializeCondition 1 2 1 t T t T out      out 1 0 t Event 1 t Event 2 t Event 1 t Event 2 t out 1 t update 1 1 1 2 2 2 1 0 if t t then out t t T endif if t t then out t t T endif             initializeCondition 1 2 1 t T t T out      t  t  t  t  t 
To transform zero-crossing events into a date to reach, the approach uses a tangent method to extrapolate the time where a variable should reach a desired value. If the time derivatives are not available, finite differences from the previous step are used, as shown in figure 4. As seen, such a process is generic. At each major time step of RK44, the time to reach has to be refresh. Closer the variable is from the value to reach, better the time to reach is extrapolated. For the design of electrical drives, two simple models of the switches can be used [START_REF] Kassakian | Simulating power electronics systems -a new approach[END_REF].

In update (illustration of the principle of the zero crossing for test i<0

III.1.1. Ideal switch on/off

A switch is represented like in figure 5 [START_REF] Burdio | A time-domain simulator for power electronic converters based on discrete-time modeling of switches[END_REF], [START_REF] Tourkhani | A variable-topology simulation tool for switchmode power supplies[END_REF], [START_REF] Merdassi | Automatic Generation of Average Models for Power Electronics Systems in VHDL-AMS and Modelica Modelling Languages[END_REF].

C i v v i State on v>0 i<0 State on State off C C (i.e. C=0) (i.e. C=1) 0 v  0 i  State off 0 v  0 i  Figure 5: ideal switch on/off
Such a model allows to obtain a simple and reduced state equation for each state (configuration) of the static converter. However, a state equation has to be defined for each available state of the static converter. So, it is difficult to apply such a modelling if there are numerous available configurations.

Furthermore, the management of the switching tests can be delicate when there are soft switching. Indeed, some turning off of some switches depends on the other turning on other switches and vice versa; some voltage may become floating. Indeed, some parts of the circuit may disappear according the switch states which may create difficulties to test the changes of configuration (creating dependences between the switching of several switches, e.g. in switching cells).

Average modelling is also possible from such a representation, but it is very problematic with soft switchings or big power electronics structures.

However, for simple structure, this ideal model uses simple switching tests, and the equations are very simple.

III.1.2. Binary resistance ron/Roff

A switch is represented like in figure 6, by a resistor (and possibly with a voltage drop) which resistance changes according the state of the switch [START_REF] Bordry | Computer-aided analysis of power-electronic systems[END_REF].

Here, the circuit state equation is unique (whatever the states of the switches are) but bigger than the state equations with the on/off model. It has artificial time constants due to the value of the switch resistances. These time constants may disrupt the solving process (the time step). The switching tests of the switches are independent, so easy to formulate. This modelling is generally the basic modelling in power electronics simulation tools (PSpice, Psim, Saber, Portunus, Simplorer…). This representation is better for big structures. In the paper, the application case being simple (three available configurations, see section IV), the ideal on/off model is used.

III.2. Time sizing criteria

In a power electronics structure, performances can be obtained from time simulation. The paper focuses only on time performances, so, EMC performances that require a frequency model are note discussed. Among the time performances, the following criteria can be calculated:

-average values (integrals)

-rms values (integrals)

-extrema (tests)

-powers (integrals)

-losses (conduction, switching) (integrals or sums)

Excepted for extrema, their computation requires a simulation at steady state. In this case, their computation needs to be carried out on an integer number (at less one) of reference periods of the circuit. This reference period is often the operating period of the static converter: T .

III.2.1. Performances based on integrals

The expressions of the average values, rms values and powers contain an integral. For example, the average value of ( , ) In the same way, it is easy to obtain any power, by applying the average value expression to the product of two variables.

z P t is: 0 0 1 ( , )
For the integrals, in both the performance expressions and their derivatives, the trapeze method is used, with an integration step equal to the major step of Runge Kutta 44, in the last operating periods of the time simulation, during the time simulation.

III.2.2. Extrema

The process to find the extrema of a variable in a simulation is not continuous, because it uses tests and temporary variables. However, in the paper, the extremum of a variable is searched during the time simulation, by default on the last operating period, at steady state. The derivative of the extremum with respect to a sizing parameter 1..

P in P 
is the derivative of the variable with respect to the parameters 1..

P in P 
at the date where the variable reaches its extremum, as it is carried out by some automatic code differentiation [START_REF] Hascoët | The Tapenade Automatic Differentiation Tool: Principles, Model, and Specification[END_REF].

III.2.3. Implementation in the solving process

In the solving process with Runge Kutta 44, the computation of the sizing performances are carried out on the last period of the simulation, at steady state. In this way, the management of the events is used to activate the computation of the performances at the last operating period before the end of the simulation. So, the design outputs are computed at the same time than the state variables, but only during the last period of the simulation (see figure 7). This allows to store no simulation values.

In addition, in the initialization part of the simulation process, the computation of the sizing criteria to compute have to be initialized.

III.2.4. Stead state

However, as said before, such performances need a steady state to be computed. The best way is to have an automatic detection of the steady state that activates the computation of the design output on the last operating period of the static converter and then that stops the simulation. For power electronics, such a detection is not easy [START_REF] Maranesi | Computer-aided design of HF converters: new needs, new tools[END_REF], mainly because the switching sequence is not defined a priori and the variables to check may be chopped. The aim of the paper being mainly to propose formulations for the model jacobian than defining a real simulation software, such a detection has not yet been implemented.

III.2.5. Use of finite differences

Some derivation problems appear for the derivatives according control variables, e.g. the duty cycle of a static converter. For simple choppers (buck, boost, flyback…), analytical expressions can be defined for the sizing criteria, and so the derivation is easy (Bath, 1990). When simulations are used, the modelling according such parameters becomes discontinuous. Indeed, in the modelling, due to the use of numerical time solving, control variables (e.g. duty cycles) may appear in tests (e.g. by using if or while loops). Even if some modelling gives continuous expressions according control variable; here, the way to write the model for dynamic simulation is discontinuous according them. The paper proposes to use finite differences in this case. In fact, it is easy to observe by several simulations that static converters have generally a continuous behaviour according their duty-cycles.. This is a limit of the approach.

III.3. Implementation

By respecting the simulation process presented in figure 7, an object-oriented programming has been carried out, allowing to separate:

 generic aspects (time solving method, time management, event management, methods for the computation of the sizing outputs and their gradients…), that are implemented in specific classes with the methods for the solving and the gradients  specific aspects of a problem (the state equations of the power electronics circuit, the modelling of the control, the state changes of the switches (however generic)).

This also allows to profit of the concept of inheritance in programming.

Java programming is used. This allows to use optimisation framework compatible with Java e.g.: Matlab (Fmincon), CADES [START_REF] Delinchant | An Optimizer using the Software Component Paradigm for the Optimization of Engineering Systems[END_REF]...

IV. Electrical drive application

IV.1. Study case

The approach is illustrated with a simple static converter feeding a synchronous machine (see Figure 8).

The machine is represented by a complex model based on Maxwell's equations (not presented here), which can give a simple RLE circuit representation according the sizing parameters [START_REF] Diarra | Sizing by SQP optimisation of an electrical drive: application to a commuted capacitor driven synchronous machine application[END_REF]. This last circuit model is used for the electrical drive model representing the power electronics and the control (aim of the paper).

The control angle (or duty-cycle) that controls the switches, impacts the operating modes of the static converter, as shown in figure 9. In this way, according to the switch states, three configurations (corresponding to three state equations) appear in the various operating modes of the static converter, maybe several time per operating period and according different sequences.

There are soft switchings, so, is very important. The change of state equation according time is managed by the generic switching tests presented in section III.1. and the zero-crossing approach presented in section II.3.2..

In the proposed approach, the only specific aspect to define for an application is the model (state equations) of the power electronics part and its control. As the paper aims to present and validate the approach, this aspect has been manually carried out and implemented. Maple software tool has been used for the derivatives of the state equations and their translation into Java. To use of another machine, the machine sizing model has only to compute the RLE circuit parameter to be connected with the circuit model. The steady state is obtained after few operating periods for the sizing parameter values used in the optimisation. So, for the specifications of the sizing problem, simulations that last 40 operating periods, have always given a steady state for the application during the optimisation process.

The currents and voltages have been compared to results from PSIM. The derivatives for the design have been compared to derivative obtained by finite differences. For all these aspects, the results are very similar;

differences lower than 1/1000 for the variables and about 1/100 for the gradients compared to finite differences.

The computation times without data saving (used only to check the simulation), is about some seconds, including the computation of the gradients.

IV.2. Optimisation

The paper does not detail optimisation results, because the paper focuses more on the derivatives of the time sizing criteria useful for sensitive analysis or sizing by optimisation than on the optimisation itself. For such an application, an optimisation is interesting with a complex model of the machine coupled to the static converter model previously presented. This has been carried out, with a machine model based on Maxwell equations, included core losses. The sizing constraints are mainly on the machine, but also the control angle, the power in the load resistor, the maximum value of capacitor voltage, the rms value of the stator current.

For a global model having 9 inputs and 13 outputs, a design by SQP optimisation lasts about 1 minute on a laptop (Windows 10, core i5@2.6GHz, 4Go Ram). The sizing of this application and the machine model are detailed in [START_REF] Diarra | Sizing by SQP optimisation of an electrical drive: application to a commuted capacitor driven synchronous machine application[END_REF]. The computation of a Pareto front (figure 10) lasts less than a quarter of hour.

CONCLUSIONS

The paper focuses on a a way to include time criteria in the sizing by optimisation of power electronics structures, by using time simulation with the more exact possible jacobian. To test the approach, only the modelling of the power electronics structure is manually made here, as the derivatives of the state equations (using partially Maple for derivation and Java code generation). The solving process and the sizing criteria with their derivatives are implemented to be re-used for any applications. So, the paper proposes a real solution for dynamic model, limiting the use of finite differences for the gradients. The made prototype shows a good accuracy of the modelling and the gradient formulation.

In future works, an aid at the establishing of the state variables and its derivatives should be useful [START_REF] Webster | Computer-based symbolic circuit analysis and simulation[END_REF]) [START_REF] Merdassi | Automatic Generation of Average Models for Power Electronics Systems in VHDL-AMS and Modelica Modelling Languages[END_REF], using the basic ron/Roff ideal model (only one state equation, simple switching tests). The steady state should be automatically detected to be more generic.

Figure 1 :

 1 Figure 1: Steps of Runge Kutta 44

Figure 2 :

 2 Figure 2: Runge Kutta 44: basic implementation At the beginning of each major time step, method "update" allows to modify the state equations according the values of all the variables computed at the previous time step. It deals also with discrete aspects (e.g. control,

FigureFigure 3 :

 3 Figure 3b: Adaptive time step

Figure 4 :

 4 Figure 4: example of zero-crossing management with adaptive time step and prediction process III. Time modelling for power electronics structures III.1. Chosen switch model

Figure 6 :

 6 Figure 6: ideal switch ron/Roff

Figure 7 :

 7 Figure 7: Computations of the design outputs in the simulation process

Figure 8 :Figure 9 :

 89 Figure 8: Principle schematic of the studied application

Figure 10 :

 10 Figure 10: example of obtained Pareto front

), at actual time , and // = previous time (i.e. one step before) where // i to reach is and the process must found the coressonging zero-crossing date where // t_toReach = time extrapoled for i= i_toReach

																	time	i		i
																previous	actual
		time											i		i
					to	Re	ach					previous
																to i	Re	ach	to time	Re	ach	i		to i	Re	ach
	//	accuracy		=	accuracy	of	the	zero-crossing,	for	example	10 10 
	if	i						i						accuracy	then
		to	Re	ach					actual
		i				i
		actual			to	Re	ach	i	( time	)
	else
		if		 time actual i Re  to ach previous i time   0 actual 	then  to i 	Re	ach		actual i		   	actual actual time i	 	previous previous time i	   	i	previous
	endif
		if		time									time	then	i
								to	Re	ach	actual	actual
				ask	the	solver	to	reach	time
																to	Re	ach
		endif
	endif
	…..
																to	Re	ach
	//	at	the	end	of	update
	time								time
			previous										actual
	i					i
	previous		actual


Pierre Simon

Simonetta Gribaldo
email: simonetta.gribaldo@pasteur.fr

Guillaume Borrel
email: guillaume.borrel@pasteur.fr

Diversity and Evolution of Methane-Related Pathways in Archaea

Keywords: methanogenesis, archaea, evolution, alkanotrophy, methanotrophy

Methane is one of the most important greenhouse gases on Earth and holds an important place in the global carbon cycle. Archaea are the only organisms that use methanogenesis to produce energy and rely on the methyl-coenzyme M reductase (Mcr) complex. Over the last decade, new results have significantly reshaped our view of the diversity of methane-related pathways in the Archaea. Many new lineages that synthesize or use methane have been identified across the whole archaeal tree, leading to a greatly expanded diversity of substrates and mechanisms. In this review, we present the state of the art of these advances and how they challenge established scenarios of the origin and evolution of methanogenesis, and we discuss the potential trajectories that may have led to this strikingly wide range of metabolisms.

INTRODUCTION

Methane is one of the major greenhouse gases and is crucial to current global environmental changes [START_REF] Saunois | The growing role of methane in anthropogenic climate change[END_REF]. Biological production of methane may have started as early as 3.5 Ga (104), with a direct impact on the evolution of the Earth's climate [START_REF] Kasting | Life and the evolution of Earth's atmosphere[END_REF]. Archaea are the only organisms that generate methane as a by-product of their energy metabolism. Methanogenic archaea (or methanogens) are strict anaerobes dwelling in all types of anoxic niches, from sediments and rice paddies to the gastrointestinal tracts of animals [START_REF] Liu | Metabolic, phylogenetic, and ecological diversity of the methanogenic archaea[END_REF]101). In most of these environments, they form syntrophic partnerships with fermentative bacteria [START_REF] Sieber | Genomic Insights into Syntrophy: The Paradigm for Anaerobic Metabolic Cooperation[END_REF], allowing the complete degradation of organic matter and therefore acting as major players in the global carbon cycle [START_REF] Conrad | Importance of hydrogenotrophic, aceticlastic and methylotrophic methanogenesis for methane production in terrestrial, aquatic and other anoxic environments: a mini review[END_REF] (Supplemental Figure 1). It is estimated that through these associations, methanogens are responsible for up to 50% of organic matter mineralization in freshwater environments [START_REF] Bastviken | Fates of methane from different lake habitats: connecting whole-lake budgets and CH 4 emissions[END_REF] and for the overall production of 1 Gt of methane per year [START_REF] Thauer | Biochemistry of methanogenesis: a tribute to Marjory Stephenson[END_REF]. Only half of this methane reaches the atmosphere [START_REF] Conrad | The global methane cycle: recent advances in understanding the microbial processes involved[END_REF][START_REF] Reeburgh | Oceanic methane biogeochemistry[END_REF], because it is consumed by anaerobic archaeal methanotrophs as well as anaerobic and aerobic bacterial methanotrophs.

Most known methanogens are highly specialized microorganisms that can only use a narrow range of one-or two-carbon compounds to obtain energy (Figure 1a,b). A key enzymatic complex of both archaeal methanogens and methanotrophs is the methyl-coenzyme M (CoM) reductase complex (Mcr), which is directly responsible for the production and/or oxidation of methane [START_REF] Thauer | Methyl (alkyl)-coenzyme M reductases: nickel F-430-containing enzymes involved in anaerobic methane formation and in anaerobic oxidation of methane or of short chain alkanes[END_REF]. Methanogenesis pathways have been historically grouped into three categories: (a) hydrogenotrophic, for the reduction of CO 2 into CH 4 using H 2 as the electron donor, (b) methylotrophic, for the dismutation of methyl compounds into CH 4 and CO 2 , and (c) acetoclastic, for the dismutation of acetate into CH 4 and CO 2 . The reduction of methyl compounds with H 2 has often been classified as methylotrophic. However, since hydrogen is the electron donor in this reaction, it would be more correct to qualify it as hydrogenotrophic. We thus propose referring to this pathway as "methyl-reducing hydrogenotrophic methanogenesis" and, to avoid confusion, using "CO 2 -reducing hydrogenotrophic methanogenesis" for the reduction of CO 2 into CH 4 using H 2 as an electron donor (Figure 1a). More broadly, the terms CO 2 -reducing methanogenesis and methyl-reducing methanogenesis may also be used to include cases where alcohol or formate is the electron donor. In this review we also use the term methyldismutating methanogenesis instead of methylotrophic methanogenesis when methyl groups are used as both carbon and electron donors for methanogenesis (Figure 1a). 1 and2). (c) Taxonomic distribution of methane-related pathways across the reference phylogeny of Archaea. Colored squares at the tips of branches correspond to the presence of each type of metabolism. The proportions of genomes of each taxon coding for main components of the pathways are indicated by color gradient (0%, 1-25%, 26-50%, 51-75%, 76-100%). The different colors correspond to functional categories. The analysis was conducted on 832 archaeal genomes, and the presence of complexes or pathways was determined using MacSyFinder (1) (Supplemental Table 3). Because MHC is part of a large protein family, the average number of homologs per genome (identified by proteins containing at least two CxxCH motifs) is indicated (minimum, 0.0; maximum, 17.0). Abbreviations: ANME, anaerobic methanotrophs; Acr, alkyl-Coenzyme M reductase complex; ß-oxidation, ß-oxidation pathway; CBWL, carbonyl-branch of the Wood-Ljungdahl pathway; CoA, coenzyme A; CoB, coenzyme B; CoM, coenzyme M; DPANN, "Ca. Diapherotrites," "Ca. Parvarchaeota," "Ca. Aenigmarchaeota," "Ca. Nanohaloarchaeota," and "Ca. Nanoarchaeota"; F 420 , F 420 cofactor (F 420 H 2 when reduced); Fd, ferredoxin (Fd red , reduced and Fd ox , oxidized); H 4 MPT, tetrahydromethanopterin; MBWL, methyl-branch of the Wood-Ljungdahl pathway; Mcr, Methyl-Coenzyme M reductase complex; MFR, methanofuran; MHC, Multi-heme cytochrome protein. For all enzymes, see Terms and Definitions section.

Studies on methanogenesis and methanogens started in the late nineteenth century [START_REF] Söhngen | Sur le rôle du méthane dans la vie organique[END_REF], and over 200 species capable of this metabolism are currently characterized. Until 2012, all known methanogens were classified into six orders, gathered into Class I, comprising Methanobacteriales, Methanococcales, and Methanopyrales, and Class II, comprising Methanosarcinales, Methanomicrobiales, and Methanocellales (6) (Figure 1c). These archaea mostly perform CO 2 -reducing methanogenesis and use the methyl branch of the Wood-Ljungdahl pathway (MBWL), as well as Mtr (tetrahydromethanopterin S-methyl-transferase complex) and Mcr (89) (Figure 1b). These enzymes are conserved in all Class I and Class II methanogens, with the exception of Methanimicrococcus (102), regardless of their methane metabolism (Figure 1c).

In only a decade, metagenomic approaches have revealed a wealth of novel deep-branching lineages of Mcr-containing archaea (Figure 1c). Strikingly, of these newly discovered lineages, only two ["Candidatus Methanohydrogenales"/"Ca. Nezhaarchaeota" (10, 109) and "Ca.

Methanomixophus" in Archaeoglobales [START_REF] Liu | Genomic and transcriptomic evidence supports methane metabolism in Archaeoglobi[END_REF]109)] are predicted to be CO 2 -reducing methanogens, while the vast majority are methyl-reducing hydrogenotrophic methanogens. The latter belong to the Methanotecta [Methanonatronarchaeia [START_REF] Sorokin | Discovery of extremely halophilic, methyl-reducing euryarchaea provides insights into the evolutionary origin of methanogenesis[END_REF]], the Diaforarchaea [Methanomassiliicoccales [START_REF] Borrel | Phylogenomic data support a seventh order of methylotrophic methanogens and provide insights into the evolution of methanogenesis[END_REF][START_REF] Dridi | Methanomassiliicoccus luminyensis gen. nov., sp. nov., a methanogenic archaeon isolated from human faeces[END_REF]], the Acherontia ["Ca. Nuwarchaeales" (NM3) [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF]111), "Ca. Methanofastidiosa" (79)], the TACK ["Ca. Methanomethyliales" (105), "Ca.

Methanodesulfokores" [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF][START_REF] Mckay | Co-occurring genomic capacity for anaerobic methane and dissimilatory sulfur metabolisms discovered in the Korarchaeota[END_REF]], and a basal Thaumarchaeota lineage [START_REF] Hua | Insights into the ecological roles and evolution of methyl-coenzyme M reductase-containing hot spring Archaea[END_REF]. These methanogens rely on substrate-specific methyltransferases, and all lack Mtr and a complete MBWL pathway (13) (Figure 1a). This type of methanogenesis, previously thought to have a very narrow distribution, is now known to be the most widely distributed across all the Archaea phylogeny.

All reactions taking place in the core enzymes of CO 2 -reducing methanogenesis are fully reversible, allowing the anaerobic oxidation of CH 4 into CO 2 . The possibility that such capacity exists in archaea was first suggested in the 1990s [START_REF] Hoehler | Field and laboratory studies of methane oxidation in an anoxic marine sediment: evidence for a methanogen-sulfate reducer consortium[END_REF] and was later supported by microscopic (11a), isotopic (80a), and metagenomic evidence [START_REF] Hallam | Reverse methanogenesis: testing the hypothesis with environmental genomics[END_REF]. Anaerobic methanotrophs (ANME) belong to "Ca. Methanophagales" (ANME-1) and several lineages in the Methanosarcinales [START_REF] Knittel | Anaerobic oxidation of methane: progress with an unknown process[END_REF] (Figure 1c). Several names have been proposed for ANME lineages in Methanosarcinales: ANME-2d "Ca. Methanoperedens" [START_REF] Haroon | Anaerobic oxidation of methane coupled to nitrate reduction in a novel archaeal lineage[END_REF], ANME-2a "Ca. Methanocomedens," ANME-2b "Ca.

Methanomarinus," ANME-2c "Ca. Methanogasteraceae," and ANME-3 "Ca. Methanovorans" [START_REF] Chadwick | Comparative genomics reveals electron transfer and syntrophic mechanisms differentiating methanotrophic and methanogenic archaea[END_REF]. Marine ANME archaea transfer electrons from the oxidation of methane to syntrophic sulfate-reducing bacteria (SRB) affiliated with the Desulfobacterales (51), while freshwater lineages can directly reduce inorganic compounds such as Fe(III) [START_REF] Leu | Lateral gene transfer drives metabolic flexibility in the anaerobic methane-oxidizing archaeal family Methanoperedenaceae[END_REF]. The recent availability of genomic data from members of all identified ANME clades has now enabled more detailed predictions on the functioning of anaerobic methanotrophy [START_REF] Chadwick | Comparative genomics reveals electron transfer and syntrophic mechanisms differentiating methanotrophic and methanogenic archaea[END_REF]103). It was also suggested that "Ca. Methanomixophus" (61) and "Ca. Methanodesulfokores" might be capable of this metabolism [START_REF] Mckay | Co-occurring genomic capacity for anaerobic methane and dissimilatory sulfur metabolisms discovered in the Korarchaeota[END_REF].

Another recent exceptional finding brought by exploration of the uncultured diversity of

Mcr-containing archaea was the discovery of many lineages predicted to use multicarbon alkanes ranging from 2 carbons (ethane) to more than 39 carbons as a source of energy (110, 121) (Figure 1b). This metabolism, termed alkanotrophy, was first proposed in the "Ca.

Syntropharchaeales", which oxidize short-chain alkanes [propane (C 3 ) and butane (C 4 )] into CO 2 by using an alkyl-CoM reductase (Acr), a distant homolog of Mcr, combined with the βoxidation and Wood-Ljungdahl pathways [START_REF] Laso-Pérez | Thermophilic archaea activate butane via alkyl-coenzyme M formation[END_REF]. Additional Mcr-like homologs, likely also involved in the activation of multicarbon alkanes, were found in several members of the Stygia ["Ca. Hadesarchaea" (45, 109)], Asgard ["Ca. Helarchaeota" (88, 119)], TACK ["Ca.

Bathyarchaeota" (32)], and Methanotecta ["Ca. Methanoliparia" [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF][START_REF] Laso-Pérez | Anaerobic degradation of non-methane alkanes by "Candidatus Methanoliparia" in hydrocarbon seeps of the Gulf of Mexico[END_REF]121), Archaeoglobales [START_REF] Boyd | Divergent methylcoenzyme M reductase genes in a deep-subseafloor Archaeoglobi[END_REF], "Ca. Santabarbaracales" (111), "Ca. Alkanophagales" (111), Methanosarcinales [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF][START_REF] Chen | Anaerobic oxidation of ethane by archaea from a marine hydrocarbon seep[END_REF][START_REF] Hahn | Candidatus Ethanoperedens," a thermophilic genus of archaea mediating the anaerobic oxidation of ethane[END_REF]]. Most of these lineages have the same core enzymes as "Ca. Syntropharchaeales" (Figure 1c). However, several enzymatic steps between the initial activation of the alkyl and the βoxidation pathway are still unknown (110).

A novel type of methanogenesis (alkanotrophic methanogenesis) has been recently proposed based on the first metagenome-assembled genomes (MAGs) of the "Ca. Methanoliparia," which encode Acr and Mcr as well as other core proteins for alkanotrophy and CO 2 -reducing methanogenesis (Figure 1b,c). Dismutation of multicarbon alkanes [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF][START_REF] Laso-Pérez | Anaerobic degradation of non-methane alkanes by "Candidatus Methanoliparia" in hydrocarbon seeps of the Gulf of Mexico[END_REF], and possibly longchain fatty acids [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF], would be coupled with methanogenesis within one cell, contrasting with the current paradigm of archaeal/bacterial syntrophy in this process [START_REF] Gray | Methanogenic degradation of petroleum hydrocarbons in subsurface environments: remediation, heavy oil formation, and energy recovery[END_REF]118). This proposal has been nicely confirmed experimentally from enrichments of "Ca. Methanoliparia," which showed that these archaea are able to use a large panel of alkanes, alkylcyclohexanes, and alkylbenzenes (linear chains greater than 13 carbons) (121).

Finally, the substrate range of methanogens has also been greatly extended recently by the discovery of dismutation of various methoxylated coal compounds in Methermicoccus shengliensis (Methanosarcinales), which is carried out by the same core enzymes as methyldismutating methanogenesis but with specific methyltransferases (54, 67) (Figure 1b,c).

These new results have significantly reshaped our view of the diversity of methane-related metabolisms and provided key insights into their functioning and societal impact. Due to their large phylogenetic distribution in the Archaea, several of these pathways may have an ancient origin and represent some of the earliest microbial metabolisms. These enzymes are directly involved in the oxidoreductions and transfers of the carbon substrates, regeneration of electron transporters, and conservation of energy. Their great modularity likely facilitated the emergence of a wide range of metabolisms and allowed archaea to occupy unique environmental niches. This review presents the current state of knowledge on the diversity and evolution of these metabolisms and discusses their origin and evolutionary trajectories.

CONSERVATION AND VARIABILITY OF METHANE-RELATED PATHWAYS

Eight main pathways (Figure 1a) are centered around Mcr and Acr. In all cases, the energy is conserved by the generation of a chemiosmotic gradient (based on Na + or H + ) that is exploited by a membrane ATP synthase to produce ATP from ADP. While the enzymatic steps directly involved in the oxidoreduction of the carbon substrates are mostly uniform in each pathway, there exists a stunning variability in the mechanisms of energy conservation, regeneration of electron transporters, and transmission of electrons to the final acceptor (Figures 2 and3). complex. The other enzyme names grouped in the same circle are known or expected to form a complex. Abbreviations: CBWL, carbonyl branch of the Wood-Ljungdahl pathway; CoB, coenzyme B; F 420 , F 420 cofactor (F 420 H 2 when reduced); Fd, ferredoxin (Fd red , reduced and Fd ox , oxidized); HDS, heterodisulfide; MBWL, methyl branch of the Wood-Ljungdahl pathway; MP, methanophenazine (MPH 2 when reduced). For all enzymes, see Terms and Definitions section.

Methyl-CoM and Alkyl-CoM Reductases, the Central Enzymes

For methanogenesis, Mcr catalyzes the reduction of a methyl group linked to CoM (CoM-S-CH 3 ) using coenzyme B (HS-CoB), which leads to the formation of CH 4 and CoM-S-S-CoB [also called heterodisulfide (Figures 2 and3)]. Even if this reaction is highly exergonic [ΔG°′ = 30 kJ/mol [START_REF] Thauer | Methyl (alkyl)-coenzyme M reductases: nickel F-430-containing enzymes involved in anaerobic methane formation and in anaerobic oxidation of methane or of short chain alkanes[END_REF]], it can be reverted in methanotrophic archaea. Similar to Mcr, which can only catalyze reactions involving methane, Acr seems specialized for a specific alkane chain length.

Acr enzymes may thus be subdivided into ethyl-CoM reductase (Ecr) of "Ca. Argoarchaeum"/ "Ca. Ethanoperedens" on ethane (39), short-chain alkyl-CoM reductase (Scr) [START_REF] Laso-Pérez | Thermophilic archaea activate butane via alkyl-coenzyme M formation[END_REF], and longchain alkyl-CoM reductase (Lcr) in "Ca. Methanoliparia" (121). Mcr and Acr are composed of three subunits (McrABG/AcrABG) that are assembled in a dimer of heterotrimers [START_REF] Ermler | Crystal structure of methyl-coenzyme M reductase: the key enzyme of biological methane formation[END_REF][START_REF] Hahn | Crystal structure of a key enzyme for anaerobic ethane activation[END_REF]. The interface between the dimers forms the active site, which contains the Ni(I) F 430 cofactor that is essential for catalysis (117). About 30 genes are almost ubiquitous in archaea possessing

Mcr/Acr but are absent from other archaea [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF]. Some are involved in F 430 cofactor biosynthesis

CO 2 -Reducing Hydrogenotrophic Methanogenesis

The CO 2 -reducing hydrogenotrophic methanogenesis pathway is present mostly in Class I and Class II methanogens and can be divided into five central enzymatic steps (Figures 1b and2a) The CoM-SH and HS-CoB must be regenerated from CoM-S-S-CoB, and a ferredoxin (Fd) must be reduced to serve in the initial step of the H 4 MPT-MBWL pathway (Figures 1b and2a).

(
In most Class I and Class II methanogens, and possibly in "Ca. Nezhaarchaeota," this reaction is performed by the flavin-based electron-bifurcating HdrABC-MvhADG complex using two H 2 as electron donors [START_REF] Kaster | Coupling of ferredoxin and heterodisulfide reduction via electron bifurcation in hydrogenotrophic methanogenic archaea[END_REF]108). MvhA is a [NiFe] hydrogenase, HdrB is a CoM-S-S-CoB reductase, and HdrA contains the electron-bifurcating flavin and is responsible for Fd reduction. Using the electrochemical gradient, additional complexes (Eha, Ehb, Ech, and Mbh) can perform the exergonic reduction of Fd with H 2 to replenish Fd red removed from methanogenesis by biosynthetic pathways or imperfect coupling in electron bifurcation (60a). In Methanosarcina, the regeneration of CoM-SH and HS-CoB and the reduction of Fd rely instead on three membrane complexes [Vho (or Vht)/HdrDE/Ech] and methanophenazine, a membrane-soluble electron transporter [START_REF] Mand | Energy conservation and hydrogenase function in methanogenic archaea, in particular the genus Methanosarcina[END_REF]100). Vho (hydrogenase) and HdrDE (CoM-S-S-CoB reductase) reduce CoM-S-S-CoB using H 2 . Methanophenazine transfers the electrons between these two complexes. This exergonic reaction is associated with buildup of an electrochemical gradient that is used by the Ech complex to perform the endergonic reduction of Fd with H 2 (Figure 2a).

Finally, several methanogens without cytochromes use formate instead of H 2 and CO 2 (Supplemental Figure 2). FdhAB oxidizes formate into CO 2 and generates F 420 H 2 [START_REF] Baron | Reconstitution and properties of a coenzyme F420-mediated formate hydrogenlyase system in Methanobacterium formicicum[END_REF], both used by the H 4 MPT-MBWL. The reduction of Fd and CoM-S-S-CoB by formate is done by an electron-bifurcating FdhAB-MvhD-HdrABC complex (25). Other electron donors for CO 2 reduction have been described, such as ethanol, isopropanol, 2-butanol, and Fe 2+ (reviewed in 53).

Acetoclastic Methanogenesis

Present in Methanosarcinales (Class II methanogens), acetoclastic methanogenesis comprises four central enzymatic steps (Figures 1b and2b). 2b). This reaction is coupled to energy conservation by the buildup of the electrochemical gradient.

Methyl-Reducing Hydrogenotrophic Methanogenesis

The methyl-reducing hydrogenotrophic methanogenesis pathway is found across all Archaea [Diaforarchaea, Methanotecta, TACK, Acherontia (Figure 1c; Supplemental Table 1) and consists of two central enzymatic steps (Figures 1b and2c). (a) The methyl group (CH 3 -) of a substrate is first transferred to a corrinoid protein by a substrate-specific methyltransferase, MT1 (e.g., MtaBC) [START_REF] Kurth | Several ways one goal-methanogenesis from unconventional substrates[END_REF][START_REF] Söllinger | Methylotrophic methanogens everywhere-physiology and ecology of novel players in global methane cycling[END_REF], and then transferred to CoM-SH by a more generic methyltransferase, MT2 (e.g., MtaA) (Supplemental Table 3) Differently from CO 2 -reducing and acetoclastic methanogenesis, the Mtr complex is not involved in energy conservation. Instead, a large diversity of mechanisms to conserve energy is predicted among methyl-reducing methanogens relying on the direct or indirect reduction of CoM-S-S-CoB by H 2 (Figure 2c). In Methanomassiliicoccales, an HdrABC-MvhADG complex uses two H 2 to reduce CoM-S-S-CoB and Fd. The Fd red is then used to reduce another CoM-S-S-CoB by the membrane Fpo-l complex likely associated with HdrD, coupling this reaction with energy conservation by translocating H + outside the cell [START_REF] Kröninger | Energy conservation in the gut microbe Methanomassiliicoccus luminyensis is based on membranebound ferredoxin oxidation coupled to heterodisulfide reduction[END_REF]. A similar mechanism may exist in "Ca. Methanodesulfokores" ("Ca. Korarchaeota"), but HdrB might be replaced by HdrD in the Hdr-Mvh complex [START_REF] Mckay | Co-occurring genomic capacity for anaerobic methane and dissimilatory sulfur metabolisms discovered in the Korarchaeota[END_REF]. In Methanosphaera, "Ca. Methanofastidiosa," and "Ca. Nuwarchaeales, (NM3), an HdrABC-MvhADG complex also generates Fd red . In this case however, Fd red is used by the membrane complex Ehb to reduce 2H + , which is coupled to translocation of Na + outside the cell [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF][START_REF] Nobu | Chasing the elusive Euryarchaeota class WSA2: genomes reveal a uniquely fastidious methyl-reducing methanogen[END_REF]100). "Ca. Methanomethyliales," a proposed Ehd membrane complex (formed by HdrBC-Ech homologs) may directly reduce CoM-S-S-CoB with H 2 and couple this reaction to H + translocation in the extracellular space [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF]. In Methanosarcina and Methanonatronarchaeia (methanogens with cytochromes), CoM-S-S-CoB reduction by H 2 is performed by the Vho and HdrDE complexes [START_REF] Mand | Energy conservation and hydrogenase function in methanogenic archaea, in particular the genus Methanosarcina[END_REF][START_REF] Sorokin | Discovery of extremely halophilic, methyl-reducing euryarchaea provides insights into the evolutionary origin of methanogenesis[END_REF]. In Methanonatronarchaeia, formate can be used as an electron donor to reduce methanophenazine, with the Fdn complex replacing Vho.

Finally, the model of the pathway of Thaumarchaeota has not been fully resolved yet [START_REF] Hua | Insights into the ecological roles and evolution of methyl-coenzyme M reductase-containing hot spring Archaea[END_REF], but the taxonomic distribution of components and the literature suggest the use of a methanophenazine-based system involving HdrDE and a yet unknown reducer.

Methyl-Dismutating Methanogenesis

Methyl-dismutating methanogenesis is found only in Methanosarcinales (Figure 1). One methyl group is used as an electron donor to reduce three other methyl groups into methane [START_REF] Keltjens | Conversion of methanol and methylamines to methane and carbon dioxide[END_REF] in four main steps (Figure 2d).

Methoxyl-Dismutating Methanogenesis

Methoxydotrophic methanogenesis has been recently described in M. shengliensis , where methyl groups from various methoxylated coal compounds (R-O-CH 3 ) are dismutated into CO 2 and CH 4 (54, 67) (Figure 2e). This pathway resembles methyl-dismutating methanogenesis, but the methyl group from the substrate is transferred to H 4 MPT instead of CoM-SH, using the MtoABC methyltransferases/corrinoid protein (Supplemental Table 2). Thus, differently from methyldismutating methanogenesis, Mtr does not consume energy during methyl oxidation, and it conserves energy when the methyl is reduced into CH 4 . The methyl transfer to H 4 MPT thus brings thermodynamic efficiency to the overall reaction well above what is observed in other methanogens (and anaerobes) [START_REF] Kurth | Methanogenic archaea use a bacteria-like methyltransferase system to demethoxylate aromatic compounds[END_REF]. It was suggested that the cell decreases this efficiency by alternating the direction of the H 4 MPT-MBWL pathway, where part of the Fd red and F 420 H 2 would be used to reduce CO 2 instead of being used for energy conservation by the reduction of CoM-S-S-CoB [START_REF] Kurth | Methanogenic archaea use a bacteria-like methyltransferase system to demethoxylate aromatic compounds[END_REF], which is supported by the production of CH 4 from CO 2 during methoxydotrophic methanogenesis (67).

Methanotrophy

No isolates of ANME archaea are currently available; thus, most knowledge of how this metabolism works comes from field measurements, enrichment cultures, and genomic analyses [START_REF] Chadwick | Comparative genomics reveals electron transfer and syntrophic mechanisms differentiating methanotrophic and methanogenic archaea[END_REF][START_REF] Knittel | Anaerobic oxidation of methane: progress with an unknown process[END_REF][START_REF] Mcglynn | Energy metabolism during anaerobic methane oxidation in ANME archaea[END_REF]103). In this pathway, methane is oxidized into CO 2 using Mcr, Mtr, and the H 4 MPT-MBWL functioning in the reverse direction than in the CO 2 -reducing pathway (Figures 1 and3a SH, and CoB-SH (5, 71). The F 420 H 2 derived from H 4 MPT-MBWL and HdrABC-MvhD-FhdB can be used by either a membrane Fpo complex to reduce methanophenazine in ANME-2a and ANME-2c, or a membrane Fqo complex to reduce menaquinone in "Ca. Methanophagales" and "Ca. Methanoperedens." This reaction is coupled to energy conservation by generating a chemiosmotic gradient. In terrestrial ANME ("Ca. Methanoperedens," "Ca. Methanophagales" ANME-1-THS), reduced menaquinones transfer their electrons to different compounds. "Ca.

Methanoperedens" can reduce NO 3

 with NarGH/HCOII, NO 2  with Nrf, and Fe(III) and Mn(IV) using multi-heme cytochrome (MHC), which are nanowire-like proteins conducting electrons, and possibly a much wider range of electron acceptors [START_REF] Ettwig | Archaea catalyze irondependent anaerobic oxidation of methane[END_REF][START_REF] Haroon | Anaerobic oxidation of methane coupled to nitrate reduction in a novel archaeal lineage[END_REF][START_REF] Leu | Anaerobic methane oxidation coupled to manganese reduction by members of the Methanoperedenaceae[END_REF][START_REF] Lu | Cr(VI) reduction coupled with anaerobic oxidation of methane in a laboratory reactor[END_REF][START_REF] Luo | Microbial selenate reduction driven by a denitrifying anaerobic methane oxidation biofilm[END_REF]. "Ca.

Methanophagales" ANME-1-THS lacks MHC-VhoC but instead have a Psr-like protein, possibly able to reduce S 2 to H 2 S by using electrons from reduced menaquinone [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF]. In the other ANME lineages living in marine environments, electrons from reduced menaquinone/methanophenazine are then transferred to sulfate-reducing bacteria using MHC.

This process-called direct interspecific electron transfer (DIET)-has been supported by different approaches beyond the identification of MHC-coding genes [START_REF] Mcglynn | Single cell activity reveals direct electron transfer in methanotrophic consortia[END_REF]113). As an alternative to DIET, it was proposed that soluble electron carriers such as H 2 , formate (76), zero-valent sulfur [START_REF] Milucka | Zero-valent sulphur is a key intermediate in marine methane oxidation[END_REF], or methyl sulfide (75) could bring more energy to the syntrophic partner, but there is a lack of experimental evidence for this. It was also suggested that both DIET and a lowpotential soluble electron transporters could be used during syntrophy so that both methanotrophs and SRB obtain sufficient energy for their growth [START_REF] Chadwick | Comparative genomics reveals electron transfer and syntrophic mechanisms differentiating methanotrophic and methanogenic archaea[END_REF].

Alkanotrophy

The oxidation of short-chain alkanes for energy production based on Acr has been recently described [START_REF] Chen | Anaerobic oxidation of ethane by archaea from a marine hydrocarbon seep[END_REF][START_REF] Hahn | Candidatus Ethanoperedens," a thermophilic genus of archaea mediating the anaerobic oxidation of ethane[END_REF][START_REF] Hahn | Crystal structure of a key enzyme for anaerobic ethane activation[END_REF][START_REF] Laso-Pérez | Thermophilic archaea activate butane via alkyl-coenzyme M formation[END_REF] and inferred in a growing number of lineages (Figures 1 and3b).

Enrichment cultures have been obtained only for "Ca. Syntropharchaeales" and "Ca.

Argoarchaeum"/ "Ca. Ethanoperedens." In all archaea having this metabolism, the alkane is oxidized into alkyl-CoM (e.g., butane  butyl-CoM) by Acr [START_REF] Chen | Anaerobic oxidation of ethane by archaea from a marine hydrocarbon seep[END_REF][START_REF] Hahn | Candidatus Ethanoperedens," a thermophilic genus of archaea mediating the anaerobic oxidation of ethane[END_REF][START_REF] Hahn | Crystal structure of a key enzyme for anaerobic ethane activation[END_REF][START_REF] Laso-Pérez | Thermophilic archaea activate butane via alkyl-coenzyme M formation[END_REF]. Then, the alkyl is oxidized into acyl and transferred to CoA (e.g., butyl-CoM  butyryl-CoA) by unknown enzymes, for which candidates have been suggested [START_REF] Hahn | Candidatus Ethanoperedens," a thermophilic genus of archaea mediating the anaerobic oxidation of ethane[END_REF][START_REF] Laso-Pérez | Anaerobic degradation of non-methane alkanes by "Candidatus Methanoliparia" in hydrocarbon seeps of the Gulf of Mexico[END_REF][START_REF] Laso-Pérez | Thermophilic archaea activate butane via alkyl-coenzyme M formation[END_REF]. In ethane-oxidizing "Ca.

Argoarchaeum" and "Ca. Ethanoperedens", these enzymes generate acetyl-CoA from ethyl-CoM [START_REF] Chen | Anaerobic oxidation of ethane by archaea from a marine hydrocarbon seep[END_REF][START_REF] Hahn | Candidatus Ethanoperedens," a thermophilic genus of archaea mediating the anaerobic oxidation of ethane[END_REF] NADH, and Fd red , and its coupling with energy conservation, in "Ca. Syntropharchaeales" and "Ca. Argoarchaeum"/"Ca. Ethanoperedens" is similar with that in ANME. It may in fact involve HdrABC-MvhD-FhdB and Fqo complexes but also MHC-mediated DIET to sulfate-reducing bacteria [START_REF] Chen | Anaerobic oxidation of ethane by archaea from a marine hydrocarbon seep[END_REF][START_REF] Hahn | Candidatus Ethanoperedens," a thermophilic genus of archaea mediating the anaerobic oxidation of ethane[END_REF][START_REF] Laso-Pérez | Thermophilic archaea activate butane via alkyl-coenzyme M formation[END_REF]. All other lineages are missing one or several of these complexes, but they all encode a [NiFe]-hydrogenase (Mvh). Such a hydrogenase has been reported in "Ca.

Helarchaeota" [START_REF] Seitz | Asgard archaea capable of anaerobic hydrocarbon cycling[END_REF]119), suggesting that electrons from alkane oxidation can be transferred via H 2 to a syntrophic partner that remains unknown because no enrichment culture is available.

Alkanotrophic Methanogenesis

It was recently revealed that alkanotrophy can be coupled to methanogenesis in "Ca.

Methanoliparia" (13, 55, 121) (Figure 3c). A range of long-chain alkanes (more than 13 carbons), as well as alkylcyclohexanes and alkylbenzenes, can be used by "Ca. Methanoliparia."

This pathway is similar to other alkanotrophic pathways, up to the generation of CO [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF][START_REF] Laso-Pérez | Anaerobic degradation of non-methane alkanes by "Candidatus Methanoliparia" in hydrocarbon seeps of the Gulf of Mexico[END_REF]. This discovery changes the long-standing paradigm on the division of labor between bacteria and archaea for the methanogenic degradation of complex molecules. Many aspects of this novel metabolism remain to be elucidated, including the complexes involved in electron cycling [possibly Rnf, HdrABC-MvhD-GltD-like protein, HoxEF-FrhB, NfnAB [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF][START_REF] Laso-Pérez | Anaerobic degradation of non-methane alkanes by "Candidatus Methanoliparia" in hydrocarbon seeps of the Gulf of Mexico[END_REF]].

EVOLUTION OF METHANOGENESIS AND METHANE-RELATED METABOLISMS

Methane-related pathways involve many enzymatic complexes that display high variability among archaea. Each complex is encoded by conserved genomic clusters, suggesting coevolution [START_REF] Adam | Evolutionary history of carbon monoxide dehydrogenase/acetyl-CoA synthase, one of the oldest enzymatic complexes[END_REF][START_REF] Adam | An archaeal origin of the Wood-Ljungdahl H 4 MPT branch and the emergence of bacterial methylotrophy[END_REF][START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF]. The wide but patchy taxonomic distribution of methane-related enzymes suggests both a deep origin and a complex evolutionary history during archaeal diversification.

Several analyses have been recently carried out to decipher the origin and evolution of methanogenesis and more broadly of methane-related pathways in Archaea (2, 3, 6, 10, 12-14, 31, 33, 45, 60, 111, 116).

When Did Methanogenesis Originate?

Since Mcr is the only known complex directly involved in methane production, most studies addressing the evolution of methanogenesis rely on the phylogeny of one of its subunits (McrA) or a concatenation of the three (McrABG). An early study showed that Mcr sequences form two distinct clades corresponding to Class I and Class II methanogens, leading to the conclusion that Mcr originated in the Euryarchaeota and was then inherited vertically [START_REF] Bapteste | Higher-level classification of the Archaea: evolution of methanogenesis and methanogens[END_REF]. More recently, culture-based and metagenomic-based analyses have uncovered Mcr homologs involved in methanogenesis, methanotrophy, and alkanotrophy (Acr) in a large number of novel lineages across the whole tree of Archaea, enriching the corresponding phylogeny [START_REF] Berghuis | Hydrogenotrophic methanogenesis in archaeal phylum Verstraetearchaeota reveals the shared ancestry of all methanogens[END_REF][START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF][START_REF] Borrel | Phylogenomic data support a seventh order of methylotrophic methanogens and provide insights into the evolution of methanogenesis[END_REF][START_REF] Boyd | Divergent methylcoenzyme M reductase genes in a deep-subseafloor Archaeoglobi[END_REF][START_REF] Evans | Methane metabolism in the archaeal phylum Bathyarchaeota revealed by genome-centric metagenomics[END_REF][START_REF] Hua | Insights into the ecological roles and evolution of methyl-coenzyme M reductase-containing hot spring Archaea[END_REF][START_REF] Liu | Genomic and transcriptomic evidence supports methane metabolism in Archaeoglobi[END_REF][START_REF] Nobu | Chasing the elusive Euryarchaeota class WSA2: genomes reveal a uniquely fastidious methyl-reducing methanogen[END_REF][START_REF] Sorokin | Discovery of extremely halophilic, methyl-reducing euryarchaea provides insights into the evolutionary origin of methanogenesis[END_REF]105,109,111). A consensus of these analyses is shown in Figure 4a. Currently, Mcr sequences cluster into four main groups, each corresponding to a type of methane metabolism: Group I is mainly linked to CO 2 -reducing methanogenesis and groups II and III to methylreducing methanogenesis, and group IV (Acr) is associated with alkanotrophy (Figure 4a). Some clades remain largely consistent with the archaeal phylogeny, notably Class I and II methanogens, and the TACK, implying that Mcr was present at least in the common ancestor of these clades [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF]111) (Figure 4c). Some clear incongruences in groups II and IV suggest the occurrence of horizontal gene transfer (HGT) events. Moreover, the deepest relationships are not well resolved, probably due to the lack of phylogenetic signal of single-gene trees at such taxonomic depth. For example, some studies have supported the monophyly of group II and III Mcr sequences (31) while others have not [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF]111). This makes it difficult to trace back with certainty the origin of the Mcr complex, and consequently of methane-related metabolisms in the Archaea. Moreover, interpretation of the Mcr tree strongly depends on where the root of the archaeal reference phylogeny lies, and especially the placement of the DPANN clade ("Ca.

Diapherotrites," "Ca. Parvarchaeota," "Ca. Aenigmarchaeota," "Ca. Nanohaloarchaeota," and "Ca. Nanoarchaeota"). Some studies have proposed that DPANN are placed at the base of the archaeal tree, which would exclude an ancestral presence of methanogenesis in the last common ancestor of Archaea (LACA), as the DPANN lack the Mcr complex (Figure 1c). Alternatively, the DPANN are episymbionts with drastically reduced metabolic capacities [START_REF] Castelle | Biosynthetic capacity, metabolic variety and unusual biology in the CPR and DPANN radiations[END_REF], and so the absence of Mcr may also be due to secondary loss. It has been proposed that the deep emergence of the DPANN might be a tree reconstruction artifact caused by their fast evolutionary rate and that they would have in fact emerged later (1a, 81). Under this scenario, Mcr would be inferred as present in the LACA and consequently methanogenesis would be an ancestral trait in Archaea (Figure 4c). This would fit with very early geological evidence of biological methane (3.5 Ga) (104) as well as molecular dating (111,116). 115) and (bottom) Raymann et al [START_REF] Raymann | The two-domain tree of life is linked to a new root for the Archaea[END_REF]. Abbreviations: ANME, anaerobic methanotrophs.

Finally, the emergence of Acr is still unclear, as the clustering of the corresponding sequences in the phylogeny might be an artifact due to their high divergence following independent functional shifts from Mcr. Alternatively, Acr may have emerged from a duplication of mcrABG genes at the base of the "Ca. Syntropharchaeia" or Methanotecta and subsequently been transferred multiple times by HGT [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF]111).

What Is the Ancestral Type of Methanogenesis?

Despite current evidence for a likely early origin of the Mcr complex, the nature of the first type of methane metabolism is still unsettled. Based on the wide distribution of CO 2 -reducing and methyl-reducing methanogenesis in the Archaea, the question mostly centers on which of these two types is ancestral to all present-day methanogens [START_REF] Berghuis | Hydrogenotrophic methanogenesis in archaeal phylum Verstraetearchaeota reveals the shared ancestry of all methanogens[END_REF][START_REF] Borrel | Methanogenesis and the Wood-Ljungdahl pathway: an ancient, versatile, and fragile association[END_REF][START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF]111). For this, the analysis of additional enzymes involved in either of these two metabolisms is key.

CO 2 -reducing methanogenesis first?

CO 2 -reducing methanogenesis involves the enzymes of the H 4 MPT-MBWL pathway, which are linked to Mcr by the Mtr complex (Figure 1). Bapteste et al. [START_REF] Bapteste | Higher-level classification of the Archaea: evolution of methanogenesis and methanogens[END_REF] proposed that in addition to Mcr, the H 4 MPT-MBWL pathway and Mtr were also vertically inherited from the last common ancestor of Class I and Class II methanogens. Recent phylogenic analyses including novel lineages confirmed that the H 4 MPT-MBWL pathway is ancestral in Archaea and evolved vertically [START_REF] Adam | An archaeal origin of the Wood-Ljungdahl H 4 MPT branch and the emergence of bacterial methylotrophy[END_REF]115). Combined with the inference of a CBWL pathway (Cdh) in the last universal common ancestor [START_REF] Adam | Evolutionary history of carbon monoxide dehydrogenase/acetyl-CoA synthase, one of the oldest enzymatic complexes[END_REF], this implies that the LACA had a complete Wood-Ljungdahl pathway, a strong argument in favor of CO 2 -reducing methanogenesis being the first type of methanogenesis. However, the Wood-Ljungdahl pathway can work independently of methanogenesis [e.g., for CO 2 fixation, oxidation of acetyl-CoA produced by various catabolic pathways (50)], and several nonmethanogen lineages encode Wood-Ljungdahl pathway genes (3). Thus, presence of both Mcr and Wood-Ljungdahl pathway enzymes in the LACA does not directly imply ability for CO 2 -reducing methanogenesis. The origin of the Mtr complex is therefore of fundamental importance.

The most recent phylogeny of Mtr including sequences from TACK methanogens ("Ca.

Methanohydrogenales"/"Ca. Nezhaarchaeota" and "Ca. Bathyarchaeota") shows that Mtr was acquired horizontally in separate events from Class I/II methanogens (111) (Figure 4b). The authors thus proposed that Mtr emerged within Euryarchaeota. Nevertheless, another analysis with similar datasets reached opposite conclusions (present in the LACA) (4). This divergence is due to the uncertainties on the position of the root of the archaeal tree. Indeed, two different roots have been proposed, one between the TACK and Euryarchaeota, and the other within Euryarchaeota (84, 115) (Figure 4c). Therefore, the answer to the question of whether Mtr-and consequently CO 2 -reducing methanogenesis-was present in the ancestor of all methanogens strongly relies upon future analyses aimed at robustly resolving the root of the archaeal phylogeny.

Methyl-reducing methanogenesis first?

Another candidate for the ancestral metabolism in Archaea is methyl-reducing methanogenesis.

An early phylogenetic study of some of the methyltransferases and corrinoid proteins showed a clear monophyly of Class I and Class II, suggesting an ancestral presence in Archaea [START_REF] Borrel | Phylogenomic data support a seventh order of methylotrophic methanogens and provide insights into the evolution of methanogenesis[END_REF].

However, the discovery of this type of metabolism in a growing number of TACK members [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF][START_REF] Borrel | Phylogenomic data support a seventh order of methylotrophic methanogens and provide insights into the evolution of methanogenesis[END_REF][START_REF] Mckay | Co-occurring genomic capacity for anaerobic methane and dissimilatory sulfur metabolisms discovered in the Korarchaeota[END_REF][START_REF] Nobu | Chasing the elusive Euryarchaeota class WSA2: genomes reveal a uniquely fastidious methyl-reducing methanogen[END_REF][START_REF] Söllinger | Methylotrophic methanogens everywhere-physiology and ecology of novel players in global methane cycling[END_REF][START_REF] Sorokin | Discovery of extremely halophilic, methyl-reducing euryarchaea provides insights into the evolutionary origin of methanogenesis[END_REF]105), combined with their monophyly in Mcr trees (Figure 4a), has reopened the issue. A recent phylogenetic analysis of the methyltransferases that transfer a methyl group from a corrinoid protein to CoM (MT2, i.e., MtaA, MtbA, and MtsA) concluded that these enzymes were likely present in the last common ancestor of the TACK and Euryarchaeota and, by extension, that methyl-reducing methanogenesis emerged early (111).

However, the evolutionary scenario of methyl-reducing metabolism might be much more complex. First, MT2 are part of very large protein families [START_REF] Kurth | Methanogenic archaea use a bacteria-like methyltransferase system to demethoxylate aromatic compounds[END_REF] and the associated phylogenies are difficult to infer and interpret reliably. Second, group II of the Mcr phylogeny includes methyl-reducing archaea from a mix of phylogenetically unrelated taxa, indicating potential acquisition of this metabolism by HGTs in these clades (Figure 4a). Methyl-reducing methanogenesis could be more easily transferred than other types of methanogenesis, as it relies on only two components (Mcr and methyltransferases) that are adaptable to various energy conservation strategies (Figure 2). Moreover, most core methanogenesis genes are grouped in a unique gene cluster in some of these archaea [START_REF] Borrel | Comparative genomics highlights the unique biology of Methanomassiliicoccales, a Thermoplasmatales-related seventh order of methanogenic archaea that encodes pyrrolysine[END_REF] and could be transferred at once. Supporting a late emergence, it has been recently proposed that methyl-reducing methanogenesis arose several times independently from other types of methanogenesis, in environments where it could confer a competitive advantage (102). This is the example of Methanosphaera and Methanimicrococcus, two genera that are present almost exclusively in the animal gut and can only obtain energy through methyl-reducing methanogenesis, differently from their closely related, non-host-associated relatives [START_REF] Hoedt | Culture-and metagenomics-enabled analyses of the Methanosphaera genus reveals their monophyletic origin and differentiation according to genome size[END_REF][START_REF] Miller | Methanosphaera stadtmaniae gen. nov., sp. nov.: a species that forms methane by reducing methanol with hydrogen[END_REF][START_REF] Sprenger | Methanomicrococcus blatticola gen. nov., sp. nov., a methanol-and methylamine-reducing methanogen from the hindgut of the cockroach Periplaneta americana[END_REF]102) (Figure 5a). Therefore, specialization in methyl-reducing methanogenesis likely occurred during adaptation to the gut environment (102). Indeed, the intestinal microbiome seems particularly propitious for this type of metabolism, as the methyl-reducing methanogens regularly constitute 10-100% of gut methanogens (101), whereas they are often less than 10% in open environments [START_REF] Cozannet | New insights into the ecology and physiology of Methanomassiliicoccales from terrestrial and aquatic environments[END_REF]. In Methanosphaera, methyl-reducing methanogenesis likely emerged from CO 2 -reducing methanogenesis through loss of a few genes involved in the synthesis of a cofactor (molybdopterin) of the Fwd/Fmd complex [START_REF] Fricke | The genome sequence of Methanosphaera stadtmanae reveals why this human intestinal archaeon is restricted to methanol and H 2 for methane formation and ATP synthesis[END_REF]. In contrast, in Methanimicrococcus, methylreducing methanogenesis likely emerged from methyl-dismutating methanogenesis through the loss of most of the enzymes of the H 4 MPT-MBWL pathway (102). Whether similar transitions toward rich environmental niches led to the very first emergence of methyl-reducing methanogenesis in earlier archaeal lineages remains to be studied further.

Origin and Evolution of Other Mcr-Associated Metabolisms

Another crucial issue is represented by the multiple transitions that led to the emergence of a wide diversity of substrates and methane-related pathways associated with the Mcr enzymatic complex (Figures 1 and5a). The wide phylogenetic distribution of these pathways involving Mcr or Acr (Figure 1) strongly suggests that they emerged relatively recently, possibly enabled by HGTs from bacteria or among archaea.

A burst of transitions within the Methanosarcinales.

Most orders of methanogens are extremely homogeneous in the type of methane metabolism they use, being composed of either only CO 2 -reducing or methyl-reducing members (Figure 1).

One notable exception is Methanosarcinales, which display all main types of methane metabolisms as well as ethane oxidation (Figures 1 and5b). In association with Mtr and the Wood-Ljungdahl pathway, the cytochromes and membrane-soluble electron transporters constitute a versatile platform for electron transfer that is unique to this order and may have favored such diversification. Despite this large metabolic diversity, the majority of Methanosarcinales are either methyl-dismutating methanogens or anaerobic methanotrophs (Figure 5b), likely corresponding to the most ancient metabolisms in this clade. The presence of methyl-dismutating methanogens in basal (Methermicoccus) and crown (Methanosarcinaceae) lineages suggests that this metabolism may have emerged first in Methanosarcinales.

Irrespective of the original type of methane metabolism in Methanosarcinales, transitions between methyl-dismutating methanogenesis and anaerobic methanotrophy may have occurred multiple times in this order (Figure 5a,b), possibly facilitated by the environmental and metabolic relatedness of these two metabolisms. Indeed, both can thrive in marine sediments in the presence of sulfate: Most methanotrophic archaea are syntrophic partners of sulfate-reducing bacteria [START_REF] Knittel | Anaerobic oxidation of methane: progress with an unknown process[END_REF], and methyl-dismutating methanogens do not compete with sulfate-reducing bacteria for methyl-compound utilization, in contrast to other types of methanogens that are outcompeted for hydrogen and acetate [START_REF] Oremland | Methanogenesis and sulfate reduction: competitive and noncompetitive substrates in estuarine sediments[END_REF]. Moreover, in both methyl-dismutating methanogenesis and anaerobic methanotrophy, the Mtr complex and H 4 MPT-MBWL pathway function in the oxidative direction, and most enzymatic complexes involved in methanotrophy are also involved in methyl-dismutating methanogenesis (Figure 1).

If both methyl-dismutating methanogenesis and anaerobic methanotrophy are ancient metabolisms in the Methanosarcinales, it is likely that acetoclastic methanogenesis, methoxyldismutating methanogenesis [START_REF] Kurth | Methanogenic archaea use a bacteria-like methyltransferase system to demethoxylate aromatic compounds[END_REF], and ethane oxidation [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF][START_REF] Chen | Anaerobic oxidation of ethane by archaea from a marine hydrocarbon seep[END_REF][START_REF] Hahn | Candidatus Ethanoperedens," a thermophilic genus of archaea mediating the anaerobic oxidation of ethane[END_REF] emerged more recently. The late emergence of these metabolisms is consistent with the fact that they are present only in Methanosarcinales (Figure 1). Supporting this hypothesis, several HGTs potentially linked to these metabolic shifts have been identified. For example, the genes involved in methoxyldismutating methanogenesis in M. shengliensis were acquired from bacteria [START_REF] Kurth | Methanogenic archaea use a bacteria-like methyltransferase system to demethoxylate aromatic compounds[END_REF]. Similarly, the phosphoacetyl-transferase (pta) and acetate kinase (ackA) genes involved in acetoclastic methanogenesis in Methanosarcina were acquired from Clostridiales around 240 ± 41 Ma [START_REF] Fournier | Evolution of acetoclastic methanogenesis in Methanosarcina via horizontal gene transfer from cellulolytic Clostridia[END_REF][START_REF] Rothman | Methanogenic burst in the end-Permian carbon cycle[END_REF]. The acquisition of acetoclastic methanogenesis by Methanosarcina, together with the increased availability of nickel (a limiting factor for methanogens) due to volcanism, is thought to have played a role in the end-Permian extinction that occurred in the same period [START_REF] Rothman | Methanogenic burst in the end-Permian carbon cycle[END_REF].

The exceptional diversification of the possible electron acceptors for methanotrophy in "Ca.

Methanoperedens" (ANME-2d) may also be the result of multiple HGTs [START_REF] Haroon | Anaerobic oxidation of methane coupled to nitrate reduction in a novel archaeal lineage[END_REF][START_REF] Leu | Lateral gene transfer drives metabolic flexibility in the anaerobic methane-oxidizing archaeal family Methanoperedenaceae[END_REF]. Transfers from bacteria occurred for narGH genes needed for nitrate reduction (41), several molybdopterin oxidoreductase genes for reduction of other nonmetallic electron acceptors, and several menaquinone:cytochrome c oxidoreductases, as well as some of the MHC genes for the reduction of Fe(III), Mn(IV), or humic acids [START_REF] Leu | Lateral gene transfer drives metabolic flexibility in the anaerobic methane-oxidizing archaeal family Methanoperedenaceae[END_REF].

Finally, a potential HGT of Ecr to "Ca. Argoarchaeum"/"Ca. Ethanoperedens" (GoM-Arc1) was likely responsible for a shift from methanotrophy to ethane oxidation in this lineage (Figure 5a). This transition from methanotrophy to ethane oxidation was inferred on the basis of the emergence of "Ca. Argoarchaeum"/"Ca. Ethanoperedens" within a clade consisting solely of methanotrophs [i.e., ANME-2d "Ca. Methanoperedens," ANME-2a "Ca. Methanocomedens," and ANME-2b "Ca. Methanomarinus" (13) (Figure 5b)], and may have been eased by the very similar mode of energy conservation between these ethane and methane oxidizers (Figure 3).

Emergence of methane/multicarbon alkane metabolisms in the other archaeal lineages.

The close phylogenetic relationship between anaerobic methanotrophs and short-chain alkane oxidizers is not unique to the Methanosarcinales but is also observed within the "Ca.

Syntropharchaeia" (Figure 5c), suggesting that transitions between these two metabolisms happened more than once. However, here the transition occurred from short-chain alkane oxidation to methanotrophy, i.e., in the opposite direction than in the Methanosarcinales (Figure 5a). Two arguments support this hypothesis. First, the methanotrophic "Ca. Methanophagales" are part of a clade composed of only short-chain alkane oxidizers (111) (Figure 5c). Second, "Ca. Methanophagales" acquired their mcrABG genes by HGT from methyl-reducing methanogens belonging to the Acherontia (Figure 4a) and likely replaced the acrABG genes initially present to perform methanotrophy [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF].

Another interesting and complex case of transition between methane/multicarbon alkane metabolisms concerns the Archaeoglobales. This order is closely related to several lineages of methanogens/methanotrophs and until recently was thought to be exclusively composed of nonmethanogens. The H 4 MPT-MBWL pathway and some Mcr/Acr-associated markers in these archaea were interpreted as remnants of past methane metabolism [START_REF] Bapteste | Higher-level classification of the Archaea: evolution of methanogenesis and methanogens[END_REF][START_REF] Borrel | Methanogenesis and the Wood-Ljungdahl pathway: an ancient, versatile, and fragile association[END_REF][START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF]. Surprisingly, recent data have now shown that several members of this class have more than these remnants; several MAGs belonging to "Ca. Methanomixophus" encode, in fact, both Mcr and Mtr complexes, and it has been proposed that they are able to perform CO 2 -reducing and/or methylreducing methanogenesis and/or methanotrophy [START_REF] Colman | Mixing of meteoric and geothermal fluids supports hyperdiverse chemosynthetic hydrothermal communities[END_REF][START_REF] Liu | Genomic and transcriptomic evidence supports methane metabolism in Archaeoglobi[END_REF]109). It was inferred that "Ca.

Methanomixophus" acquired its Mcr by HGT, implying a loss in the last common ancestor of Archaeoglobales and a later reacquisition [START_REF] Liu | Genomic and transcriptomic evidence supports methane metabolism in Archaeoglobi[END_REF]. The initial loss of methanogenesis at the base of this class may have been triggered by the acquisition of bacterial genes involved in sulfite reduction [dsrAB [START_REF] Klein | Multiple lateral transfers of dissimilatory sulfite reductase genes between major lineages of sulfate-reducing prokaryotes[END_REF]]. Interestingly, the Mtr complex appears to have been vertically inherited in "Ca. Methanomixophus." The role of this Mtr in the absence of Mcr (before its reacquisition) is unknown, but several "Ca. Bathyarchaeota" genomes do code for Mtr and not Mcr [START_REF] He | Genomic and enzymatic evidence for acetogenesis among multiple lineages of the archaeal phylum Bathyarchaeota widespread in marine sediments[END_REF], suggesting that this complex may be used in non-methanogenic pathways. Despite the close phylogenetic relationship with other lineages of methanogens and methanotrophs and the presence of many genes involved in these metabolisms, the evolutionary history of methane metabolisms in the Archaeoglobales remains unclear because metabolic pathways are only partially resolved. However, they represent an interesting model to define metabolic transitions associated with gains and losses of genes of methane metabolisms.

OUTLOOK AND CONCLUSIONS

The field of archaeal methanogenesis is perhaps among those that have witnessed the largest growth over the last decade. Huge knowledge gaps have been filled by the discovery of a wealth of new lineages with the genetic potential for methane-related metabolisms in poorly explored anaerobic niches such as deep sediments. The large majority of these lineages remain uncultured, and our knowledge of their metabolic potential is therefore based uniquely on sequence analysis.

Nevertheless, the validity of such inferences [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF][START_REF] Laso-Pérez | Anaerobic degradation of non-methane alkanes by "Candidatus Methanoliparia" in hydrocarbon seeps of the Gulf of Mexico[END_REF] has already been shown by first members of these lineages to be characterized, such as "Ca. Methanoliparia" (121) and "Ca.

Argoarchaeum"/ "Ca. Ethanoperedens" [START_REF] Chen | Anaerobic oxidation of ethane by archaea from a marine hydrocarbon seep[END_REF][START_REF] Hahn | Candidatus Ethanoperedens," a thermophilic genus of archaea mediating the anaerobic oxidation of ethane[END_REF]. As a matter of fact, metabolic reconstructions based on MAGs have helped guide these experimental studies. Future efforts should be placed on the isolation and functional analysis of additional members of these lineages, as well as understanding their roles in the environment.

Given the huge impact of methane-related metabolisms in the history of Earth up to the present day, understanding the complex evolutionary trajectories that have led to such huge diversity is of paramount importance. Recent phylogenetic studies strongly suggest that methanogenesis-and more broadly, methane-associated-pathways are very ancient, some likely dating back to the LACA. This implies that the current diversity of archaea may stem from loss or tinkering of such ancestral methane metabolisms. The multiple independent losses of methane metabolisms are thus key transitions in the evolution of Archaea, as they were the starting points of the colonization of a wide range of niches [START_REF] Borrel | Methanogenesis and the Wood-Ljungdahl pathway: an ancient, versatile, and fragile association[END_REF]. However, no consensus has yet been reached on the evolutionary history of these metabolisms. Its resolution in fact strongly depends on our ability to analyze such ancient events and to interpret the resulting data. One priority will surely be that of correctly placing the root of the archaeal phylogeny, as this is key to inferring the point of origin and the nature of the most ancestral methanogenesis pathway.

Nevertheless, analysis of available data has already started providing important pieces of information. For example, the hypothesis is gaining traction that at least anaerobic methanotrophy emerged late and multiple times independently in the Archaea, possibly triggered by the large availability of both methane and inorganic electron acceptors during the early Paleoproterozoic [START_REF] Catling | Anaerobic methanotrophy and the rise of atmospheric oxygen[END_REF]. These events could have contributed to the drop in methane in the atmosphere that caused the first major Earth glaciation event (112).

We are still far from understanding the huge complexity of methane-related pathways and their components. For example, the diversity of methane-related pathways does not concern only core enzymes but also the ion transporters responsible for re-reduction/reoxidation of cofactors/ferredoxins and conservation of energy. These protein complexes are of key importance in methane-related pathways, but their evolutionary histories and functions have not been thoroughly studied. This lack of information precludes a global view of the evolution of methanogenesis in Archaea and represents a priority of future studies. It is also a great methodological challenge given the patchy taxonomic distribution of these proteins, which

Figure 1 (

 1 Figure 1 (a) Nomenclature of different types of methanogenesis, depending on the carbon and electron sources. (b) Currently known methane-related pathways. Major metabolites are boxed, and carbon groups are indicated in bold. The asterisk with Mt indicates different methyltransferases (Supplemental Tables1 and 2). (c) Taxonomic distribution of methane-related pathways across the reference phylogeny of Archaea. Colored squares at the tips of branches correspond to the presence of each type of metabolism. The proportions of genomes of each taxon coding for main components of the pathways are indicated by color gradient (0%, 1-25%, 26-50%, 51-75%, 76-100%). The different colors correspond to functional categories. The analysis was conducted on 832 archaeal genomes, and the presence of complexes or pathways was determined using MacSyFinder (1) (Supplemental Table3). Because MHC is part of a large protein family, the average number of homologs per genome (identified by proteins containing at least two CxxCH motifs) is indicated (minimum, 0.0; maximum, 17.0). Abbreviations: ANME, anaerobic methanotrophs; Acr, alkyl-Coenzyme M reductase complex; ß-oxidation, ß-oxidation pathway; CBWL, carbonyl-branch of the Wood-Ljungdahl pathway; CoA, coenzyme A; CoB, coenzyme B; CoM, coenzyme M; DPANN, "Ca. Diapherotrites," "Ca. Parvarchaeota," "Ca. Aenigmarchaeota," "Ca. Nanohaloarchaeota," and "Ca. Nanoarchaeota"; F 420 , F 420 cofactor (F 420 H 2 when reduced); Fd, ferredoxin (Fd red , reduced and Fd ox , oxidized);

Figure 2

 2 Figure 2 Diversity of mechanisms for regeneration of oxidoreduction states of electron transporters in (a) CO 2 -reducing hydrogenotrophic methanogenesis, (b) acetoclastic methanogenesis, (c) methyl-reducing hydrogenotrophic methanogenesis, (d) methyl-dismutating methanogenesis, and (e) methoxyl-dismutating methanogenesis. Circles correspond to proteins and protein complexes and arrows to reactions. The color of each arrow corresponds to the type of biochemical reaction. The color of each circle indicates cellular localization. Enzymes of the MBWL and CBWL pathways are underlined. The steps that are not yet resolved are indicated by question marks. Names in blue are high-rank taxonomic groups, as in Figure 1b. Ftr/Mch, Mtd/Mer, and Pta/Ack have been grouped together for brevity but are not known to form a

[

  CfbA-E (74, 120)], Mcr/Acr activation [AtwA and possibly McrC (82)], or posttranslational modification of amino acids in the Mcr catalytic site [McmA (77), MamA (27, 65, 83), YcaO/TfuA (78)]. Others have an unknown function but may be very important for Mcr/Acr functioning, such as the 6 genes that form a unique genomic cluster conserved in most Mcr/Acrbearing archaea (13).

  reviewed in 89). (a) CO 2 is reduced into formyl by a reduced ferredoxin (Fd red ) and bound to a methanofuran (MFR) by FwdABCDE(FGH) to produce MFR-CHO (11, 106). (b) The formyl group is then transferred from methanofuran to tetrahydromethanopterin (H 4 MPT) by Ftr. (c) The formyl bound to H 4 MPT is successively reduced into methenyl, methylene, and methyl by Mch, Mtd, and Mer (see Terms and definitions sections), leading to H 4 MPT-CH 3 . The reduced F 420 cofactor (F 420 H 2 ) is the electron donor for the reactions performed by Mtd and Mer, and its regeneration is performed by the FrhABG hydrogenase complex using H 2 as an electron donor (99). (d) The methyl bound to H 4 MPT is transferred to CoM-SH by the Mtr complex (MtrABCDEFGH), which couples the exergonic (ΔG°′ = 30 kJ/mol) transfer to the export of Na + ions across the membrane, producing an electrochemical gradient that is used by the ATP synthase (36, 107). (e) Finally, CoM-S-CH 3 is reduced by HS-CoB in Mcr, producing CoM-S-S-CoB and CH 4 .

  (a) Acetate is first converted into acetyl-CoA, either by the low-affinity/high-activity AckA and Pta enzymes [e.g., Methanosarcina (58)] or by the high-affinity/low-activity Acs enzyme [e.g., Methanosaetaceae (9)]. Both systems require ATP. (b) The Cdh complex of the carbonyl branch of the Wood-Ljungdahl pathway (CBWL) converts acetyl-CoA into CO 2 and H 4 MPT-CH 3 and reduces one Fd. The methyl group bound to H 4 MPT is then (c) transferred to CoM-SH by Mtr (conserving energy) and (d) converted into CoM-S-S-CoB and CH 4 by Mcr. Depending on the species, different sets of complexes can reduce CoM-S-S-CoB with the Fd red generated by the CBWL pathway (Ech/Vho/HdrDE in Methanosarcina mazei, Rnf/HdrDE in Methanosarcina acetivorans, Fpo-I/HdrDE in Methanosaetaceae) (114) (Figure

  . (b) Mcr catalyzes the conversion of CoM-CH 3 and SH-CoB into CoM-S-S-CoB and CH 4 .

  (a) The methyl group (CH 3 -) of a substrate is transferred to CoM-SH by two methyltransferases, similar to what occurs in the methyl-reducing methanogenesis, as described above. (b) Then, one methyl group is oxidized into CO 2 using Mtr and the H 4 MPT-MBWL pathway in the reverse direction than in CO 2 -reducing methanogenesis. In this direction, methyl transfer by Mtr is energy-consuming (Na + translocated inside the cell) and the reactions of the H 4 MPT-MBWL pathway reduce two F 420 and one Fd. (c) Depending on the Methanosarcina species, the conservation of energy by generation of an electrochemical gradient can be achieved by two alternative sets of membrane complexes [HdrDE/Fpo/Rnf or HdrDE/Vho/Fpo (95)] reducing three CoM-S-S-CoB with two F 420 H 2 and one Fd red . (d) The three HS-CoB released from these reactions are used to reduce three CoM-CH 3 into CH 4 .

Figure 3

 3 Figure 3 Diversity of mechanisms for regeneration of oxidoreduction states of electron transporters in (a) methanotrophy, (b) alkanotrophy, and (c) alkanotrophic methanogenesis. Circles correspond to proteins and protein complexes and arrows to reactions. The color of each

Figure 4 (

 4 Figure 4 (a) Schematic cladogram based on a consensus of currently available Mcr phylogenies. The roman numerals correspond to the major phylogenetic groups described in the text. (b)

Figure 5

 5 Figure 5 (a) Potential evolutionary transitions between different types of methane-related pathways. Names on arrows correspond to examples of clades in which the corresponding transition may have occurred. Names in salmon font correspond to transitions in the Methanosarcinales. (b,c) Proposed scenario for the diversification of pathways in the Methanosarcinales and the "Ca. Syntropharchaeia". Crossed-out circles represent loss of metabolism, and circles that are not crossed out indicate metabolism acquisition. Abbreviation: ANME, anaerobic methanotrophs.

  . In other lineages, the acyl-CoA (e.g., butyl-CoM) is further metabolized into several acetyl-CoA molecules by the β-oxidation pathway. In all Acr-bearing alkanotrophs, the acetyl-CoA is oxidized into CO 2 by the CBWL and H 4 MPT-MBWL pathways. In the H 4 MPT-MBWL pathway of "Ca. Santabarbaracales", Mer and Mtd are likely replaced by enzymes of the H 4 F-MBWL pathway, MetFV and MtdB, respectively. The reoxidation of CoM-SH, HS-CoB, F 420 H 2 ,

  2 , Fd red , and H 4 MPT-CH 3 by the CBWL pathway. At this point, H 4 MPT-CH 3 is reduced to CH 4 through Mtr (conserving energy) and Mcr. To reoxidize the NADH and Fd red generated by the β-oxidation and the CBWL pathway, part of the CO 2 produced by the CBWL pathway is reduced into CH 4

using the H 4 MPT-MBWL pathway, Mtr, and Mcr. Thus, this alkanotrophic metabolism does not depend on direct or indirect (syntrophy) reduction of sulfate or other electron acceptors associated with methanotrophy and alkanotrophy. Accordingly, "Ca. Methanoliparia" cells do not form multispecies consortia

[START_REF] Laso-Pérez | Anaerobic degradation of non-methane alkanes by "Candidatus Methanoliparia" in hydrocarbon seeps of the Gulf of Mexico[END_REF] 121)

, and they do not encode genes involved in electron transfer to external acceptors

suggests very complex trajectories. Moreover, genomic analyses have highlighted the existence of proteins that are associated to methane-related metabolisms but that have no predicted function or have never been experimentally characterized [START_REF] Borrel | Wide diversity of methane and short-chain alkane metabolisms in uncultured archaea[END_REF][START_REF] Gao | Phylogenomic analysis of proteins that are distinctive of Archaea and its main subgroups and the origin of methanogenesis[END_REF]. This pool of proteins likely includes new methanogenesis components that await further investigation.

The ancestry and current diversity of methane-related metabolisms argue for complex interactions with geological and ecological processes during the history of Earth that should be explored by future studies combining biochemistry, environmental microbiology, and evolutionary approaches. A better characterization of the unresolved methane/multicarbon alkane metabolisms will also be relevant to tackle major societal challenges associated with environmental sustainability, industrial applications, microbiomes, and health.

DISCLOSURE STATEMENT

The authors are not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review.