Energetic cost of building a virus
Gita Mahmoudabadi
a
, Ron Milo
b
, and Rob Phillips
a,c,1
a
Department of Bioengineering, California Institute of Technology, Pasadena, CA 91125;
b
Department of Plant and Environmental Sciences, Weizmann
Institute of Science, Rehovot 7610001, Israel; and
c
Department of Applied Physics, California Institute of Technology, Pasadena, CA 91125
Edited by Ned S. Wingreen, Princeton University, Princeton, NJ, and accepted by Editorial Board Member Curtis G. Callan Jr. April 19, 2017 (received f
or review
January 30, 2017)
Viruses are incapable of aut
onomous energy production. Although
many experimental studies make it
clear that viruses are parasitic
entities that hijack the molecular resources of the host, a detailed
estimate for the energetic cost of viral synthesis is largely lacking. To
quantify the energetic cost of viruses to their hosts, we enumerated
the costs associated with two very d
istinct but representative DNA
and RNA viruses, namely, T4 and influenza. We found that, for these
viruses, translation of viral proteins is the most energetically expen-
sive process. Interestingly, the costs of building a T4 phage and a
single influenza virus are near
lythesame.Duetoinfluenza
’
shigher
burst size, however, the overall cos
t of a T4 phage infection is only
2
–
3% of the cost of an influenza infection. The costs of these infec-
tions relative to their host
’
s estimated energy budget during the in-
fection reveal that a T4 infection consumes about a third of its host
’
s
energy budget, whereas an influenza infection consumes only
≈
1%.
Building on our estimates for T4, we show how the energetic costs of
double-stranded DNA phages scale with the capsid size, revealing
thatthedominantcostofbuildin
g a virus can switch from transla-
tion to genome replication above a critical size. Last, using our pre-
dictions for the energetic cost of viruses, we provide estimates for the
strengths of selection and genetic
drift acting on newly incorporated
genetic elements in viral genomes, under conditions of energy
limitation.
viral energetics
|
viral evolution
|
T4
|
influenza
|
cellular energetics
V
iruses are biological
“
entities
”
at the boundary of life. Without
cells to infect, viruses as we know them would cease to func-
tion, as they rely on their hosts to replicate. Although the extent of
this reliance varies for different viruses, all viruses consume from
the host
’
s energy budget in creating the next generation of viruses.
There are many examples of viruses that actively subvert the host
transcriptional and translational processes in favor of their own
replication (1). This viral takeover of the host metabolism mani-
fests itself in a variety of forms such as in the degradation of the
host
’
s genome or the inhibition of the host
’
s mRNA translation
(1). There are many other experimental studies (discussed in
SI
section I
)(2
–
6) that demonstrate viruses to be capable of rewiring
the host metabolism. These examples also suggest that a viral in-
fection requires a considerable amount of the host
’
senergetic
supply. In support of this view are experiments on T4 (7), T7 (8),
Pseudoalteromonas
phage (9), and
Paramecium bursaria chlorella
virus-1
(PBCV-1) (10), demonstrating
that the viral burst size cor-
relates positively with the host growth rate. In the case of PBCV-1,
the burst size is reduced by 50% when its photosynthetic host, a
freshwater algae, is grown in the da
rk (10). Similarly, slow-growing
Escherichia coli
with a doubling time of 21 h affords a T4 burst size
of just one phage (11), as opposed to a burst size of 100
–
200 phages
during optimal growth conditions.
These fascinating observations led us to ask the following
questions: what is the energetic cost of a viral infection, and what
is the energetic burden of a viral infection on the host cell? To
our knowledge, the first attempt to address these problems is
provided through a kinetic model of the growth of Q
β
phage
(12). A more recent study performed numerical simulations of
the impact of a T7 phage infection on its
E. coli
host, yielding
important insights into the time course of the metabolic demands
of a viral infection (13).
To further explore the energetic requirements of viral syn-
thesis, we made careful estimates of the energetic costs for two
viruses with very different characteristics, namely the T4 phage
and the influenza A virus. T4 phage is a double-stranded DNA
(dsDNA) virus with a 169-kb genome that infects
E. coli
. The
influenza virus is a negative-sense, single-stranded RNA virus
(
–
ssRNA) with a segmented genome that is 10.6 kb in total
length. The influenza virus is a eukaryotic virus infecting various
animals, with an average burst size of 6,000, although note that
the burst size depends upon growth conditions (14). Similar to
many other dsDNA viruses, T4 phage infections yield a relatively
modest burst size, with the majority of T4 phages resulting in a
burst size of
≈
200 during optimal host growth conditions (15).
To determine the energetic demand of viruses on their hosts, the
cost estimate for building a single virus has to be multiplied by
the viral burst size and placed in the context of the host
’
s energy
budget during the viral infection.
Concretely, the costs associated with building a virus can be
broken down into the following processes that are common to
the life cycles of many viruses: (
i
) viral entry, (
ii
) intracellular
transport, (
iii
) genome replication, (
iv
) transcription, (
v
) trans-
lation, (
vi
) assembly and genome packaging, and (
vii
) exit. Our
strategy was to examine each of these processes for both viruses
in parallel, comparing and contrasting the energetic burdens of
each of the steps in the viral life cycle.
Energetic Cost Units and Definitions
Given that the energetic processes of the cell take place in many
different energy currencies ranging from ATP and GTP hydrolysis
to the energy stored in membrane potentials, it is important to
have a consistent scheme for reporting those energies. ATP serves
as the most common energy currency of the cell, a function that is
universally conserved across all known cellular life-forms (16, 17).
Significance
Viruses rely entirely on their host as an energy source. Despite
numerous experimental studies that demonstrate the capability
of viruses to rewire and undermine their host
’
s metabolism, we
still largely lack a quantitative understanding of an infection
’
s
energetics. However, the energetics of a viral infection is at the
center of broader evolutionary and physical questions in virol-
ogy. By enumerating the energetic costs of different viral pro-
cesses, we open the door to quantitative predictions about viral
evolution. For example, we predict that, for the majority of
viruses, translation will serve as the dominant cost of building a
virus, and that selection, rather than drift, will govern the fate of
new genetic elements within viral genomes.
Author contributions: G.M., R.M., and R.P. designed research, performed research, ana-
lyzed data, and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. N.S.W. is a guest editor invited by the Editorial
Board.
Freely available online through the PNAS open access option.
1
To whom correspondence should be addressed. Email: phillips@pboc.caltech.edu.
This article contains supporting information online at
www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1701670114/-/DCSupplemental
.
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www.pnas.org/cgi/doi/10.1073/pnas.1701670114
The triphosphate group in ATP contains phosphoanhydride bonds,
which upon hydrolysis result in a large negative free-energy change.
Specifically, the hydrolysis of ATP into ADP and orthophosphate
(P
i
) is responsible for roughly a
−
30 kJ/mol free-energy change at
standard conditions (25 °C, 1 atm, pH 7, and 1 M concentration of
reaction components) (16, 18). Under physiological conditions
more typically found in cells, the hydrolysis of ATP usually releases
about
−
50 kJ/mol (16, 18). In addition to ATP, which most com-
monly serves as the energy currency of the cell, there are other
nucleoside triphosphates such as GTP that are approximately en-
ergetically equivalent to ATP. We will refer to these molecules
as ATP-equivalent.
Although the change in free energy under standard conditions
is a constant, the actual change in free energy in a given bio-
chemical reaction is variable and dependent on the concentra-
tions of reactants and products (19). In the absence of exact
concentration measurements throughout viral processes of in-
terest here, calculating the actual change in free energy for each
reaction is not feasible. Hence, we follow others in their
reporting of cellular costs by using the number of ATP (and
ATP-equivalent) hydrolysis events as a proxy for energetic cost.
Similar to Lynch and Marinov (20), we will use the symbol P as a
shorthand notation to represent an ATP (or an ATP-equivalent)
hydrolysis event. We will additionally use subscripts to clearly
label the results obtained under different energetic cost defini-
tions, which will be introduced in the following paragraphs. Last,
in reporting some of our final cost estimates, we will convert the
number of ATP (or ATP-equivalent) hydrolysis events to units of
joules and
k
B
T
by assuming 50 kJ of negative free-energy change
per mole of P at physiological conditions.
In making viral energetic cost estimates, we are guided by two
energetic cost definitions, which despite sharing the same unit of
energy have very different physical interpretations. In our first
definition of energetic cost, termed
“
direct cost
”
or
E
D
, we will
only account for the explicit number of ATP and ATP-equivalent
hydrolysis events required during viral synthesis. This is the
definition that is implicitly used in some of the earliest investi-
gations into cellular energetics (21). Estimates made under this
definition will be denoted in the previously described units of P,
however, with a subscript (P
D
) to make it clear we are talking
about energy that is expended in viral synthesis processes. This
definition will include costs such as those incurred during the
synthesis and polymerization of building blocks. See
Fig. S1
(steps 3 and 4) and
SI section II
for a more detailed description
of direct cost.
In our second definition, termed
“
total cost
”
or
E
T
, we not
only account for the direct costs, but also for the
“
opportunity
cost
”
of building blocks,
E
O
, required during viral synthesis;
hence,
E
T
=
E
D
+
E
O
. We define the opportunity cost of a
building block as the number of ATP (and ATP-equivalent)
molecules that could have been generated had the building
block not been used in viral synthesis and will label these costs
with the notation P
O
(
Fig. S1
, steps 1
–
4, and
SI sections II
,
III
,
and
IV
). In the more recent works on cellular energetics, it is the
total cost definition that the authors implicitly adhere to (22, 23).
The units for the total cost definition will be denoted by the
symbol P
T
. A more detailed explanation and derivation of these
two cost components can be found in the SI (
SI sections II
–
IV
,
Dataset S1
, and
Figs. S1
–
S3
).
The distinction between these two different energetic cost
definitions is that, under the total cost definition, in addition to
accounting for direct costs, we attribute an energetic cost to the
building blocks that are usurped from the host during viral syn-
thesis. Both energetic cost definitions have physical significance.
For example, the direct cost definition is the more appropriate
choice when estimating heat production and power consumption
of a viral infection (
SI sections II
–
IV
). The total cost definition,
on the other hand, is aligned with traditional energetic cost es-
timates made from growth experiments in chemostats, where
substrate consumption and cell yield is monitored, and allows for
a clear comparison between the cost of an infection and the cost
of a cell (
SI sections II
–
IV
). This is because the cost of a cell,
derived through chemostat experiments, implicitly includes the
opportunity cost component, which is the cost of diverting pre-
cursor metabolites from energy-producing pathways toward the
synthesis of molecular building blocks. In addition, although our
approach would certainly benefit from detailed experimental
studies that reveal the fluxes in the host metabolome during an
infection, the assignment of an energetic value to each metab-
olite allows us to simplify the problem from reporting changes in
the concentration of hundreds of metabolites to reporting a
single energetic value associated with the viral infection. This
value can then be compared with the cellular energy budget.
We will generally estimate the cost of a certain viral process
for a single virus, and then multiply this cost by the viral burst
size to determine the infection cost of a given process. Subscript
v
will denote the cost estimates made for a single virus, and the
subscript
i
will refer to a cost estimate made for an infection. We
relegate the energetic cost estimates for all viral processes to
SI
sections V
–
XI
.
Results
The Energetic Costs of T4 and Influenza.
By estimating the energetic
costs of influenza and T4 life cycles, we show that, surprisingly,
the costs of synthesizing an influenza virus and a T4 phage are
nearly the same (Table 1). The outcome of the analysis to be
discussed in the remainder of the paper is summarized pictorially
in Fig. 1 for bacteriophage T4 and Fig. 2 for influenza. For both
viruses, the energetic cost of translation outweighs other costs
(Table 1 and Figs. 1
–
3), although as we will show at the end of
the paper, because translation scales with the surface area of the
viral capsid and replication scales with the volume of the virus,
for dsDNA phages larger than a critical size, the replication cost
outpaces the translation cost.
To get a sense for the numbers, here we provide order-of-
magnitude estimates of both the costs of translation and repli-
cation and refer the interested reader to
SI sections II
–
XI
for full
details. As detailed in the
Tables S1
and
S2
, both T4 and in-
fluenza are composed of about 10
6
amino acids. We can estimate
the total cost of translation by appealing to a few simple facts.
First, the average opportunity cost per amino acid is about 30 P
O
.
Second, the average direct cost to produce amino acids from
precursor metabolites is 2 P
D
per amino acid. Finally, each
polypeptide bond incurs a direct cost of 4 P
D
. We can see that
the total cost of an amino acid is
≈
36 P
T
(30 P
O
+
6P
D
). As a
result, the translational cost of an influenza virus and a T4 phage
both fall between 10
7
to 10
8
P
T
(Table 1).
The cost of viral replication can be approximated in a similar
fashion: we have to consider that the T4 genome is composed of
roughly 4
×
10
5
DNA bases and that the influenza genome is
composed of an order of magnitude fewer RNA bases (
≈
10
4
).
The total costs of a DNA nucleotide and an RNA nucleotide,
including the opportunity costs as well as the direct costs of
synthesis and polymerization, are
≈
50 P
T
(
SI sections II
–
IX
,
Figs. S1
–
S3
, and
Dataset S1
). As a result of T4
’
s longer genome
length, its total cost of replication (
≈
10
7
P
T
) is about an order
of magnitude higher than that of an influenza genome (Table 1,
Figs. 1 and 2, and
SI section VII
).
The cost estimates of different viral processes during T4 and
influenza infections are summarized in Figs. 1
–
3 and Table 1.
The overall cost of a T4 infection is obtained by the sum of
replication (
E
REP
=
i
), transcription (
E
TX
=
i
), translation (
E
TL
=
i
), and
genome packaging (
E
Pack
=
i
) costs required during the infection
(
SI sections V
–
XI
, Table 1, and Figs. 1 and 3). These costs to-
gether amount to
≈
3
×
10
9
P
D
in direct cost and 1
×
10
10
P
T
in
total cost (
SI sections V
–
XI
, Table 1, and Figs. 1 and 3, assuming
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a burst size of 200). The total cost of a T4 infection is also
equivalent to the aerobic respiration of
≈
4
×
10
8
glucose
molecules by
E. coli
[26 ATP per glucose (24)]. Alternatively, it is
equivalent to
≈
2
×
10
11
k
B
T
(assuming 1 ATP
≈
20
k
B
T
) (25).
Similarly, the cost of an influenza infection is obtained by
adding up the costs of entry (
E
Entry
), intracellular transport
(
E
Transit
=
i
), replication (
E
REP
=
i
), transcription (
E
TX
=
i
), translation
(
E
TL
=
i
), and exit (
E
Exit
=
i
) required during the infection (
SI sec-
tions V
–
XI
, Table 1, and Figs. 2 and 3). These processes have
a cumulative cost of
≈
8
×
10
10
P
D
and 6
×
10
11
P
T
, for the
assumed burst size of 6,000. The sum of costs in an influenza
infection (6
×
10
11
P
T
) is equivalent to the aerobic respiration
of
≈
2
×
10
10
glucose molecules by a eukaryotic cell (32 ATP
per glucose). It is also equivalent to
≈
10
13
k
B
T
. It is interesting
to note that, for both viral infections, the opportunity cost
component is the dominant component of the total cost
(Table 1).
Even though individually a T4 phage and an influenza virus
have comparable energetic costs, because of their different burst
sizes, the direct cost of a T4 phage infection is
≈
3% of the
direct cost of an influenza infection. Similarly, the total cost of a
T4 phage infection is
≈
2% of the total cost of an influenza
infection. To contextualize these numbers, the host energy
budget during the infection has to be taken into account. The
total cost of a cell is experimentally tractable through growth
experiments in chemostats, in which cultures are maintained at a
constant growth rate. The number of glucose molecules taken up
per cell per unit time can be determined. The number of glucose
molecules can then be converted to an energetic supply by as-
suming typical conversion ratios of 26 or 32 ATPs per glucose
molecule depending on the organism (24). This energetic cost
estimate will be a total cost estimate because not all glucose
molecules taken up by the cell are fully metabolized to carbon
dioxide and water to generate ATPs and are used as building
blocks for biomass components instead. During the cellular life
cycle, the cell has to double its number of building blocks before
division, and to do so, a fraction of glucose molecules taken up is
diverted away from energy production toward biosynthesis
pathways. Hence, cellular energetic cost estimates that are de-
rived from chemostat experiments are total cost estimates be-
cause they report on the combined opportunity and direct costs
of a cell (
SI sections II
–
IV
).
Based on chemostat growth experiments (20), the total energy
used by a bacterium and a mammalian cell with volumes of 1 and
2,000
μ
m
3
, respectively, are
≈
3
×
10
10
P
T
and
≈
5
×
10
13
P
T
,
during the course of their viral infections (
SI section XII
). A
simpler estimate for arriving at the total cost of
E. coli
with a
30-min doubling time is by considering the dry weight of
E. coli
(
≈
0.6 pg at this growth rate) (ref. 26; BNID 100089). Given that
about one-half of the cell
’
s dry weight is composed of carbon
(ref. 26; BNID 100649), an
E. coli
is composed of
≈
2
×
10
10
carbons, supplied from
≈
3
×
10
9
glucose molecules, because
each glucose contributes 6 carbons. With the 26 ATP per glucose
conversion for
E. coli
, this is equivalent to a total cost of
≈
7
×
10
10
P
T
, which is similar to the number obtained from chemostat growth
experiments (20) (
SI section XII
).
Moreover, we estimate the fractional cost of a viral infection
as the ratio of total cost of an infection,
E
T
=
i
, to the total cost of
the host during the infection,
E
T
=
h
. For the T4 infection with a
burst size of 200 virions,
E
T
=
i
≈
1
×
10
10
P
T
(Table 1) and
E
T
=
h
≈
3
×
10
10
P
T
; therefore, the fractional cost of the T4 infection is
≈
0.3. Interestingly, a calorimetric study of a marine microbial
community demonstrated that 25% of the heat released by mi-
crobes is due to phage activity (27). If we assume that the ma-
jority of the direct cost of a cell is associated with translation (20,
25), these calorimetric studies square well with our estimate for
the ratio of direct costs. In contrast, the influenza infection de-
spite its larger burst size (6,000 virions) leading to a higher
E
T
=
i
(
≈
6
×
10
11
P
T
) has a fractional cost of just 0.01 as the host cell is
much bigger. Finally, we estimate that the heat release due to the
T4 and influenza viral infections are approximately 0.2 and 2 nJ,
respectively (
SI section XIII
). Although an influenza infection
results in an order of magnitude more heat, the average power
estimates of both infections are surprisingly very similar, on the
order of 200 fW (
SI section XIII
).
Scaling of Viral Energetics with Size for dsDNA Phages.
Although we
have concluded that for the influenza virus and the T4 phage the
translational cost outweighs the replication cost, the ratio of
these two costs varies according to the dimensions of a virus. In
the case of T4 and influenza, these two viruses have comparable
dimensions and consequently were composed of a similar num-
ber of amino acids (
Tables S1
and
S2
). However, because for
dsDNA phages the capsid is mostly comprised of proteins
whereas the virion interior is mostly dedicated to the genetic
material (28), it follows that with the diminishing surface area-to-
volume ratio of a spherical object as it grows in size, the ratio of
translational cost to replication cost also diminishes. This simple
rule governs not just nucleotide or amino acid composition of a
Table 1. The direct, opportunity, and total energetic costs of viral processes for T4 and influenza
Cost
Replication Transcription Viral entry Packaging Intracellular transport Viral exit Translation Sum
Direct cost (P
D
)
Per virion
T4 4
×
10
6
7
×
10
5
—
3
×
10
5
——
7
×
10
6
10
7
Flu 3
×
10
5
7
×
10
4
——
10
3
2
×
10
6
10
7
10
7
Per infection T4 9
×
10
8
10
8
—
7
×
10
7
——
10
9
3
×
10
9
Flu 2
×
10
9
4
×
10
8
10
3
—
6
×
10
6
10
10
6
×
10
10
8
×
10
10
Opportunity cost (P
O
) Per virion
T4
10
7
7
×
10
5
————
3
×
10
7
4
×
10
7
Flu 8
×
10
5
2
×
10
5
———
3
×
10
7
5
×
10
7
9
×
10
7
Per infection T4 2
×
10
9
10
8
————
6
×
10
9
8
×
10
9
Flu 5
×
10
9
10
9
———
2
×
10
11
3
×
10
11
5
×
10
11
Total cost (P
T
)
Per virion
T4 2
×
10
7
10
6
—
3
×
10
5
——
4
×
10
7
6
×
10
7
Flu
10
6
3
×
10
5
——
10
3
4
×
10
7
6
×
10
7
10
8
Per infection T4 3
×
10
9
3
×
10
8
—
7
×
10
7
——
8
×
10
9
10
10
Flu 6
×
10
9
2
×
10
9
10
3
—
6
×
10
6
2
×
10
11
4
×
10
11
6
×
10
11
The T4 infection costs are estimated based on an average burst size of 200, and the influenza infection costs are based on an average burst size of 6,000.
Direct costs shown represent the number of phosphate bonds directly hydrolyzed during the viral lifecycle (P
D
), whereas the total costs (P
T
) include both direct
costs (P
D
) as well as opportunity costs (P
O
) incurred during the viral life cycle (
SI sections V
–
XI
). Empty entries correspond to viral processes that did not result in
an energetic cost or were not applicable to the given virus. Note that, to obtain the total cost estimates, the sum of opportunity and direct costs used e
xact
numbers and was then rounded (this is why the sum of the rounded versions of direct and opportunity costs do not exactly match up to the total costs
presented in this table).
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Mahmoudabadi et al.
Fig. 1.
The energetics of a T4 phage infection. The direct and total costs of vira
l processes are denoted and can be di
stinguished by their subscripts (P
D
and P
T
, respectively). The
energetic requirements of transcription (step 3), translation (step 4),
genome replication (step 5), and ge
nome packaging (step 7) are shown. See
SI sections V
–
XI
and Table 1.
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Fig. 2.
The energetics of an influenza infection. The direct and total costs of viral processes are denoted and can be distinguished by their subscripts (P
D
and
P
T
, respectively). The energetic requirements of viral entry (steps 2 and 3), intracellular transport (steps 4, 5, and 9), transcription (step 6), tran
slation (step 7),
genome replication (step 8), and viral exit (step 10) are shown. See
SI sections V
–
XI
and Table 1.
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Mahmoudabadi et al.
virus, but more fundamentally, it governs the elemental com-
position of viruses with spherical-like geometries (28).
The full derivation of replication and translational cost estimates
as a function of viral capsid inner radius,
r
, can be found in
SI
section XIV
. From these expressions, it is clear that the trans-
lational cost of a virus scales with
r
2
, whereas the replication cost
scales with
r
3
(Fig. 4). The critical radius at which replication will
outweigh translation in cost is
≈
60 nm for total cost estimates,
r
crit
−
Tot
(Fig. 4 and
SI section XIV
). For the direct cost estimates, the
critical radius,
r
crit
−
Dir
,is
≈
40 nm. Interestingly, a survey of struc-
tural diversity encompassing 2,600 viruses inhabiting the world
’
s
oceans reveals that the average outer capsid radius is 28 nm (29)
(25-nm inner radius), which is much smaller than the critical radii at
which replication becomes the dominant cost (Fig. 4). As such, for
the majority of viruses, we predict translation is the dominant cost
of a viral infection.
Furthermore, we provide genome replication to translation cost
ratios for about 30 different double-stranded viruses, primarily
phages (
Dataset S2
and Fig. 4). Although we have omitted cal-
culations for the virus tails, they can be simply treated as hollow
cylinders and will further decrease the expected replication-to-
translation cost ratio for the tailed viruses. Although we have
calculated these ratios primarily for dsDNA phages, similar prin-
ciples can be applied to modeling the energetics of other
viral groups.
Forces of Evolution Operating on Viral Genomes.
Inspired by efforts
to consider the evolutionary implications of the cost of a gene to
cells of different sizes (20, 23), we were curious whether similar
considerations might be in play in the context of viruses. For
example, we asked which evolutionary forces are prominently
operating on neutral genetic elements that are incorporated into
viral genomes, either by horizontal gene transfer, gene duplica-
tion, or other similar types of events. We further asked whether
the viral size is a parameter of interest in the tug of war between
different forces of evolution. We will address these topics by
assuming that the viral infection, consistent with our findings for
T4, consumes a substantial portion of the host energy budget.
We further assume that the energetic cost of a genetic element
translates to a proportional fitness cost. We believe this as-
sumption to be relevant when the host growth condition is energy
or carbon substrate limited.
For a genetic element to remain in the population, regardless of
whether it is beneficial or not, it must face the consequences of
genetic drift, which scales with the viral effective population size,
N
e
,
as
N
e
−
1
. We follow the treatment of Lynch and Marinov who argue
that the net selective advantage of a genetic element is
s
n
=
s
a
−
s
c
,
where
s
a
and
s
c
denote the selective advan
tage and disadvantage,
respectively (Fig. 5
B
). For a genetic element within a viral genome
that is nontranscribed and nontranslated (Fig. 5
C
), only the ener-
getic cost of its replication poses a selective disadvantage. Assuming
the genetic element provid
es no benefit to the virus (
s
a
=
0), the net
selective advantage can be stated as
s
n
=
−
s
c
, the absolute value of
which must be much greater than
N
e
−
1
for selection to operate
effectively. Following Lynch and Marinov and others (23, 30), we
make the simplifying assumption that a neutral genetic element
’
s
selection coefficient,
s
c
, is proportional to its fractional energetic
cost,
E
g
(Fig. 5
C
). This means that the viral infection is energy (or
carbon source) limited. Because we assumed that the energetic cost
of a viral infection is comparable to the total energy budget of a cell,
any increase to the cost of a virus would necessitate a smaller burst
size. Using the viral burst size as a proxy for the viral growth rate, we
are then able to relate the addition
al fractional energetic cost of a
neutral genetic element to a fitness cost.
In the case of a nontranscribed genetic element,
E
g
=
E
REP
=
v
=
E
v
,
where
E
REP
=
v
corresponds to its replication cost and
E
v
is the sum
of all costs of a virus (Fig. 5
C
). Given that replication cost scales as
r
3
, the effects of selection relative to genetic drift could be dif-
ferent for viruses of different sizes. Consider two viruses with the
same burst size, with virus A, having a radius that is two times
larger than that of virus B (Fig. 5
D
). Because both viruses are
assumed to have radii larger than the critical radius, we imagine
the scenario in which the cost of genome replication is the dom-
inant cost of synthesizing these viruses. The fractional cost of a
genetic element in the smaller virus,
E
g
Virus
B
is then equal to
8
E
g
Virus
A
,where
E
g
Virus
A
is the fractional cost of the genetic el-
ement in the larger virus. This is because the length of the genome
is proportional to
r
3
, and consequently,
E
g
is inversely proportional
to
r
3
(Fig. 5
D
).
Fig. 5
E
and
Dataset S3
provide
E
g
estimates for genetic ele-
ments of different lengths (1
–
10,000 bp) within 30 dsDNA
viruses. To illustrate the effect of scaling in the example provided
above, we made the simplifying assumption that the viruses are
large enough that their
E
v
are approximately equal to their
replication costs. However, for
E
v
values in Fig. 5
E
and
Dataset
S3
, we provide more precise estimates, treating
E
v
as the sum of
both the replication cost and the translational cost of a virus. The
cost of replicating a double-stranded genetic element can be
obtained from
Eq.
S3
. For a 1-kb element, which is about the
average length of a bacterial gene, the direct and total costs of its
replication per virus,
E
REP
=
v
, are 3
×
10
4
P
D
and 9
×
10
4
P
T
,
respectively. Both direct and total cost estimates indicate that the
strength of selection acting on a 1 kb, nontranscribed element
ranges from 2
×
10
−
2
to 7
×
10
−
6
(
Dataset S3
and Fig. 5
E
) when
considering viruses with radii ranging from
≈
20 to 400 nm. The
difference between direct and total estimates of selection
strength is minimal within this range of capsid radii and con-
tinues to diminish as the capsids grow in size.
To examine whether selection or genetic drift will decide the
fate of a genetic element, we need to assess each virus
’
s effective
population size. This is difficult because the effective population
size of most viruses is unknown and subject to great variability
due to several environmental factors (31). The current effective
Fig. 3.
A breakdown of the direct cost (
Top
) and the total cost (
Bottom
)of
various viral processes during T4 (
Left
) and influenza (
Right
) viral infections
(normalized to the sum of all costs during an infection, as shown in the
center of each pie chart). The direct cost of a T4 phage infection is
≈
3
×
10
9
P
D
, whereas the total cost is 10
10
P
T
. The direct and total costs of an influenza
infection are
≈
8
×
10
10
P
D
and 6
×
10
11
P
T
, respectively. Numbers are
rounded to the nearest percent, and viral processes costing below 0.5% of
the infection
’
s cost are not shown. See
SI sections V
–
XI
for energetic cost
estimates for viral entry, intracellular transport, transcription, viral assembly,
and viral exit.
Mahmoudabadi et al.
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population size estimates regarding HIV, influenza, dengue, and
measles fall within 10
1
to 10
5
(31
–
33). Based on the wide range of
variation in these effective population sizes, it is difficult to make
conclusive statements. It is, however, apparent that the strength of
selection on neutral genetic elements is a nonlinear function of the
viral capsid radius and becomes much weaker as viruses get larger
(Fig. 5
E
). In fact, for giant viruses (with outer-radius
R
>
200 nm),
assuming an
N
e
−
1
=
10
−
5
, genetic drift could overpower selection,
allowing for the persistence of neutral elements of lengths 100 bp
or shorter in the population. For the majority of viruses [
R
=
28
±
6.5 nm (29)], however, selection is likely to be the dominant force
and drift may only play a role for genetic elements that are just a
few base pairs long (Fig. 5
E
and
Dataset S3
).
Discussion
There have been several experiments that imply that a viral in-
fection requires a significant portion of the host energy budget
(3, 5, 10, 11, 34
–
36). Following these experimental hints, we
enumerated the energetic requirements of two very different
viruses on the basis of their life cycles, and thereby estimated the
energetic burdens of these viral infections on the host cells.
According to our total cost estimates, a T4 infection with a burst
size of 200 will consume a significant portion (about 30%) of the
host energy supply. This result, demonstrating a significant
fraction of the host energy used by an infection, supports the
experimental findings that the T4 burst size is correlated posi-
tively with the host growth rate (7, 11). It also lends further
credence to the hypothesis that auxiliary metabolic genes within
phage genomes are not just evolutionary accidents; rather, they
have come to serve a functional role in boosting the host
’
s
metabolic capacity, which translates into larger viral burst sizes
(3, 4, 36, 37). These calculations make it all the more interesting
to develop high-precision, single-cell calorimetry techniques to
monitor energy use during viral infections. Perhaps the most
Fig. 4.
Generalizing viral energetics. A p
lotofthegenomereplicationcost(
E
REP
)-to-translational cost (
E
TL
)ratioasafunctionofthevirusinnerradius,
r
.Theplot
uses the geometric parameters of dsDNA viruses with icosahedral geometries (
Dataset S2
and
SI section XIV
). The predicted numbers of amino acids and nucleotides
are derived in
Dataset S2
. Cost ratios are shown for both direct and total cost estimates. All viruses shown infect bacteria except Sputnik, which is a satellite virus of
the giant Mimivirus. We have zoomed in on viruses Sputnik (
r
=
22 nm), P22 (
r
=
27.5 nm), T7 (
r
=
27.5 nm), HK97 (
r
=
30 nm), and Epsilon15 (
r
=
31.2 nm). The capsid
structures for these representative viruses were obtained from the VIPERdb (43), and image sizes were scaled based on radii shown in
Dataset S2
to accurately
represent the relative sizes of each capsid. The critical radii for the total cost (
r
crit
−
Tot
)andthedirectcost(
r
crit
−
Dir
) estimates are shown. We have also included the
mean (
r
mean
=
25 nm) and SD (gray vertical box,
±
6.5 nm) of viral capsid inner radii from 2,600 viruses colle
cted by the Tara Oceans Expeditions (29). Note, here, we
have subtracted the mean capsid thickness (3 nm) from the mean capsid radius reported by Brum et al. (29) to arrive at the mean inner capsid radius.
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Mahmoudabadi et al.
promising support for T4
’
s cost estimate is the observation that
the maximum T4 burst size is 1,000 virions (15). Using the total
cost to make new viruses, at a burst size of 1,000, the viral in-
fection would consume 170% of the host normal energy supply at
a 30-min growth rate, consistent with the observed apparent
upper limits on burst size.
It is, however, important to note that, in all of our estimates,
we make the assumption that the sources of nitrogen, sulfur,
phosphorus, and other trace elements are in excess, which is
typical of culture conditions in the laboratory and from which
most burst measurements are obtained (
SI section II
), but this
assumption may not be valid in certain natural environments as
demonstrated by the phosphorus-limited environments of ma-
rine ecosystems (38). In such limited environments, phages are
shown to carry auxiliary genes and to actively rewire the host
metabolism (full discussion can be found in
SI section I
). It
would be interesting to have additional experimental studies that
go beyond the ideal conditions of a laboratory experiment to
fully explore the range of possible limiting factors in a viral
infection.
Although there are several fascinating studies that explore the
link between the host metabolism and phage infections (3, 6, 12,
13), similar studies focusing on viruses of multicellular eukary-
otes are largely lacking. To that end, we chose to estimate the
energetic cost of a representative virus for this category, namely,
the influenza virus. The influenza virus and T4 phage are func-
tionally and evolutionarily very different viruses. However, they
have a very similar per-virus cost, regardless of whether the total
or the direct cost estimates are being considered. This is pri-
marily due to the fact that they have a similar translational cost,
which dominates all other costs. Their comparable cost of
translation is due to the fact that these viruses have similar di-
mensions and are both composed of about a million amino acids.
Perhaps even more surprising is that both viral infections have
ABCD
E
R
r
Net selection: S
n
= S
a
- S
c
1
/
N
e
S
a
Drift opposing
negative
and
positive
selection forces
S
c
A genetic element
within the viral genome,
non-transcribed and
functionally neutral
S
a
= 0, |S
n
| = S
c
= E
g
1
/
N
e
1
/
N
e
S
c
= 8E
g_Virus A
Virus A
Virus B
r
S
c
= E
g_Virus A
2r
Selection-driven
|S
n
| >
1
/
N
e
Drift-driven
1
/
N
e
> |S
n
|
Assuming
N
e
= 10
5
log
10
of Selection Coefficient, |S
n
| = S
c
= E
g
Capsid Radius, R (nm)
Mean and S.D. of capsid diameters
from viruses (N = 2600) inhabiting
the world’s oceans (Brum, 2013)
R = 28 +/- 6.5 nm
050100
200
400
0
−1
−2
−3
−4
−5
−6
−7
−8
−9
Length of genetic elements
10,000 bp
1000 bp
100 bp
10 bp
1 bp
Fig. 5.
Evolutionary forces acting on genetic elements within viral genomes. (
A
) Schematic of a virus as a spherical object, with an inner radius,
r
, an outer
radius,
R
, and a capsid thickness,
t
. The capsid is composed of viral proteins, whereas the inner volume holds the viral genome. (
B
) Positive and negative
selective forces (
s
a
and
s
c
) at a tug of war with the force of genetic drift, which scales as
N
e
−
1
, where
N
e
is the viral effective population size. (
C
) A schematic of
a genetic element within a viral genome. It is assumed to be nonfunctional (
s
a
=
0) and nontranscribed, resulting in
j
s
a
j
=
s
c
=
E
g
, where
s
a
corresponds to the
net selection coefficient and
E
g
corresponds to the fractional cost of a genetic element. (
D
) The evolutionary forces acting on a genetic element within virus A
and virus B genomes. The fractional cost of a genetic element in virus B,
E
g
VirusB
, is eight times higher than the fractional cost of the same element in virus A,
E
g
VirusA
. Note that virus A has twice the radius of virus B, and therefore its genome is eight times longer than that of virus B (schematically represented by the
number of genetic segments). Both viruses are assumed to have radii greater than critical radii,
r
crit
−
Tot
and
r
crit
−
Dir
.(
E
)Log
10
E
g
estimates for nontranscribed
and neutral genetic elements of different lengths (1
–
10,000 bp) within the context of 30 dsDNA viruses ranging from
≈
20 to 400 nm in radius (
Dataset S3
;
viruses with
R
>
50 nm are hypothetical dsDNA viruses). Log
10
E
g
estimates derived from both direct and total cost estimates are included (there is minimal
difference between these estimates, which is not visible in this figure;
Dataset S3
). Assuming
N
e
=
10
5
, the region above the horizontal dashed line represents
a selection-dominated regime, and the region below it represents a drift-dominated regime. For comparison, we have included the mean (vertical dash
ed
line, 28 nm) and SD (gray vertical box,
±
6.5 nm) of viral capsid outer radii obtained from 2,600 viruses collected during the Tara Oceans Expeditions (29).
Mahmoudabadi et al.
PNAS
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|
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BIOPHYSICS AND
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PNAS PLUS
very similar average power consumptions, on the order of 200 fW
(
SI section XIII
).
Even with its higher burst size, an influenza infection has a
total cost that is just 1% of the total energetic budget of a
eukaryotic cell over the characteristic time of the viral infection.
This is because a typical eukaryotic cell is estimated to have
much higher energy supply than a typical bacterium under the
same growth conditions. So far in our estimates, we do not ac-
count for the possible inefficiencies at various stages of the viral
infection, which may drain more of the host energy than we es-
timated. Specifically, burst sizes are typically reported from
plaque assays, which count the number of infectious virions that
create plaques. However, we do not have a good estimate for the
number of noninfectious viruses that arise from faulty genome
replication, transcription, or viral assembly, for example.
This point is especially important when considering RNA-
based viruses such as influenza or HIV, which have higher
mutation rates [10
−
4
to 10
−
6
mutations per base pair per
generation (39)] compared with dsDNA viruses such as T4
[10
−
6
to 10
−
8
mutations per base pair per generation (39)]. As
a result of these higher error rates, RNA-based viruses may
have greater hidden costs associated with aborted or faulty
viral synthesis.
Even infectious viruses cannot all be guaranteed to enter the
lytic cycle upon infecting a host cell. For example, only 10% of
influenza-infected host cells have been shown to generate in-
fectious virions (40), demonstrating the cumulative inefficiency
of an influenza infection. Hence, counting plaques to measure
viral burst sizes likely underestimates the true burst size and
results in an underestimation of the infection cost. As such,
single-cell studies of viral infection could provide a detailed
breakdown of inefficiencies at various steps of the viral life cycle
and enable more exact cost estimates. We further explore other
factors related to the fractional cost of influenza and T4 infec-
tions in
SI section XV
.
Finally, we will need future experimental studies to test the
assumptions underlying the relationship between the fractional
cost of a neutral genetic element and the strength of negative
selection acting on the viral population. There is also a great
need for estimates of the effective population sizes of different
viruses within their natural environments. With current effective
population size estimates for viruses, it appears that selection
likely determines the fate of genetic elements for the majority of
viruses, which have on average 28-nm radii (29) (Fig. 5
E
and
Dataset S3
). However, for larger viruses (
R
>
200 nm), the
diminishing, fractional cost of a gene may enable the interfer-
ence of genetic drift to the extent that neutral genetic elements
could persist in the viral population. The result of such a phe-
nomenon could be genome expansions in the form of gene du-
plication events, cooption of previously noncoding, horizontally
transferred elements into functional genes and regulatory do-
mains, and perhaps even a trend toward greater autonomy over
large evolutionary timescales. This effect may explain the un-
usual number of duplication events in the genomes of giant
viruses such as that of the Mimivirus (41, 42).
ACKNOWLEDGMENTS.
We are grateful to David Baltimore, Markus Covert,
Michael Lynch, Bill Gelbart, Joshua Weitz, Forest Rohwer, Thierry Mora,
Aleksandra Walczak, Ry Young, David Van Valen, Georgi Marinov, Elsa Birch,
Yinon Bar-On, Ty Roach, Franz Weinert, as well as members of the
R.P. Laboratory and the Boundaries of Life Initiative for their many insightful
recommendations. This study was supported by the National Science
Foundation Graduate Research Fellowship (Grant DGE
‐
1144469), The John
Templeton Foundation (Boundaries of Life Initiative; Grant 51250), the Na-
tional Institute of Health
’
s Maximizing Investigator
’
s Research Award (Grant
RFA-GM-17-002), the National Institute of Health
’
s Exceptional Unconven-
tional Research Enabling Knowledge Acceleration (Grant R01- GM098465),
and the National Science Foundation (Grant NSF PHY11-25915) through the
2015 Cellular Evolution course at the Kavli Institute for Theoretical Physics.
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PNAS
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Published online May 16, 2017
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